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Last time…

Begin circuits
Today…


Resistor circuits
Start resistor-capacitor circuits
Tue. Oct. 13, 2009
Physics 208 Lecture 12
1
Resistors
Circuits
Physical layout
Schematic layout
Tue. Oct. 13, 2009
Physics 208 Lecture 12
2
Quick Quiz
Which bulb is brighter?
I
A. A
I
B. B
C. Both the same
I
Current through each must be same
I
Conservation of current (Kirchoff’s current law)
Charge that goes in must come out
Tue. Oct. 13, 2009
Physics 208 Lecture 12
3
Question
When current flows, charge moves around the circuit.
Suppose that positive charge carriers flow around
the circuit. What is the change in potential energy
of a positive charge as moves from c to d?
A. qVd – qVc
B. qVc – qVd
C. qVd + qVc
D. zero
Tue. Oct. 13, 2009
Physics 208 Lecture 12
4
Quick Quiz
What is the change in kinetic energy
as it moves from c to d?
A. qVd – qVc
B. qVc – qVd
C. qVd + qVc
D. zero
Tue. Oct. 13, 2009
Physics 208 Lecture 12
5


Power dissipation (Joule heating)

Charge loses energy from c to d.
E lost  E  KE  U   0  qVd  Vc 

Ohm’s law:


Vc  Vd   IR
Elost  qIR

Energy dissipated in resistor as
 Heat (& light) in bulb

Power dissipated in resistor =
dE lost dq

IR  I 2 R
dt
dt
Tue. Oct. 13, 2009
Physics 208 Lecture 12
Joules / s = Watts
6
Light bulbs and power

Household voltage is 120V







60W  60J /s  I 2R  IIR  VI
I  60W /120V  0.5A
R V /I 120V /0.5A  240
60 Watt
Cost

24 hours on requires
60J /s24hour3600s /hour  5,184,000J


MG&E ~ 13¢ / kWatt-hour
1kW  hour  1000J /s3600s /hour  3,600,000J
19¢ / day
Tue. Oct. 13, 2009
Physics 208 Lecture 12
7
Two different bulbs
I
b
P1  I 2 R1
c
P2  I R2
2

Current same through each
Power dissipated different

I
R2
e

I
R1
a
d
I
Brightness different
Tue. Oct. 13, 2009
Physics 208 Lecture 12
8
Kirchoff’s junction law

Charge conservation
I2
I1
Iin
I3
I1=I2+I3
I1
I3
Iout = Iin
Iout
Tue. Oct. 13, 2009
I2
I1+I2=I
Physics 208 Lecture 12
3
9
Quick Quiz
What 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. 13, 2009
Physics 208 Lecture 12
10
Question
As more and more resistors are added to the
parallel resistor circuit shown here the total
current flowing I…
I
R1
A.
B.
C.
D.
E.
R2
R3
R4
….
Increases if each Ri getting bigger
Increases if each Ri getting smaller
Always increases
Each resistor added
Always decreases
adds V/Ri to the
Stays the same
total current I
Tue. Oct. 13, 2009
Physics 208 Lecture 12
11
Question
You use one power strip to plug in your toaster,
coffee pot, microwave.
10 A
Toaster
5A
12 A
Coffee Pot
Microwave
Everything works great until you plug in your space heater,
then you smell smoke. This is because
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. 13, 2009
Physics 208 Lecture 12
12
More complicated
circuits

Both series & parallel


Determine equivalent
resistance
Replace combinations
with equivalent
resistance
Tue. Oct. 13, 2009
Physics 208 Lecture 12
13
Quick Quiz
The circuit below contains three 100W light bulbs.
The emf e = 110 V. Which light bulb(s) is(are)
brightest ?
A. A
B. B
C. C
D. B and C
E. All three are equally bright.
Tue. Oct. 13, 2009
Physics 208 Lecture 12
14
Measurements in a circuit


A multimeter can measure currents (as an ammeter), potential
difference (as a voltmeter)
Electrical measuring devices must have minimal impact in the
circuit
VV
V
I
V
R
e
A
IA
Ammeter
The internal resistance of the
ammeter must be very small
I = IA
e= V+VA = RI + rAI  RI
for rA 0
Tue. Oct. 13, 2009
IV
R
IR
VA
I
Voltmeter
e
The internal resistance of the
voltmeter must be very large
I = Iv+IR
e e
e

VV = e
I   rV

Physics 208 Lecture 12
rV
R
15
R
Kirchoff’s loop law

Conservation of energy
Tue. Oct. 13, 2009
I1
R1
e
R2
I2
Physics 208 Lecture 12
R3
I3
16
Resistorcapacitor circuit

What happens to charges on
the capacitor after switch is
closed?

Why does the charge flow
through the resistor?

Why does the charge on the
capacitor change in time?
Thur. Oct. 16, 2008
Physics 208 Lecture 14
17

Charging a capacitor

Again
Kirchoff’s loop law:
e  IR  Q /C  0
 I  e /R  Q
C
C
/RC
e
Looks like resistor & battery:
uncharged cap acts like short circuit
e
VC increases, so VR decreases
Time t = 0: Qc  0  I  /R
t increases: Qc  0  I  /R

Time t = : VC  e VR  0  I  0

Thur. Oct. 16, 2008
Fully charged capacitor acts
like open circuit
Physics 208 Lecture 14
18
Discharging the capacitor

Kirchoff’s loop law
VB  VA   VD  VC   0
Vc  Qc /C

IR
B
C
A
D
Qc
I
RC
Charges in the current I come from capacitor:

Thur. Oct. 16, 2008
dQc
I
dt
Physics 208 Lecture 14
19
RC discharge

RC time constant
  RC
Q  Qoe
I  I oe
Thur. Oct. 16, 2008
t / 
t / 
Physics 208 Lecture 14
20
Charging a capacitor
Q  Qmax 1 et /  

Thur. Oct. 16, 2008
Physics 208 Lecture 14
21
Question
The circuit contains three identical light
bulbs and a fully-charged capacitor.
Which is brightest?
A. A
B. B
C. C
D. A & B
E. All equally bright
Thur. Oct. 16, 2008
Physics 208 Lecture 14
22
Question
The circuit contains three identical light
bulbs and an uncharged capacitor.
Which is brightest?
A. A
B. B
C. C
D. A & B
E. All equally bright
Thur. Oct. 16, 2008
Physics 208 Lecture 14
23
RC discharge

RC time constant
  RC

time t
Tue. Oct. 13, 2009
Physics 208 Lecture 12
24

RC analysis

Kirchoff loop law:
VC  VR  0
QC

 IR  0
C

I related to QC
dQC
I 
dt


Tue. Oct. 13, 2009
QC
dQC
R
0
C
dt
dQC
QC

dt
RC
Physics 208 Lecture 12
25
RC analysis
dQC
QC

dt
RC
dQC
1

dt
QC
RC
Q

Qo
dQC
1

QC
RC
t
 dt
0
t
ln QC Q  
o
RC
QC t   Qo exp t /RC 
Q t 
Tue. Oct. 13, 2009
Physics 208 Lecture 12
26