Fundamentals of Physics
Chapter 26 Current & Resistance
1.
2.
3.
4.
5.
6.
7.
8.
9.
Moving Charges & Electric Currents
Electric Current
Current Density
Resistance & Resistivity
Ohm s Law
A Microscopic View of Ohm s Law
Power in Electric Circuits
Semiconductors
Superconductors
Review & Summary
Chapter Questions
Exercises & Problems
2006
Physics 2112
Fundamentals of Physics
Chapter 26
1
Moving Charges and Electric Currents
electron motion
electric current
An electric current arrow is drawn in the direction in which positive charge
carriers would move, even if the actual charge carriers are negativelycharged electrons moving in the opposite direction.
Due to historical reasons only (Ben Franklin!)
2006
Physics 2112
Fundamentals of Physics
Chapter 26
2
Moving Charges and Electric Currents
Current - steady net movement of conduction electrons through a conductor.
electron motion
electric current
A battery produces an electric field within the loop of wire.
A force is exerted on the conduction electrons, which then move around
the loop.
The electron flow rapidly reaches a steady state.
The electric current has the same value at all points in the above circuit.
Conservation of charge.
2006
Physics 2112
Fundamentals of Physics
Chapter 26
3
Electric Current
Current - motion of positive electric charges
Direct Current (DC) - motion in one direction
Q is the amount of charge that flows through cross-sectional area A in time t
Current
Units:
2006
i
q
t
1 Ampere = 1 Coulomb / Second
Physics 2112
Fundamentals of Physics
Chapter 26
4
Current Density
The current is the same through each cross section of the wire.
Current Density = Current / Area
J
2006
Physics 2112
i
A
Fundamentals of Physics
Chapter 26
5
Electric Current
i0 = i1 + i2
Charge is conserved.
Currents are scalars, not vectors.
2006
Physics 2112
Fundamentals of Physics
Chapter 26
6
Checkpoint
2006
Physics 2112
Fundamentals of Physics
Chapter 26
7
Drift Velocity
A conductor contains a very large number (~1 per atom) of electrons that are
only loosely bound to their atoms.
These conduction electrons move at very high speed (~ 106 m/s) in random
directions, but soon collide with the stationary atoms of the conductor,
drastically changing the direction of their velocity. (a la the motion of atoms in
a gas).
Drift Velocity: an applied electric field accelerates these moving conduction
electrons in the direction opposite to the field, thus superimposing a small drift
velocity (~ 10-4 m/s) on their random motions.
2006
Physics 2112
Fundamentals of Physics
Chapter 26
8
Current Density
Positive charge carriers drift with velocity vd in the direction of the electric field
inside a wire of area A.
J
A
n = # of charge carriers per unit volume
vd = drift velocity of charge carriers
nAL = # of charge carriers in length L
J
2006
Physics 2112
i
q
t
n ALe
L
vd
i
A
n A e vd
n e vd
Fundamentals of Physics
Chapter 26
9
Example 2
a)
b)
2006
Current density in a cylindrical wire of radius R = 2.0 mm is uniform across
a cross section of the wire and is J = 2.0 x 105 A/m2. What is the current
through the outer portion of the wire between R/2 and R ?
What is the current through that portion if J = ar2
Physics 2112
Fundamentals of Physics
Chapter 26
10
Example 3
What is the drift speed of the conduction electrons in a copper wire
with radius r = 900 m when it has a uniform current i = 17mA?
Assume that each copper atom contributes one conduction electron to
the current and the current density is uniform across the wires cross
section
2006
Physics 2112
Fundamentals of Physics
Chapter 26
11
Resistance & Resistivity
Resistance between any two points of a conductor:
apply a potential difference (V)
measure the current (i)
R
Units:
V
i
1 ohm = 1
= 1 volt per ampere
Resistor: a conductor whose function in a circuit is to provide a specified resistance,
usually independent of current and temperature.
2006
Physics 2112
Fundamentals of Physics
Chapter 26
12
Conductivity & Resistivity
Resistivity is a property of a resistive material.
(Not an attribute of a particular resistor.)
E
J
Unit:
ohm m
Conductivity = (Resistivity)-1
Unit: mho / m
J
2006
Physics 2112
E
Fundamentals of Physics
Chapter 26
13
Conductivity & Resistivity
A
E
J
E
J
V
L
i
V
EL
i
JA
R
A
R
V
i
L
A
Resistivity is a property of a resistive material.
Resistance is a property of a circuit element.
Risistivity Increase with T: The random
motion of atoms in the metal increases with
temperature, increasing the probability that
the current-carrying electrons will collide
with them.
2006
Physics 2112
Fundamentals of Physics
Chapter 26
14
Checkpoint
Rank according to the current passing through them with an applied voltage V
2006
Physics 2112
Fundamentals of Physics
Chapter 26
15
Ohm s Law
Ohm s Law : the current through a device is proportional to the voltage applied
across the device.
R
V
i
A conducting material obeys Ohm s law when its resistivity is independent of the
magnitude and direction of the applied electric field.
2006
Physics 2112
Fundamentals of Physics
Chapter 26
16
A Microscopic View of Ohm s Law
1.6 10
6 m
s
constant (quantum mechanics)
ele
ctr
on
vel
o
city
ve
drift velocity
not to scale!
2006
Physics 2112
vd
5 10
vd
ve
10
Fundamentals of Physics
7 m
s
13
Chapter 26
17
A Microscopic View of Ohm s Law
vel
o
city
= mean time between collisions
F
m
vd
a
J
n e vd
ele
ctr
on
drift velocity
a
eE
m
eE
m
m
e2n
E
E
J
J
m
e2n
2006
Physics 2112
Fundamentals of Physics
Chapter 26
18
Power in Electric Circuits
Decrease in potential energy:
Va
dU
dq Va
Vb
dU
dq V
i dt V
Energy per unit time:
P
Vb
Units:
dU
dt
1 Watt = 1 V A = (1 J/C)(1C/s) = 1 Watt
i
P
2006
Physics 2112
iV
V
R
iV
2
i R
Fundamentals of Physics
V2
R
Chapter 26
19
Transistor Diode
(Take note of the scales)
2006
Physics 2112
Fundamentals of Physics
Chapter 26
20
Superconductivity
Resistivity suddenly goes to zero.
Bardeen, Cooper, Schrieffer (BCS) Theory
2006
Physics 2112
Fundamentals of Physics
Chapter 26
21
This document was created with Win2PDF available at http://www.daneprairie.com.
The unregistered version of Win2PDF is for evaluation or non-commercial use only.