Charge carrier motion in a conductor in two parts

1
Chapter 26 Current, Resistance and Electromotive
Force
Charge carrier motion in a conductor in two
parts Constant Acceleration Randomizing
Collisions (momentum, energy) gtResulting
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
I
Negative charge carriers move in opposite
direction of conventional current.
3
Connection with microscopic picture
E
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) -constant current of 2A -n 8.5x1028
m-3 (property of copper) find J, vd
5
Current as a response to an applied electric field
6
slope 1/r
J
linear response Ohms Law
nonlinear response
E
diode nonlinear response direction dependence!

• r depends upon
• material
• E
• Temperature
• If r does not depend on E, the material is said
  to obey
• Ohms Law

7
For a cylindrical conductor
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 r
1.72x10-8 W.m find E,V, R
8
Temperature Dependence of r
r
r
r
T 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 re
d 2 gold 5 orange 3 yellow 4 value n1n2x10n3
x green 5 blue 6 violet 7 gray 8 white 9 10
x1025
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 E
11
Measurements Voltmeters measure Potential
Difference (or voltage) across a device by being
placed in parallel with the device.
Ammeters measure current through a device by
being placed in series with the device.
A
12
Real Sources and Internal Resistance
Ideal emf E determined by how energy is converted
into electrical energy Internal Resistance r
unavoidable internal losses aging batteries gt
increasing internal resistance
13
Open Circuit I0 Vr0 Vab E
r
E
A
a
b
Short Circuit Vr Ir E Vab 0
r
E
A
a
b
14
Complete Circuit
r
E
A
a
b
I
R
Charging Battery
I
E
r
a
b
15
Energy and Power
I
-

a
b
VIR
16
Power and Real Sources
r
E
Discharging Battery
a
b
I
I
r
E
Charging Battery
a
b
I
I
17
Real Battery with Load
18
Complete Circuit Example
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 500kW wet skin R 1000W