Question

A series RC circuit with C = 44 μF and R = 6.4 Ω has a 24 V source in it. With the capacitor initially uncharged, an open switch in the circuit is closed.

a) After the switch has been closed for t = 3 τ, what is the charge on the capacitor?

Answer 1

Here we have given that,

A series RC circuit

C = 44 μF

R = 6.4 Ω

Voltage =24 V

capacitor initially uncharged

Maximum charge over the capacitor Qo is given as,

Qo = CV = 1.056 ×10^-3 C

Now time constant for this circuit will be given as,

T = RC = 2.816 ×10^-4

Now when the switch is closed then the expression for the charge over the capacitor as a function of time is given as,

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

a) After the switch has been closed for t = 3 τ, the charge on the capacitor is given as,

Q = 1.056(1- e^-(3T/T)) = 1.0034 ×10^-3 C = 1.0034 mC

Hence the charge on the capacitor whej switch is closed for t = 3T will be

Q (t=3T) = 1.0034 × 10^(-3) C

Or Q = 1.0034 mC