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

Last time…

Combining capacitors Begin circuits

Resistor circuits Start resistor-capacitor circuits

Today…


Resistors

Schematic layout

Circuits

Physical layout


Kirchoff’s junction law

Charge conservation

Iin

Iout

Iout = Iin

I1

I2

I3I1=I2+I3

I2

I3

I1

I1+I2=I3


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


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


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


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


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


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


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


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


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


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


More complicated circuits

Both series & parallel Determine equivalent

resistance Replace combinations

with equivalent resistance


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.


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


Kirchoff’s loop law

Conservation of energy

R1

R2 R3

I1

I2 I3


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?


RC discharge RC time constant

time t

€

τ =RC

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