Previous lectures on Electrostatics

Previous lectures on electrostatics:Ch 21-24

Charges, conductors and InsulatorsElectric force and E-fieldsElectric Potential and Electric Potential energyCapacitance 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 = nqvd

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

Ohm’s Law: J = σ E 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

Current Density

ΔV = EL and J = σE = σ ΔV/L = I/A Resistance in ohms (Ω)€

J =IA

= nevd =ne2τm

E =σE

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 circuitsResistors can be composite or wire-wound

Temperature dependence of resistance and resistivity

ρo is the resistivity at To = 20° C α = temperature coefficient in SI units of oC-1

Similarly: R = Ro[1 + α(T - To)]

The higher T the greater atomic vibrations that increases collision probability

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

Once a current is set up in a superconductor, it persists without any applied voltage Since R = 0

€

ρ = ρ0 1+αΔT( )

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

€

dUdt

=ddt

QΔV( ) = IΔV

Power companies transmit electricity at high voltages and low currents on power lines to minimize power losses despite higher risk