A capacitor of capacity 1 µF is connected in closed series circuit with a resistance of 107 ohms, an open key and a cell of 2V with negligible internal resistance:
(i) When the key is switched on at time t=0, find;
(a) The time constant for the circuit.
(b) The charge on the capacitor at steady state.
(c) Time taken to deposit charge equaling half that at steady state.
(ii) If after fully charging the capacitor, the cell is shorted by zero resistance at time t=0, find the charge on the capacitor at t = 50s.