1. Chapter 25: Current, Resistance and Electromotive Force
Charge carrier motion in a conductor in two parts
Constant Acceleration
Randomizing Collisions (momentum, energy)
=>Resulting Motion
Average motion = Drift Velocity = vd ~10-4 m/s
Typical speeds ~ 106 m/s

2. Current Flow = net motion of charges = Charge carriers charge q
speed vd
I = Current = rate at which charge passes the area vd I vd I
Negative charge carriers move in opposite direction of conventional current.

3. Connection with microscopic picture:A vd q
dQ = charge that passes through A
= number that pass through A  charge on each
= (n A vd dt) q, n = number density = number/volume
Current Density:
(works for negative charge carriers, multiple types of charge carriers as well)

4. Example: 18 gauge copper wire (~1. 02 mm in diameter)
Example: 18 gauge copper wire (~1.02 mm in diameter) -constant current of 2A
-n = 8.5x1028 m (property of copper)
find J, vd

5. Current as a response to an applied electric field

6. If  does not depend on E, the material is said to obey “Ohm’s Law”J E J E
slope = 1/ J
linear response
Ohm’s Law
nonlinear response E
diode
nonlinear response
direction dependence!
 depends upon
material E
Temperature
If  does not depend on E, the material is said to obey
“Ohm’s Law”

7. For a cylindrical conductorE J I a b
see also example 28-3 re: alternate geometries
Example: 50 meter length of 18 gauge copper wire (~1.02 mm in diameter)
constant current of 2A
 = 1.72x10-8 .m
find E,V, R

8. Temperature Dependence of 
Metallic Conductor T
Semiconductor T
Superconductor
For small changes in temperature:

9. Resistor Color Codes
Color number color range
black 0 none ±20%
brown 1 silver ±10%
red 2 gold ±5%
orange 3
yellow 4 value: n1n2x10n3±x%
green 5
blue 6
violet 7
gray 8
white x102±5%

10. Electromotive Force and Circuits Steady current
requires a complete circuit
path cannot be only resistance
cannot be only potential drops in direction of current flow
Electromotive Force (EMF)
provides increase in potential E
converts some external form of energy into electrical energy
Single emf and a single resistor:
V = IR
V = IR = E + - I E

11. Measurements
Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device. V
Ammeters measure current through a device by being placed in series with the device. A

12. Real Sources and Internal Resistanceb
Ideal emf E
determined by how energy is converted into electrical energy
Internal Resistance r
unavoidable “internal” losses
aging batteries => increasing internal resistance

13. V
Open Circuit
I=0
Vr=0
Vab= E E r A a b V
Short Circuit
Vr = Ir = E
Vab= 0 E r A a b

14. V
Complete Circuit E r A a b I R
Charging Battery V I E r A a b

15. Energy and Power I + -
V= E + - a b a b
V=IR

16. Power and Real Sources E r
Discharging Battery a b I I E r
Charging Battery a b I I

17. Real Battery with Load I A E r a b V R

18. Complete Circuit Example
E=12V
r = 2 a b V
R = 4

19. Theory of Metallic Conduction
Constant Acceleration between randomizing collisions (momentum, velocity randomized)

20. Example: What is the mean time between collisions and the mean free path for conduction electrons in copper?

21. Physiological Effects of Current
Nerve action involves electrical pulses
currents can interfere with nervous system
~.1A can interfere with essential functions
(heartbeat, e.g.)
currents can cause involuntary convulsive muscle action
~.01 A
Joule Heating (I2R)
With skin resistance
dry skin: R ~ 500k
wet skin: R ~ 1000