AP Physics

Ch 27 and 28 Review

DC Circuits

1. A light bulb is rated at 30 W when operated at 120 V. How much charge enters (and leaves) the light bulb in 1.0 min?

!

I = PV

=30w

120V= 0.25A

q = I t

q = 0.25A( ) 60sec( )

q =15C

2. What maximum power can be generated from an 18-V emf using any combination of a 6.0-" resistor and a 9.0-" resistor?

!

PSer =V 2

R=

18V( )2

15 "= 21.6w

R// =6"( ) 9"( )

15"= 3.6 "

P// =V 2

R=

18V( )2

3.6 "= 90w

3. A small bulb is rated at 7.5 watts when operated at 125 V. Its resistance (in ohms) is:

!

P =V

2

R

R =V 2

P=

125V( )2

7.5w= 2083.3 "

4. At what rate is thermal energy being generated in the 2R-resistor when $ = 12 V and R = 3.0 "?

!

3 "

!

3 "

!

3 "

!

6 "

!

RTotal = 6 "

!

I =V

R=

12V

6"= 2A

!

12V

!

3 "

!

3 "

!

3 "

!

6 "!

12V

!

6V

!

6V

!

3V

!

3V

!

P =V

2

R

P =6V( )

2

6 "P = 6w

5. What is the magnitude of the potential difference across the 20-" resistor?

!

7.76V

!

5 "

!

10 "

!

20 "

!

11V

!

10 "

!

10 "

!

12 "!

Rt =12 "+ 5 "

Rt =17 "

!

I =V

R=

11V

17"= 0.647A

!

V = IR = 0.647A 5"( )

V = 3.24V

11V # 3.24V = 7.76V

!

3.24V

8

6. What is the current in the 10-" resistor?

!

21V

!

15V!

6V

!

5 "!

10 "

!

5 "

!

5 "

!

2 "

!

RT

= 2 "+ 5 "

RT = 7 "

!

I =V

R=

21V

7"= 3A

!

V = IR = 3A( ) 5"( ) =15V

21V #15V = 6V

I =V

R=

6V

10"= 0.6A

7. At what rate is thermal energy generated in the 5-" resistor

when $ = 24 V?

!

24V

!

4V

!

4V

!

16V

!

5 "

!

10 "

!

24V

!

10 "

!

10 "

!

10 "

!

5 "!

4V

!

8V

!

R/ /

=R

1R

2

R1 + R2

R/ / = 5 "

Rser

= 5"+ 5" =10 "

R/ /

=R1R2

R1

+ R2

= 5 "

RT = 5" +10" =15 "

!

I =V

R=

24V

15"=1.6A

V = IR = 1.6A( ) 10"( ) = 16V

!

P =V 2

R=

4V( )2

5"= 3.2w

8. When a 20-V emf is placed across two resistors in series, a current of 2.0 A is present in each of the resistors. When the same emf is placed across the same two resistors in parallel, the current through the emf is 10 A. What is the magnitude of the greater of the two resistances?

!

V = IR

20V = 2A R1 + R2( )

10 " = R1 + R2

!

V = IR

20V =10AR1R2

R1 + R2

&

' (

)

* +

2 " =R1R2

R1 + R2

!

10 " = R1 + R2

10 # R2 = R1

!

2 =R1R2

R1 + R2

2 =10# R2( )R2

10 # R2( ) + R2

2 =10R2 # R2

2

10

20 =10R2 # R2

2

R2

2 #10R2 + 20 = 0

!

R2

2 #10R2 + 20 = 0

R2 =10 ± 102 # 4 1( )20

2

R2 = 7.24 "

R1 = 2.76 "

9. What is the current in the 15-" resistor when $ = 90 V?

!

1

R/ /

=1

15"+

1

30"

1

R/ /

=2

30"+

1

30"

R// = 10"

!

RT = 20"+ 10" = 30"

I =V

R=

90V

30"= 3A

!

3A

3A flows through the 20 ! resistor dropping off 60V. This leaves 30V for the rest of the circuit. Because they are in parallel, both resistors get 30V.

!

V = IR

V = 3A( ) 20"( )

V = 60V

!

I =V

R

I =30 V

15 "= 2A

!

60V

!

30V

!

2A

16

10. Determine $ when I = 0.50 A and R = 12 ".

!

24 "

!

12 "

!

24 "

!

IT = I1 + I2

IT =1A

R/ / =12 "

V/ / = IA 12"( ) =12V

12V +12V = 24V

!

1A

$

17

11. Determine the current in the 10-V emf.

!

I1

!

I2

!

I3

!

I1 + I2 # I3 = 0

!

abefa% 5"I1 # 5"I2 = 10V ÷ 5"

I1 # I2 = 2A

!

a

!

b

!

c

!

d

!

e

!

f

!

debcd % 5"I3 + 5"I2 =15V ÷ 5"

I2 + I3 = 3A18

!

I1 + I2 # I3 = 0 1 1 #1 0

I1 # I2 = 2 1 #1 0 2 sub 2 from 1

I2

+ I3

= 3 0 1 1 3

!

1 1 #1 0

0 2 #1 #2

0 1 1 3 , by 2 and sub from 2

!

1 1 #1 0

0 2 #1 #2

0 0 #3 #8

!

#3I3 = #8A

I3 = 2.6 A

19

!

I2 + I3 = 3A

I2 = 3A # I3

I2 = 3A # 2.6 A

I2 = 0.3 A

!

I1 # I2 = 2A

I1 = 2A + I2

I1 = 2A + 0.3 A

I1 = 2.3 A

!

#3I3 = #8A

I3 = 2.6 A

20

12. What is the magnitude of the current in the 20-" resistor?

!

A

!

B

!

C

!

D

!

E

!

F

!

I1

!

I2

!

I3

!

I1 + I2 # I3 = 0

!

ABEFA%10"I1

+ 20"I3

= 10V ÷10"

I1 + 2I3 =1A

!

CBEDC %10"I2 + 20"I3 =15V ÷ 5"

2I2 + 4I3 = 3A

!

I1+ I

2# I

3= 0 1 1 #1 0

I1 + 2I3 = 2 1 0 2 1 sub 2 from 1

2I2 + 4I3 = 3 0 2 4 3

!

1 1 #1 0

0 1 #3 #1 , by 2 and sub 3 from 2

0 2 4 3

!

1 1 #1 0

0 2 # 6 #2

0 0 #10 #5

!

#10I3 = #5A

I3 = 0.5A

22

!

#10I3 = #5A

I3 = 0.5A

23!

I1 + 2I3 = 1A

I1 =1A# 2I3

I1 =1A# 2 0.5A( )I1 = 0 !

I1 + I2 # I3 = 0

I2 = I3 # I1

I2 = 0.5A

13. Determine the potential difference Va # Vb shown in the

circuit below.

!

+

!

+

!

#

!

#

!

10 "

!

10 "!

10 "

!

10 "

!

15V

!

10V

a

b

!

I1

!

I2

!

I3

!

A

!

B

!

C

!

D

!

E

!

F

!

I1 # I2 # I3 = 0

!

+

!

+

!

#

!

#

!

10 "

!

10 "!

10 "

!

10 "

!

15V

!

10V

a

b

!

I1

!

I2

!

I3

!

A

!

B

!

C

!

D

!

E

!

F

!

BCFAB % 10"I2 #15V +10"I1 #10V = 0 ÷ 5"

2I1 + 2I2 = 5A

!

CDEFC % 20"I3 +15V #10"I2 = 0 ÷ 5"

# 2I2 + 4 I3 = #3A

!

I1# I

2# I

3= 0

2I1 + 2I2 = 5A

# 2I2 + 4I3 = #3A

!

1 #1 #1 0

2 2 0 5 , top by 2 and sub middle

0 #2 4 #3

!

1 #1 #1 0

0 #4 #2 #5

0 #2 4 #3 ,B by 2 and sub from M

!

1 #1 #1 0

0 #4 #2 #5

0 #2 4 #3 ,B by 2 and sub from M

!

1 #1 #1 0

0 #4 #2 #5

0 0 #10 1

!

#10I3 =1A

I3

= #0.1A

27

28

!

I1# I

2# I

3= 0

2I1 + 2I2 = 5A

# 2I2 + 4I3 = #3A

!

#2I2 + 4I3 = #3A

#2I2 = #3A # 4I3

2I2 = 3A + 4 #0.1A( )

I2 =3A #0.4A

2=1.3A!

I1 = I2 + I3

I1 = 1.3A( ) + #0.1A( )

I1 = 1.2A

29

!

+

!

+

!

#

!

#

!

10 "

!

10 "!

10 "

!

10 "

!

15V

!

10V

a

b

!

I1

!

I2

!

I3

!

A

!

B

!

C

!

D

!

E

!

F!

ABCD%Va #Vb

#10V + #0.1A( )10" = #11V

!

AFCD%Va #Vb

#12V + 15V #13V #1V = #11V

!

AFED%Va #Vb

#12V +1V = #11V

30

14. Determine the magnitude and direction of the current in the 500-" resistor when I = 30 mA.

!

A

!

B

!

C

!

D

!

ABCDA%

500"I2 #10V + 12V # 30V = 0

500"I2 = 28V

I2 = 0.056A L to R

!

+

!

#

!

#

!

+

!

400 "

12V

!

+

!

+

!

#

!

+

31

15. Determine the resistance R when I1 = 1.5 A.

!

I1

!

I2

!

I3

!

I1+ I

2# I

3= 0

I1 + I2 = I3 = 2.5A

!

A

!

B

!

C

!

D

!

E

!

F!

DEBCD%

30V # 50V + I3R = 0

I3R = 20V

!

ABCDEFA%

I3R + 10"I2 # 30V = 0

20V +10"I2# 30V = 0

10"I2 = 10V

I2 = 1A

!

I1

!

I3R = 20V

R =20V

2.5A= 8 "

32

16. What is the potential difference VB # VA when the I = 1.5 A in the circuit segment below?

!

1.5A

!

+

!

+

!

+

!

#

!

#

!

#

!

30V

!

VB #VA = #12V # 30V + 20V

VB #VA = #22V

Read Voltage from B to A

33

17. If R = 4.0 k", C = 3.0 mF, $ = 15 V, Q = 12 mC, and

I = 2.0 mA, what is the potential difference Vb # Va?

!

+

!

+

!

+

!

+

!

#

!

#

!

#

!

#

!

3 mF

!

V =q

C=

12 mC

3 mF= 4V

!

Vb#V

a= +4V + 8V #15V

Vb#V

a= #3V

!

15V

!

8V

!

V = IR

V = 0.002A( ) 4000"( )V = 8V

!

4V

34

18. If R = 3.0 k", C = 6.0 nF, $ 1 = 10.0 V, Q = 18 nC,

$ 2 = 6.0 V, and I = 5.0 mA, what is the potential

difference Vb # Va?

!

+

!

+

!

+

!

+

!

+

!

+

!

+

!

#

!

#

!

#

!

#

!

10V

!

15V

!

3V

!

6V

!

R = 3000 "

!

Vb #Va = #6V + 3V #15V #10V

Vb#V

a= #28V

!

V = IR

V = 0.005A( ) 3000"( )V =15V

!

V =q

C=

18 nC

6 nF= 3V

35

19. If the current in the 4.0-" resistor is 1.4 A, what is the magnitude of the potential difference, VA # VB?

!

A

!

B!

8 "

!

4 "

!

16 "!

2 "!

2 "

!

2 "

!

1.4 A

!

16.8V

!

1.05A

!

2.45A

!

4.9V

!

21.7V

!

10.85A

!

13.3A

!

26.6V

!

VA #VB = 26.6V + 21.7V

VA #VB = 48.3V

36

20. If Q = 400 µC and the potential difference VA # VB = #10V in the circuit segment shown below, what is the current in the resistor?

!

VC =q

C=

400µC

10µF= 40V

!

VA#V

B= #10V = 40V + V

R# 30V

VR = #20V

!

I =V

R=

#20V

20000"= #1mA

Current flows from A to B with a magnitude of 1mA.

37

21. At t = 0 the switch S is closed with the capacitor

uncharged. If C = 50 µF, $ = 20 V, and R = 4.0 k", what

is the charge on the capacitor when I = 2.0 mA?

$

When I = 2.0mA, the Voltage drop on R is:

This mean, because its a series circuit, The capacitor is charged to 12V

!

q = CV

q = 50µF( ) 12V( )

q = 600µC

!

V = IR

V = 0.002A( ) 4000"( )

V = 8V

!

8V!

12V

!

20V

38

22. What is the equivalent resistance between points a and b when R = 13 "?

!

13 "

!

13 "!

26 "

!

39 "

b

a

!

1

R/ /

=1

R1

+1

R2

+1

R3

R/ / = 7.09 "

!

RT = R// + R4

RT = 7.09 "+13 "

RT = 20.09 "

39

23. What is the equivalent resistance between points A and B in the figure when R = 20 "?

!

R2

!

R

!

2R

!

RT = 3.5R = 70 "

40

24. What is the equivalent resistance between points A and B in the figure when R = 20 "?

!

3R

!

2R

!

6R

!

A

!

B

!

1

RT

=2

6R+

3

6R+

1

6R

RT =6R

6= 20 "

41

25. When a capacitor is fully charged, the current through the capacitor isa. zero, because current can’t flow through an open circuit.

42

26. The circuit below contains three 100 watt light bulbs.

The emf $ = 110 V. Which light bulb(s) is(are) the

brightest?

A is the brightest because A gets all the current.

43

27. The circuit below contains 4 light bulbs. The emf is 110 V. Which light bulb(s) is(are) brightest?

D doesn’t light at all because no current flows through D.

B lights the brightest because B gets all the current.