Transcript Document 7376656

Fig 28-CO, p.858
Chapter 28 Direct Current Circuits
28.1 Electromotive “Force” (emf)
Resistive
medium
Vr
VR
P28.1 (p.800)
CT1: If R1 = 2R2, which resistor
dissipates more power?
A. R1
B. R2
C. Both the same.
CT2: If R1 = 2R2, which resistor
dissipates more power?
A. R1
B. R2
C. Both the same.
Chapter 28 Direct Current Circuits
28.2 Resistors in Series and Parallel
Resistors in Series
For resistors in series, the same current flows
through each resistor from conservation of charge.
R2
R1
Req
A, L1
A, L2
A, L1 + L2
R1 =  L1/A
R2 =  L2/A
Req =  (L1 + L2 ) /A = R1 + R2
For many resistors in series the equivalent resistance
Req = R1 + R2 + R3 + …
is the sum of all the individual resistances
Series Resistors
1. Current same through each
resistor (conservation of
charge)
2. Add
Resistors in Parallel
For resistors in parallel, the voltage across each
resistor is the same from conservation of energy.
R1
A1, L
Req
R2
A2, L
A1 + A2, L
1/R1 = A1/ L
1/R2 = A2/ L
1/Req = (A1 + A2)/ L = 1/R1 + 1/R2
For many resistors in parallel the reciprocal of the equivalent resistance
1/Req = 1/R1 + 1/R2 + 1/R3 + …
is the sum of all the reciprocals of the individual resistances
Parallel Resistors
1. Voltages same across each
resistor (conservation of energy)
2. Add reciprocals
P28-15 (p.801)
Q28.11
p. 779
CT3-8 (i,ii,iii,iv,v,vi)
A. increase
B. decrease
C. no change
D. drop to zero
Circuit Elements
-
+
Source of emf

= V
“Perfect” conductor R = 0
Capacitor
C = Q / V
Resistor
R = V / I
Switch
Open R =

Closed R = 0
28.3 Kirchhoff’s Rules
• Junction Rule: The sum of the currents
entering any junction equals the sum of the
currents leaving that junction. This is due to
conservation of charge.
I2
I1
I1 = I2 + I3
I3
• Loop Rule: The sum of the potential
differences across each element around any
R
closed loop is zero. This is
due to the conservation
of energy.
I
 - IR = 0

Kirchhoff’s Rules
I
Analogy: River flowing down
hill through a gravel bed.

R
Loop Notes
1. Go through a battery from - to +: +
2. Go through a battery from + to -: -
3. Go through a resistor with current: -IR
4. Go through a resistor against current: +IR
P28.40 (p. 804)
CT9: Which circuit
requires Kirchoff’s
Rules to solve?
A. circuit A
B. circuit b
C. circuit c
D. circuit d
P28.40 (p. 804)
CT10: Which circuit
delivers the least
power to the 10 
resistor?
A. circuit A
B. circuit b
C. circuit c
D. circuit d
Chapter 28 Direct Current Circuits
P28.17 (p.802)
P28-55
p. 805
Each bulb is 60 W at
120V
Calculate Ptotal and
V across each bulb.
Chapter 28 Direct Current Circuits
28.4 RC Circuits
Q28.14 RC Circuits
p. 800
Assuming the capacitor is
initially uncharged,
that the time constant is
several seconds, and
that the bulb lights when
connected directly to
the battery terminals, state
what happens when
the switch is closed.
Include in your answer a
discussion of why the three
assumptions are necessary.
Chapter 28 Direct Current Circuits
28.4 RC Circuits
P28.27
p. 802
CT9: A fully charged capacitor stores
energy U0. How much energy remains
when the charge has decreased to half
its original value?
A. U0
B. U0/2
C. U0/4
D. U0/8
Chapter 28 Direct Current Circuits
28.5 Electrical Meters
Ideal Voltmeter R =

Ideal Ammeter R = 0