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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