Answer 1

Given:-

Initial charge given to the capacitor = Q

When the capacitor is connected to a battery, it will charge through the battery. The initial charge will also decay.

The growth of charge across the capacitor due to the battery of emf E,

\[q = CE\left( 1 - e^{- \frac{t}{RC}} \right)\]

The decay of charge through the capacitor,

\[q' = Q e^{- \frac{t}{RC}}\]

The net charge on the capacitor at any time t,

\[q_{net} = q + q'\]

\[ = CE\left( 1 - e^{- \frac{t}{RC}} \right) + Q e^{- \frac{t}{RC}}\]