Topics:
•  Conductivity and Resistivity
•  Resistance and Ohm’s Law
•
•
•
Capacitors in series and parallel
Resistors in series and parallel
Kirchhoff’s Rules
PHYS 1022: Chap. 31-32, Pg 2
1
PHYS 1022: Chap. 31-32, Pg 3
PHYS 1022: Chap. 31-32, Pg 4
2
New Topic



PHYS 1022: Chap. 31-32, Pg 5
The electric field is directly proportional to the current
density in the wire.
ρ is called resistivity, R is the resistance
 a measure of how hard a charge can move in a material
SI unit: V.m / A = Ω. m
V = RI
€

A perfect conductor has zero resistivity. A perfect insulator has infinite resistivity
  The reciprocal of resistivity (1/ρ) is called conductivity σ.
PHYS 1022: Chap. 31-32, Pg 6
3

The resistivity of a material depends on temperature.
Metal near room temperature:
PHYS 1022: Chap. 31-32, Pg 7
PHYS 1022: Chap. 31-32, Pg 8
4
PHYS 1022: Chap. 31-32, Pg 9
PHYS 1022: Chap. 31-32, Pg 10
5
PHYS 1022: Chap. 31-32, Pg 11
PHYS 1022: Chap. 31-32, Pg 12
6
Topics:
•  Conductivity and Resistivity
•  Resistance and Ohm’s Law
•
•
•
Capacitors in series and parallel
Resistors in series and parallel
Kirchhoff’s Rules
PHYS 1022: Chap. 31-32, Pg 13
New Topic
PHYS 1022: Chap. 31-32, Pg 14
7
  Since
Q = C V, we have
 C1V+ C2V + C3V = CV
C is called an equivalent
capacitor.
PHYS 1022: Chap. 31-32, Pg 15
  Since
V = Q/C, we have
 Q/C1+ Q/C2 + Q/C3 = Q/C
1 1
1
1
=
+
+
C C1 C2 C 3
PHYS 1022: Chap. 31-32, Pg 16
8
1)
What is the equivalent
capacitance of the combination
shown ?
2)
3)
4)
5)
3C/2
2C/3
3C
2C
C/2
o
Ceq
C
C
C
o
PHYS 1022: Chap. 31-32, Pg 17
How does the voltage V1 across
the C1 compare to the voltage
V2 across C2?
1)
2)
3)
4)
V1 = V2
V1 > V2
V1 < V2
all voltages are
zero
PHYS 1022: Chap. 31-32, Pg 18
9
How does the charge Q1 across
C1 compare to the charge Q2
across C2?
1)
2)
3)
4)
Q1 = Q2
Q1 < Q2
Q1 > Q2
all charges are
zero
PHYS 1022: Chap. 31-32, Pg 19
PHYS 1022: Chap. 31-32, Pg 20
10

Find the charge, potential difference, and energy stored in each capacitor.
PHYS 1022: Chap. 31-32, Pg 21
New Topic
PHYS 1022: Chap. 31-32, Pg 22
11
PHYS 1022: Chap. 31-32, Pg 23
Req is the reciprocal of the sum of the reciprocals.
PHYS 1022: Chap. 31-32, Pg 24
12
New Topic
PHYS 1022: Chap. 31-32, Pg 25
(or: what goes in has to come out!)
PHYS 1022: Chap. 31-32, Pg 26
13

“The sum of voltage drops and gains around any
closed circuit loop must be zero”
ΔV1 + ΔV2 + ΔV3 + ΔV4 + … = 0
Sign convention:
– sign for voltage drop and +
sign voltage gain.
It depends on several factors:
1.  emf or resistor
2.  direction of current
3.  direction of loop travel
What is the current at
point P?
PHYS 1022: Chap. 31-32, Pg 27
5A
P
8A
2A
1)
2)
3)
4)
2A
5A
6A
10 A
PHYS 1022: Chap. 31-32, Pg 28
14
PHYS 1022: Chap. 31-32, Pg 29
PHYS 1022: Chap. 31-32, Pg 30
15
PHYS 1022: Chap. 31-32, Pg 31
PHYS 1022: Chap. 31-32, Pg 32
16
PHYS 1022: Chap. 31-32, Pg 33
PHYS 1022: Chap. 31-32, Pg 34
17
Current in each resistor?
–IR = –8 V
I
Total resistance = 6 Ω
–IR = – 4 V
Ohm’s Law: I = V / R
= 12 V / 6 Ω
=2A
2Ω
4Ω
12 V
Start
Voltage drop across resistor?
V=IR
+ε = 12 V
ΔV = + 12 V – 8 V – 4 V = 0 
PHYS 1022: Chap. 31-32, Pg 35
The first thing we have to do is?
Define currents!
–I2R1
I2
I3
–I2R2
R1
–ε
I1
+ε
R3
Next: Define travel direction:
top loop (CW)
bottom loop (CW)
R2
Now apply Loop rule to each loop
Start
ΔV = + ε – I2R1 – I2R2 = 0
Start
ΔV = + I3 R3 – ε = 0
+ I3R3
PHYS 1022: Chap. 31-32, Pg 36
18
PHYS 1022: Chap. 31-32, Pg 37
PHYS 1022: Chap. 31-32, Pg 38
19
PHYS 1022: Chap. 31-32, Pg 39
PHYS 1022: Chap. 31-32, Pg 40
20