An uncharged capacitor and a resistor are connected in serie

An uncharged capacitor and a resistor are connected in series to a source of emf. If epsilon = 10.00 V, C = 15.0 muF, and R = 100 Ohm, find the following: (a) the time constant of the circuit s (b) the maximum charge on the capacitor muC (c) the charge on the capacitor after one time constant muC

Solution

The time constant of the circuit

        t = R* C = 100 *15 x 10^-6 F = 0.0015 s

The maximum charge on the capacitor     

         q_o = CV_o = 15 x 10^-6 F * 10 V = 150 x 10^-6= 150 uC

The charge on the capacitor after one time constantis

           q= q_o (1 - e^-t/RC )

Given that t = 1 RC so that

           q= q_o (1 - e^-1 ) = 150 * (1 - 0.368 ) = 94.8 uC