Chapter 28 Direct Current circuits 28.1 Electromotive Force (emf ...

28.4 RC Circuitst < 0I(t) = R et / RC t / RC= I 0 eCharging a capacitor:t < 0: C is NOT charged and I = 0t = 0: The switch is closed.t > 0: C begins to charge.When t > 0, at any given moment,Kirchhoff’s loop rule gives: IR q C = 0(1) Initial Current:At t = 0, q = 0. No potential drop onC, all the potential drop is on R.Therefore, I 0 = R(current at t = 0)St > 0ISCR+q-qRC0.632Cq = RCtTime constant: = RC, has a unit of seconds.At t = , I = e 1 I 0 = 0.368I 0 ,q = q max [1 e 1 ] = 0.632q max = 0.632CI 00.368I 0II 0 = Rt(2) When t , C is charged to its maximum q max , and thecurrent is 0. All the potential drop is on C. No potential dropon R.q max = C (maximum charge)(3) Between the above two limiting cases, the charge is governeddqby eq:dt = R qRCThe solution:q(t) = C[1 e t / RC ] = q max [1 e t / RC ]The work done by the battery during the charging:W battery = Q max = C 2When C is fully charge, the energy stored in C:U = U = 1 2 q max = 1 2 C 2 = 1 2 W batteryThe other half of energy goes into joule heat in the resistor.