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E5 - Current • • So far we’ve looked at stationary charges – electrostatics Now we’re ready for moving charges!!! General Physics 2 Current & Resistance 1 Drude Model • When an electric field is present, the electron’s collisions with atoms results in a drift velocity opposite to the direction of the electric field General Physics 2 Current & Resistance 4 Current Density and conductivity • Current density indicates how rapidly charge is flowing near a certain point in a conductor v r r J v d nqv d • • • • Where ρ is the density of charge carriers, and n is the number density of charge carriers Current density is proportional to the electric field r v J cE σc is the conductivity Note that σ ≠ σc General Physics 2 Current & Resistance 6 Current Flow • Current is the total rate at which charge crosses a boundary dQ I dt • • Unit of current is the ampere See Table E5.1 General Physics 2 C 1 A 1 s Current & Resistance 7 Microscopic View of Current • • • • Current is the amount of charge in coulombs passing a given point per second. How fast are individual electrons moving? Electrons move due to electric field inside wire, but collisions with other particles slow them down. e- are moving to the left. Which way is E? Which way is I? General Physics 2 Current & Resistance 8 Electric Current • conventional current - direction a positive charge would flow General Physics 2 Current & Resistance 9 Surface Charges Direct Flow • Surface charges in a conductor move so that current is constant General Physics 2 Current & Resistance 10 Resistance • Resistance of a conducting object R I • • Where Δϕ is the potential difference between the ends Unit of resistance is the ohm General Physics 2 Current & Resistance 11 Ohm’s Law: Resistors metal • For a metal conductor nonohmic device ohm’s law resistance • Ohm () = unit of resistance General Physics 2 Current & Resistance 12 Power Dissipated in a Conductor • Power is the rate at which electrostatic potential is converted to thermal energy P I PI R R 2 2 • Unit of power is the watt = J/s = N m/s = kg m3/s3 General Physics 2 Current & Resistance 13 Discharging a Capacitor • The potential difference VC at any time t VC t Ae t RC • Where R is the resistance and C is the capacitance General Physics 2 Current & Resistance 17 Discharging a Capacitor VC t Ae t RC VC t 9e x e x 1 x e e 1 e e 2 e e 3 e 1RC RC 2RC RC 3RC RC 0.37 0.14 0.05 General Physics 2 Current & Resistance 18