Previous lectures on Electrostatics
Previous lectures on electrostatics:
Ch 21-24
Charges, conductors and Insulators
Electric force and E-fields
Electric Potential and Electric Potential
energy
Capacitance and Capacitors

Current and Resistance
Ch 25
•Current
•Ohm’s Law
•Resistance and Resistors
•Electric Circuits
•Kirchoff’s Laws
•RC Circuits
Electric Current

Electric current = rate of flow of charge through some region
of space

SI unit: ampere 1 A = 1 C / s

Average current:

Instantaneous value
Charge Carrier Motion in a Conductor
Iav = ΔQ/ Δt = nqvdA

Current density
 Magnitude J = I/A (A/m2)
 J = nqv
d
Copper wire: r = 0.815 mm
ρ = 8.93 g/cm3
Molar mass M = 63.5 g/mol
NA = 6.02 x 1023 atoms/mol
n= ρNA/M = 8.47 x 1028 atoms/m3
vd = I/(neπr2)=3.54 x 10-5 m/s
Current Density





Ohm’s Law:
J=σE
σ = conductivity = 1/ρ = 1/resistivity
Materials that obey Ohm’s law are said to be ohmic
Microscopically: a = F/m = eE/m
τ = mean time between 2 collisions electron-atoms
I
ne 2τ
J = = nev d =
E = σE
A
m

€
ΔV = EL and J = σE = σ ΔV/L = I/A
Resistance in ohms (Ω)
Ohmic and non-Ohmic Materials

ohmic device: relationship
current and voltage is linear

Nonohmic materials: not
linear
A diode is a common
example of a nonohmic
device

Resistivity

Resistivity:
ρ=1/σ
 SI units of Ω . m
The resistance depends
on resistivity and
conductor geometry:


Resistors control
the current level in
circuits
Resistors can be
composite or wirewound

Temperature dependence of resistance
and resistivity

ρo is the resistivity at To = 20° C

α = temperature coefficient in SI units of oC-1

The higher T the greater atomic vibrations
that increases collision probability
Similarly: R = Ro[1 + α(T - To)]
Semiconductors



Semiconductors are
materials that exhibit a
decrease in resistivity
with an increase in
temperature
α is negative
There is an increase in
the density of charge
carriers at higher
temperatures
Superconductors
Below a certain temperature, TC =
critical temperature
resistance falls to virtually zero

ρ = ρ 0 (1+ αΔT )
€

Once a current is set up in a
superconductor, it persists without
any applied voltage

Since R = 0
Electric power and Joule Heating

As a charge moves from a to b, the
electric potential energy of the
system increases by ΔU=QΔV

Power dissipated by R
dU d
= (QΔV ) = IΔV
dt dt
€
Power companies transmit electricity at high
voltages and low currents on power
lines to minimize power losses despite higher
risk