Slide 1 70

Electric Currents amp DC Circuits

Slide 2 70

1 The length of an aluminum wire is quadrupled and the radius is doubled By which factor does the resistance change

A 2B 4C 12D 14E 1

Slide 3 70

2 A copper wire has a length L and cross-sectional area A What happens to the resistivity of the wire if the length is doubled and cross-sectional area halved

A Four times as largeB Two times as largeC Stays the sameD Half as largeE Quarter as large

Slide 4 70

3 Which circuit has greater resistance between the terminals

A AB BC CD DE C and D

Slide 5 70

4 Which circuits have the same resistance between the terminals

A A and BB B and CC C and DD D and AE C and A

Slide 6 70

5 In the circuit shown above what is the value of the net resistance

A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω

Slide 7 70

6 What is the current in 4 - Ω resistor

A 1AB 2AC 3AD 4AE 5A

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 2 70

1 The length of an aluminum wire is quadrupled and the radius is doubled By which factor does the resistance change

A 2B 4C 12D 14E 1

Slide 3 70

2 A copper wire has a length L and cross-sectional area A What happens to the resistivity of the wire if the length is doubled and cross-sectional area halved

A Four times as largeB Two times as largeC Stays the sameD Half as largeE Quarter as large

Slide 4 70

3 Which circuit has greater resistance between the terminals

A AB BC CD DE C and D

Slide 5 70

4 Which circuits have the same resistance between the terminals

A A and BB B and CC C and DD D and AE C and A

Slide 6 70

5 In the circuit shown above what is the value of the net resistance

A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω

Slide 7 70

6 What is the current in 4 - Ω resistor

A 1AB 2AC 3AD 4AE 5A

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 3 70

2 A copper wire has a length L and cross-sectional area A What happens to the resistivity of the wire if the length is doubled and cross-sectional area halved

A Four times as largeB Two times as largeC Stays the sameD Half as largeE Quarter as large

Slide 4 70

3 Which circuit has greater resistance between the terminals

A AB BC CD DE C and D

Slide 5 70

4 Which circuits have the same resistance between the terminals

A A and BB B and CC C and DD D and AE C and A

Slide 6 70

5 In the circuit shown above what is the value of the net resistance

A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω

Slide 7 70

6 What is the current in 4 - Ω resistor

A 1AB 2AC 3AD 4AE 5A

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 4 70

3 Which circuit has greater resistance between the terminals

A AB BC CD DE C and D

Slide 5 70

4 Which circuits have the same resistance between the terminals

A A and BB B and CC C and DD D and AE C and A

Slide 6 70

5 In the circuit shown above what is the value of the net resistance

A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω

Slide 7 70

6 What is the current in 4 - Ω resistor

A 1AB 2AC 3AD 4AE 5A

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 5 70

4 Which circuits have the same resistance between the terminals

A A and BB B and CC C and DD D and AE C and A

Slide 6 70

5 In the circuit shown above what is the value of the net resistance

A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω

Slide 7 70

6 What is the current in 4 - Ω resistor

A 1AB 2AC 3AD 4AE 5A

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 6 70

5 In the circuit shown above what is the value of the net resistance

A 1 ΩB 2 ΩC 3 ΩD 4 ΩE 6 Ω

Slide 7 70

6 What is the current in 4 - Ω resistor

A 1AB 2AC 3AD 4AE 5A

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 7 70

6 What is the current in 4 - Ω resistor

A 1AB 2AC 3AD 4AE 5A

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 8 70

7 What is the voltage between points L and M

A 2 VB 3 VC 4 VD 3 VE 5 V

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 9 70

8 A lamp L1 a voltmeter V an ammeter A and a battery with zero internal resistance are connected as shown above Connecting another lamp L2 in series with the first lamp as shown by the dashed lines would

A Increase the ammeter reading

B Decrease the ammeter reading

C Increase the voltmeter reading

D Decrease the voltmeter reading

E Produce no change in either meter reading

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 10 70

9 Into which circuit should the battery be connected to obtain the greatest steady power dissipation

ABCDE

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 11 70

10 Which circuit will retain stored energy if the battery is connected to it and then disconnected

A AB BC CD DE E

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 12 70

A AB BC CD DE E

11 The five resistors shown below have the lengths and cross sectional areas indicated and are made of material with the same resistivity Which has the smallest resistance

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 13 70

12 Two capacitors are connected in parallel as shown above A voltage V is applied to the pair What is the ratio of charge stored on C1 to the charge stored on C2 when C1 = 3C2

A 49B 23C 31D 32E 94

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 14 70

13 The circuit shown above left is made up of a variable resistor and a battery with negligible internal resistance A graph of the power P dissipated in the resistor as a function of the current I supplied by the battery is given above right What is the emf of the battery

A 5 VB 8 VC 10 VD 20 VE 40 V

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 15 70

14 The total equivalent resistance of the circuit shown on the diagram is

A 3 ΩB 4 ΩC 5 ΩD 6 ΩE 9 Ω

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 16 70

15 A heating spiral of resistance R converts elec trical energy into thermal energy that is transferred to the liquid in which the spiral is immersed If the voltage across the spiral is V the thermal energy trans ferred to the liquid in time t is

A VrtB V2RtC VR2tD VRt2

E V2tR

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 17 70

16 In the circuit two identical resistors R are connected in series with 8-Ω resistor and 12-V battery What is the value of R if the current in the circuit I = 1 A

A 1 ΩB 2 ΩC 4 ΩD 12 ΩE 18 Ω

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 18 70

17 The equivalent capacitance for this network is

A 1 μFB 2 μFC 3 μFD 4 μFE 5 μF

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 19 70

18 The charge stored in the circuit is

A 6 μCB 12 μCC 48 μCD 24 μCE 36 μC

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 20 70

19 What is the emf of the battery

A 2 VB 4 VC 36 VD 12 VE 18 V

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 21 70

20 What is the potential difference across the terminals A and B of the battery

A 12 VB 24 VC 36 VD 122 VE 184 V

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 22 70

21 What power is dissipated by the 2-ohm internal resistance of the battery

A 006 WB 12 WC 32 WD 008 WE 48 W

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 23 70

22 In the diagrams resistors R1 and R2 are shown in two different connections to the same source of emf ε that has no internal resistance How does the power dissipated by the resistors in these two cases compare

A It is greater for the series connection

B It is greater for the parallel connection

C It is the same for both connections

D It is different for each connection but one must know the values of R1 and R2 to know which is greater

E It is different for each connection but one must know the value of ε to know which is greater

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 24 70

23 The product 3 amperes x3 volts x 3 seconds is equal to

A 27 CB 27 NC 27 JD 27 WE 27 NA

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 25 70

24 The electrical resistance of the part of the circuit shown between point X and point Y is

A 43 ΩB 25 ΩC 275 ΩD 45 ΩE 65 Ω

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 26 70

25 When there is a steady current in the circuit the amount of charge passing a point per unit of time is

A the same everywhere in the circuit

B greater at point X than at point Y

C greater in the 2 Ω resistor than in the 5 Ω resistor

D the same in the 2 Ω resistor and in the 5 Ω resistor

E greater in the 3 Ω resistor than in the 5 Ω resistor

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 27 70

26 A certain coffeepot draws 20 A of current when it is operated on 110 V household lines If electrical energy costs 10 cents per kilowatt-hour how much does it cost to operate the coffeepot for 5 hours

A 24 centsB 48 centsC 80 centsD 96 centsE 11 cents

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 28 70

27 What is the net capacitance of the circuit

A 3CB 2CC 32 CD 23 CE C

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 29 70

28 What is the net charge stored in the circuit

A CVB 3CV2C 2CV3D CV2E CV3

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 30 70

29 What is the potential difference between the points X and Y

A VB 13 VC 12 VD 23 VE 32 V

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 31 70

30 What is the net resistance of the circuit

A 30 ΩB 40 ΩC 50 ΩD 60ΩE 80 Ω

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 32 70

31 What is the current in the light bulb L1

A 1 AB 2 AC 3 AD 4 AE 5 A

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 33 70

32 Which light bulb or bulbs could burn out without causing others to go out

A Only L1

B Only L2

C Only L3 and L4

D Only L4

E Only L5

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 34 70

33 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery ndash switch is open

A Calculate the net resistance of the circuitB Calculate the current in the 2-Ω resistorC Calculate the current in the 3-Ω resistorD Calculate the charge on the capacitorE Calculate the energy stored in the capacitor

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 35 70

Free Response

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 36 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

b When the switch is closed what is the current running through the battery

c What is the terminal voltage on the battery

d What is the rate of energy delivered by the heating system

e If the switch is closed for 5 min what is the total energy dissipated in the coils

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 37 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

a In a space above draw a diagram showing all the elements connected in one electrical circuit that can provide the maximum rate of heat produced Use two meters in your circuit they will help to measure the heat rate

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 38 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

First find the equivalent resistance

1Rcoil = 1173Ω + 1173ΩRcoil = 865Ω

Req = R + rReq = 865Ω + 05Ω

Req = 915Ω

Then find the current

I = VRI = 12V 915 Ω = 13 A

c When the switch is closed what is the current running through the battery

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 39 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed belowThe battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

c What is the terminal voltage on the battery

VT = E - Ir

VT = 12V - (13A)(05Ω)

VT = 1135 V

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 40 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

d What is the rate of energy delivered by the heating system

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

P1 = V12R1

P1 = (1135 V)2(865Ω)

P1 = 149 W

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 41 70

1 A physics student has an assignment to make an electrical heating system with the set of materials listed below

e If the switch is closed for 5 min what is the total energy dissipated in the coils

The battery has an emf of 12 V and an internal resistance of 05 Ω and each heating coil has a resistance of 173 Ω

W = Pt

W = (149 W)(300 s)

W = 4470 J

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 42 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

b Calculate the net resistance of the circuit

c Calculate the power dissipated in the circuit

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 43 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

a Use given materials design an electric circuit in which the electric motor will operate properly

i Draw the circuit including all devices

ii Explain your reasoning in designing this particular circuit

12V

motorRmotor = 6V05A = 12 Ω

Req = 12V05A = 24 Ω

6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 44 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

b Calculate the net resistance of the circuit

Req = 6Ω + 3Ω + 3Ω + 12 Ω = 24Ω

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 45 70

2 An electric motor in a toy car can operate when connected to a 6 V battery and has a current of 05 A A physics student wants to run the toy car but unfortunately he could find a 12 V battery in the physics lab The student also found a box with a set of five 6-Ω resistors

c Calculate the power dissipated in the circuit

P = I V = (05A)(12V) = 6 W

P = (05A)(12V) = 6 W

P = 6 W

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 46 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

b What is the power dissipated by the circuit

c How would you compare this power to the power when all bulbs are connected in parallel

d What is the current in light bulb L1

e What is the voltage across light bulb L1

f What is the voltage across light bulb L2

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 47 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

a What is the resistance of the circuit

P = V2R

R = V2P

R = (120V)2(75W)

R = 192 Ω for each light bulb

Req2amp3 = 96Ω

Rcircuit = 192Ω + 96Ω = 288Ω

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 48 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

b What is the power dissipated by the circuit

P = V2R

P = (120V)2288Ω

P = 50W

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 49 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

c How would you compare this power to the power when all bulbs are connected in parallel

This power is less

The power for bulbs connected in series is

P = 3(75W)

P = 225 W

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 50 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

d What is the current in light bulb L1

I1 = V1R1

I1 = 120V288Ω = 042A

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 51 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

e What is the voltage across light bulb L1

V = IR

V = (042A)(192Ω)

V = 80V

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 52 70

3 Three light bulbs are connected in the circuit show on the diagram Each light bulb can develop a maximum power of 75 W when connected to a 120-V power supply The circuit of three light bulbs is connected to a 120 V power supply

f What is the voltage across light bulb L2

V = IR

V = (042A)(96Ω)

V = 40V

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 53 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

b What is the voltage drop across 6-Ω resistor

c What is the current in 4-Ω resistor

d What is the emf of the battery

e What is the net power dissipation

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 54 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

a What is the net resistance of the circuit

Middle Section 16Ω + 14Ω = 512Ω Req = 24Ω

Whole circuit

Req = 96Ω + 24Ω + 12Ω

Req = 24Ω

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 55 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

b What is the voltage drop across 6-Ω resistor

V = IR

V = (025A)(24Ω) = 06V

(24Ω is the equivalent resistance of the middle section)

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 56 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

c What is the current in 4-Ω resistor

I = VR

I = (06V)(4Ω)

I = 015A

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 57 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

d What is the emf of the battery

V = IR

V = (025A)(24Ω)

V = 6V

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 58 70

4 Four resistors are connected in a circuit The circuit is connected to a battery with emf ε and negligible internal resistance The current through 96 Ω resistor is 025 A

e What is the net power dissipation

P = IV

P = (025A)(6V)

P = 15 W

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 59 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

b Calculate the current in the battery

c Calculate the terminal voltage of the battery

d Calculate the power dissipation in the 3-Ω resistor

e Calculate the power dissipation in the internal resistance

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 60 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

a Calculate the external resistance of the circuit

Top part 2Ω + 4Ω = 6Ω

Middle 13Ω + 16Ω = 36Ω Req = 2Ω

Whole circuit

Req = 4Ω + 2Ω + 2Ω = 8Ω

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 61 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

b Calculate the current in the battery

I = VR

I = (12V)(8Ω+1Ω)

I = 13A

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 62 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

c Calculate the terminal voltage of the battery

VT = E - Ir

VT = 12V - (13A)(1Ω)

VT = 117 V

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 63 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

d Calculate the power dissipation in the 3-Ω resistor

Find the potential difference across the two side resistors

V2 = (13A)(2Ω) = 52V V4 = (13A)(4Ω) = 26V

Find the potential difference across the 3Ω resistor

V3 = 117V - 52V - 26V = 39V

Find the power dissipation in the 3Ω resistor

P = V2R = (39V)2(3Ω) = 51W

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 64 70

5 Five resistors are connected to a battery with an emf of 12 V and an internal resistance of 1 Ω

e Calculate the power dissipation in the internal resistance

P = I2R

P = (13A)2(1Ω)

P = 17W

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 65 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

b Calculate the current in the 2-Ω resistor

c Calculate the current in the 3-Ω resistor

Switch is closed and the current reached constant value

d Calculate the charge on the capacitor

e Calculate the energy stored in the capacitor

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 66 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

a Calculate the net resistance of the circuit

Calculate Req of the 9 and 3 Ω resistors 9Ω + 3Ω = 12Ω

Calculate Req of the previous branch and the 6Ω resistor

112Ω + 16Ω = 312Ω Req = 4Ω

Calculate the net resistance of the circuit 4Ω + 2Ω = 6Ω

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 67 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

b Calculate the current in the 2-Ω resistor

Current in the 2Ω resistor is the same as the current in the battery

I = VR

I = (18V)(6Ω)

I = 3A

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 68 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

c Calculate the current in the 3-Ω resistor

Calculate the potential difference across the 2Ω resistor V = (3A)(2Ω) = 6V

Calculate the potential difference across the 9 amp 3Ω resistors 18V - 6V = 12V

Calculate the current though the 9 amp 3Ω resistors I = VR = (12V)(12Ω) = 1A

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 69 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is openSwitch is closed and the current reached constant value

d Calculate the charge on the capacitor

Calculate the potential difference across the 9Ω resistor which is the same as the potential difference across the capacitor

V = IR = (1A)(9Ω) = 9V

Find the charge on the capacitor Q = CV = (2μF)(9V) = 18μC

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ

Slide 70 70

6 Four resistors and a capacitor are connected to an 18 V battery with negligible internal resistance as shown on the diagram Initially the capacitor is disconnected from the battery - switch is open

Switch is closed and the current reached constant value

e Calculate the energy stored in the capacitor

Uc = frac12CV2

Uc = frac12(2μF)(9V)2

Uc = 81μJ