Electric Currents
Current
 = motion of charge
a steady flow of charge a steady force on mobile charges
Q
I
t
current = amount
of charge moving
through given
cross section per
unit time
[I] = ampere, 1 A = 1 C / s
Electric Currents
2
Current in a Complete Circuit
 current is the same at all cross sections, it does not
emerge from the positive battery terminal and
disappear in the negative terminal
 speed to establish current >> electron drift speed


I
conventional current flow:
from + to − (opposite to
electron motion)
Electric Currents
3
Resistance and Resistivity
Electric field is proportional to the potential difference between
the ends of a conductor, and current is caused by electric field
V
R
I
Ohm’s law: For many materials,
current is proportional to potential
difference (voltage)
Resistance: the proportionality factor
Resistance is for an object,
resistivity for material
Electric Currents
Resistivity ρ:
geometry
independent
L
R
A
4
Temperature Dependence of R

metal: ρ
increases with T

superconductor: ρ
drops to zero below
TC
T  0 [1   (T  T0 )]
T0
T
temperature coefficient of resistivity
Electric Currents
used in superconducting
magnets at the LHC
TC
T
5
Energy and Power in Circuits
 as charge passes through a circuit, the electric field
does work on the charge
W  VQ definition of potential difference
definition of current
Q  It
from Ohm’s law:
W
2
V
VI 
P
2
PI R
t
R
power = work/unit time
Electric Currents
6
Alternating Current
 Direct current: charges move steadily in one direction
 Alternating current: the direction changes over time
V  V0 sin t
V V0
I   sin t  I 0 sin t
R R
Electric Currents
7
Alternating Current Power
 Power is always positive, can talk about average power
2
I rms  I 0 / 2
2
0
Vrms  V0 / 2
P  I R  I sin t
2
2
0
1 2
1V
P  I0 R 
2
2 R
Electric Currents
P  I rmsVrms
8