Question

A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an ideal battery of emf $\epsilon$ through a resistance R. Find the charge on the capacitor at time t.

Answer 1

The capacitor is given a charge Q. It will discharge and the capacitor will be charged up when connected with battery Net charge at time.

$t=Q{e}^{\frac{-t}{RC}}+q\{1-e^{-\frac{t}{RC}}\}$

$t=Q{e}^{-\frac{t}{RC}}+Cϵ\{1-e^{-\frac{t}{RC}}\}$