An uncharged 30.0F capacitor is connected in series with a 25.0 resistor, a DC b

Question

An uncharged 30.0F capacitor is connected in series with a 25.0 resistor, a DC battery, and an open switch. The battery has an internal resistance of 10.0 and its open-circuit terminal voltage in 50.0 V. The leads have no appreciable resistance. At time t=0, the switch is suddenly closed. What is the maximum current through the 25.0 resistor and when does it occur (immediately after closing the switch or after the switch has been closed for a long time)? What is the maximum charge that the capacitor receives? and when the current in the circuit is 0.850 A, how much charge is on the plates of the capacitor? i know its confusing, I just dont know where to start..... An uncharged 30.0F capacitor is connected in series with a 25.0 resistor, a DC battery, and an open switch. The battery has an internal resistance of 10.0 and its open-circuit terminal voltage in 50.0 V. The leads have no appreciable resistance. At time t=0, the switch is suddenly closed. What is the maximum current through the 25.0 resistor and when does it occur (immediately after closing the switch or after the switch has been closed for a long time)? What is the maximum charge that the capacitor receives? and when the current in the circuit is 0.850 A, how much charge is on the plates of the capacitor? i know its confusing, I just dont know where to start.....

Explanation / Answer

The uncharged capacitor is C = 30.0 F = 30.0 * 10-6 F The capacitor is in series with a resistor R = 25.0 The internal resistance of the battery is r = 10.0 The open-circuit terminal voltage is Eo = 50.0 V We know from the relation E = Eo * e-t/RC when t = 0 E = Eo or I * (R + r) = Eo or I = (Eo/R + r) ------------(1) The maximum current through the resistor flows immediately after the switch is closed. The maximum charge on the capacitor is Qo = C * Eo The current flowing through the capacitor is I = Io * e-t/RC or (I/Io) = e-t/RC or ln(I/Io) = -(t/RC) or (t/RC) = -ln(I/Io) = ln(Io/I) or t = RC * ln(Io/I) -------------(2) where Io is obtained from equation (1) and I = 0.850 A The charge on the capacitor plates is Q = I * t where t is obtained from equation (2) The current flowing through the capacitor is I = Io * e-t/RC or (I/Io) = e-t/RC or ln(I/Io) = -(t/RC) or (t/RC) = -ln(I/Io) = ln(Io/I) or t = RC * ln(Io/I) -------------(2) where Io is obtained from equation (1) and I = 0.850 A The charge on the capacitor plates is Q = I * t where t is obtained from equation (2)

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