[UPSC CSE 2020] Electrostatics and Magnetostatics (Q70, 15M)

A 10\Omega resistor is connected in series with a capacitor of 1.0\mu\mathrm{F} and a battery with emf 12.0 V. Before the switch is closed at time t=0, the capacitor is uncharged. Calculate the following:

(i) The time constant.

(ii) What fraction of the final charge is on the plates at the time t=46 seconds?

(iii) What fraction of the initial current remains at the time t=46 seconds? Consider that the internal resistance of the battery is zero and neglect the resistance of all the connecting wires.