Question

The plates of a capacitor of capacitance 10 μF, charged to 60 μC, are joined together by a wire of resistance 10 Ω at t = 0. Find the charge on the capacitor in the circuit at (a) t = 0 (b) t = 30 μs (c) t = 120 μs and (d) t = 1.0 ms.

Answer 1

In the circuit, the charge on the capacitor in the circuit is 60 μC, 44 μC, 18 μC and 0.003 μC.

Explanation:

It is given in the equation that

The capacitor’s capacitance, C = 10 μF

Capacitor’s initial charge, Q = 60 μC

Circuit’s resistance, R = 10 Ω

(a)On the capacitor, the decay of charge,

Q = Qe - tRC

At t = 0,

q = Q = 60 μC

(b) At t = 30 μs,

q = Q.e – tRC ⇒ q = 60.e - 0.3

⇒q = 44 μC

(c) At t = 120 μs,

q = Q.e – tRC ⇒q = 60.e-1.2

⇒q=18 μC

(d) At t = 1 ms,

q = Q.e-tRC ⇒q = 60.e – 10

⇒q = 0.003 μC