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(C) When a capacitor is connected to a $DC$ source through a resistor,the charge $q$ on the capacitor at any time $t$ is given by $q(t) = Q_0(1 - e^{-

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Current flows in the circuit and is varying with time

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(C) When a capacitor is connected to a $DC$ source through a resistor,the charge $q$ on the capacitor at any time $t$ is given by $q(t) = Q_0(1 - e^{-t/RC})$ during charging and $q(t) = Q_0 e^{-t/RC}$ during discharging.The current $I$ in the circuit is the rate of change of charge,$I = dq/dt$.For charging: $I = \frac{d}{dt} [Q_0(1 - e^{-t/RC})] = \frac{Q_0}{RC} e^{-t/RC} = I_0 e^{-t/RC}$.For discharging: $I = \frac{d}{dt} [Q_0 e^{-t/RC}] = -\frac{Q_0}{RC} e^{-t/RC} = -I_0 e^{-t/RC}$.In both cases,the magnitude of the current $I$ decreases exponentially with time $t$. Therefore,the current flows in the circuit and varies with time.

During charging and discharging of a capacitor:

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