A RC series circuit is connected to a 12 volt battery Initia

A R-C series circuit is connected to a 12 volt battery. Initially the capacitor has zero charge. Assume R= 21 , C= 2,995 F. When the circuit is closed, calculate the time (in Millisecond) when the capacitor voltage will be 63.21% of its final voltage.

Solution

Maximum voltage E = 12 volt

Resistance R = 21 ohm

Capacitance C = 2995 x10 ^-6 F

In RC circuit , charge on capacitor at time t is

q = Q [1- e ^-t/RC ]

qC = QC [1- e ^-t/RC ]

V = Vo [1- e ^-t/RC ]

Given V = 63.21 % of Vo

             = 0.6321 Vo

Substitute values you get 0.6321Vo = Vo[1- e ^-t/RC ]

    0.6321 = [1- e ^-t/RC ]

    e ^-t/RC = 1-0.6321

            = 0.3679

     -t/RC = ln(0.3679)

             = -0.9999

          t = 0.9999 RC

            = 0.9999 (21)(2995x10 ^-6 )

            = 62.89 x10 ^-3 s

            = 62.89 ms