Tue. Oct. 14, 2008 Physics 208 Lecture 13 1

Last time…

Combining capacitors Begin circuits

Resistor circuits Start resistor-capacitor circuits

Today…

Tue. Oct. 14, 2008 Physics 208 Lecture 13 2

Resistors

Schematic layout

Circuits

Physical layout

Tue. Oct. 14, 2008 Physics 208 Lecture 13 3

Kirchoff’s junction law

Charge conservation

Iin

Iout

Iout = Iin

I1

I2

I3I1=I2+I3

I2

I3

I1

I1+I2=I3

Tue. Oct. 14, 2008 Physics 208 Lecture 13 4

Quick Quiz

Which bulb is brighter?

A. A

B. B

C.Both the same

Current through each must be same

Conservation of current (Kirchoff’s current law)

Charge that goes in must come out

I

I

I

I

Tue. Oct. 14, 2008 Physics 208 Lecture 13 5

Work and energy in a circuit

What happens as charge q moves? Uq

c=qVc

Uqd=qVd

Ohm’s law: Charge has lost potential energy Energy lost Elost = qIR Energy dissipated in resistor as

Heat (& light in bulb) Power dissipated in resistor =

€

⇒ ΔUq = q Vd −Vc( )

€

Vd −Vc( ) = −IR⇒

€

dE lostdt

=dq

dtIR = I2R Joules / s = Watts

Tue. Oct. 14, 2008 Physics 208 Lecture 13 6

Light bulbs and power

Household voltage is 120V

Cost 24 hours on requires

MG&E ~ 13¢ / kWatt-hour

60 Watt

€

60W = 60J /s = I2R = I IR( ) =VI

€

I = 60W /120V = 0.5A

€

60J /s( ) 24hour( ) 3600s /hour( ) = 5,184,000J

€

1kW − hour = 1000J /s( ) 3600s /hour( ) = 3,600,000J

€

R =V /I =120V /0.5A = 240Ω

19¢ / day

Tue. Oct. 14, 2008 Physics 208 Lecture 13 7

Two different bulbs

Current same through each Power dissipated different

Brightness different

R1

R2

a

b

c

d

e

I

I

I

I€

P1 = I2R1

€

P2 = I2R2

Tue. Oct. 14, 2008 Physics 208 Lecture 13 8

Resistors in Series

I1 = I2 = I Potentials add

ΔV = ΔV1 + ΔV2 = IR1 + IR2 =

= I (R1+R2) The equivalent resistance

Req = R1+R2

R

R=

2R

2 resistors in series:R LLike summing lengths

€

R = ρL

A

Tue. Oct. 14, 2008 Physics 208 Lecture 13 9

Quick Quiz

What happens to the brightness of the bulb B when the switch is closed?

A. Gets dimmer

B. Gets brighter

C. Stays same

D. Something else

Battery is constant voltage,ΔV across bulb B doesn’t changeso I through bulb B doesn’t change

Tue. Oct. 14, 2008 Physics 208 Lecture 13 10

Resistors in Parallel ΔV = ΔV1 = ΔV2

I = I 1 + I 2 (lower resistance path has higher current)

Equivalent Resistance

R/2

R R

Add areas

€

R = ρL

A

Tue. Oct. 14, 2008 Physics 208 Lecture 13 11

Quick QuizWhat happens to the brightness of the

bulb A when the switch is closed?

A. Gets dimmer

B. Gets brighter

C. Stays same

D. Something else

Tue. Oct. 14, 2008 Physics 208 Lecture 13 12

QuestionAs more and more resistors are added to the

parallel resistor circuit shown here the total current flowing I…

….R1

R2

R3

R4

I

A. Increases if each Ri getting bigger

B. Increases if each Ri getting smallerC. Always increasesD. Always decreasesE. Stays the same

Each resistor added adds ΔV/Ri to the total current I

Tue. Oct. 14, 2008 Physics 208 Lecture 13 13

You use one power strip to plug in your toaster, coffee pot, microwave.

Toaster Coffee Pot Microwave

10 A 5 A 12 A

Everything works great until you plug in your space heater, then you smell smoke. This is because

Question

A. The resistance of the circuit is too high

B. The voltage in the circuit is too high

C. The current in the circuit is too high

Tue. Oct. 14, 2008 Physics 208 Lecture 13 14

More complicated circuits

Both series & parallel Determine equivalent

resistance Replace combinations

with equivalent resistance

Tue. Oct. 14, 2008 Physics 208 Lecture 13 15

Quick Quiz

The circuit below contains three 100W light bulbs. The emf = 110 V. Which light bulb(s) is(are) brightest ?

A. AB. BC. CD. B and CE. All three are equally bright.

Tue. Oct. 14, 2008 Physics 208 Lecture 13 16

Electrical measurements A multimeter can measure currents (as an ammeter), potential

difference (as a voltmeter) Electrical measuring devices must have minimal impact in the

circuit

R

VVoltmeter

The internal resistance of the ammeter must be very smallI = IA= ΔV+ΔVA = RI + rAI RIfor rA 0

ΔVA

A

R

Ammeter

I

IA

ΔV

The internal resistance of the voltmeter must be very largeI = Iv+IR ΔVV =

ΔVV

IV

IR

I

€

I =ε

rV+ε

RrV →∞ ⏐ → ⏐ ⏐ ε

R

Tue. Oct. 14, 2008 Physics 208 Lecture 13 17

Kirchoff’s loop law

Conservation of energy

R1

R2 R3

I1

I2 I3

Tue. Oct. 14, 2008 Physics 208 Lecture 13 18

Resistor-capacitor circuit Why does QC (charge on

capacitor) depend on time after switch is closed?

R increases: does Qc change faster, slower, same?

C increases: does Qc change faster, slower, same?

Qc decreases: does Qc change faster, slower, same?

Tue. Oct. 14, 2008 Physics 208 Lecture 13 19

RC discharge RC time constant

time t

€

τ =RC