At t = 0 , a capacitance C , a resistance R , and an emf E are connected in series. Determine the maximum value of the potential difference across the capacitor.

Step-by-step solution

The charge on the capacitor in a series RC circuit as a function of time is given by: q(t) = C E (1 - e^ -t/RC ) The potential difference across the capacitor at any time t is: V_C(t) = q(t) C = E (1 - e^ -t/RC ) The maximum potential difference is attained at steady state, which corresponds to t . At t , e^ -t/RC 0 . Therefore, the maximum potential difference across the capacitor is: (V_C)_ max = E (1 - 0) = E Alternatively, at steady state, the capacitor acts as an open circuit. The current in the circuit become