Question

In "RC Circuit Experiment", you are using 8,768 micro Farad capacitor, 212 Ohm resistor and 10 Volt battery. Before starting the experiment, you noticed that the capacitor contains some charge which is equivalent to 38 % of the supply voltage. If you want to start experiment in this condition, how long it will take for capacitor to attain 57 % of the supply voltage?

Answer 1

Given

C = 8768*10^-6 F

R = 212 ohm

V = 10 V

initial charge is Q0 = 38% of supply voltage

we know Q = C*V

Q = 8768*10^-6*10 = 8768*10^-5 C

38% of Q = Q0 = 8768*10^-5*38/100 C = 0.0333184 C

and the charging of a capacitor in RC circuit is  

Q(t) = Q0 (1-e^(-t/T))

where T is time constant , T = R*C = 212* 8768*10^-6 s = 1.858816 s

and the time taken for the chrge become 57% of supply voltage is

first the 57% of supply voltage is Q(t) = 8768*10^-5*57/100 C = 0.0499776 C

0.0499776 = 0.0333184(1-e^(-t/(1.858816)))

t = 1.288 s