II. Electric current
1. Definition
Q
I
t
Units: [ I ] = 1A = 1 C/s
Conventional
current
Electron
flow
Example: 1020 electrons passed through the electric conductor during 4 seconds.
Find the electric current through this conductor.
q (1.6 10 19 C )(10 20 )
I 
 4A
t
4s
Example: The electric current of 0.5 A is flowing through the electric conductor.
a) What electric charge is passing through the conductor during each second?
b) What electric charge will pass through the conductor during 1 minute?
a)
b)
q  It  (0.5 A)(1 s )  0.5 C
q  It  (0.5 A)(60 s)  30 C
1
2. Ohm’s Law
Nonohmic device
I
I
V
V
3. Resistance
Definition:
V
I
R
V
R
I
Units: [ R ] = 1Ω = 1 V/A
Ohm’s Law:
R  const
V  IR
2
4. Resistivity
I
Definition:
A
L
A
R
L
L
R
A
Example: What is the resistance of 1 m of nichrome wire of 2 mm diameter ?
L
1m
6
3
R    10   m

3

10

2

2
A
 10 m


Temperature dependence of resistivity
T  0 1   (T  T0 )
T  0  0 (T  T0 )


 0 T

T
3
Example: Two cylindrical resistors, R1 and R2, are made of identical material.
R2 has twice the length of R1 but half the radius of R1. They are connected to a
battery V as shown. Compare the currents flowing through R1 and through R2.
A. I1 < I2
 2  1  
L2  2 L1
r2  r1 / 2
A  r 2
I 2 / I1  ?
C. I1 > I2
B. I1 = I2
L
R
A
A2  A1 / 4
I1
I2
V
L2
2 L1
R2  

 8R1
A2
A1 / 4
V
V
1
I2 

 I1
R2 8 R1 8
4
5a. Resistors in series
Two resistors R1 and R2 are in series when they are connected
one after the other
I
R1
V1
R2
V
I  I1  I 2
V2
Req
V
V  IReq
V  V1  V2
IReq  IR1  IR2
I
Req  R1  R2
5
5b. Resistors in parallel
Two resistors R1 and R2 are in parallel when they are connected to the
same potential difference
I1
R1
I
I
I
I2
R2
V  V1  V2
V
I  V / Req
I  I1  I 2
V / Req  V / R1  V / R2
Req
1
1
1
 
Req R1 R2
6
Example: A 14-A current flows into a series combination of a 3.0 Ω and a 4.0 Ω
resistors. What is the voltage drop across the 4.0-Ω resistor?
A) 38 V;
B) 42 V;
C) 56 V;
D) 98 V.
I  14 A
R1  3.0
V2  IR2  14 A  4.0  56V
R 2  4 .0 
V2  ?
Example: A 22-A current flows into a parallel combination of 4.0 Ω, 6.0 Ω, and 12 Ω
resistors. What current flows through the 12-Ω resistor?
A) 18 A;
B) 11 A;
C) 7.3 A;
D) 3.7 A.
I  22 A
R1  4.0
R2  6.0
R3  12.0
I3  ?
1)
1
1
1
1
1
1
1
1







 Reff  2
Reff
R1 R2 R3 4 6 12 2
2) V  IReff  22 A  2   44V
3) I 3 
V
44V

 3.7 A
R3 12
7
Symbols for circuit elements
Conductor (wire) with negligible resistance
Resistors
- +
Source of emf (for example, a battery)
Switch
Ground
V
A
Voltmeter (should be connected in parallel)
Ammeter (should be connected in series)
8
6a. Ammeter (used to measure current)
=
A
A
G
r
r is small shunt resistance or shunt
G is galvanometer
• Ammeter should be connected in series
• Ammeter has very small (ideally zero) internal resistance,
so it does not affect the current to be measured
6b. Voltmeter (used to measure voltage or potential difference)
R
A
V
V
B
=
G
R is large
• Voltmeter should be connected in parallel
• Voltmeter has very large (ideally infinite) internal resistance,
so that very little current is diverted through it.
9
6c. Voltmeter and Ammeter
•
•
•
•
Voltmeter should be connected in parallel
Ammeter should be connected in series
Voltmeter has very large (ideally infinite) internal resistance
Ammeter has very small (ideally zero) internal resistance
Example: What connection is not correct?
V
A
A
V
A
B
C
A
V
10