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 resistor.

Step-by-step solution

At t = 0 , the capacitor is uncharged, so the potential difference across it is zero, i.e., V_C = 0 . According to Kirchhoff's voltage law for the series RC circuit, E = V_R + V_C . Substituting V_C = 0 at t = 0 , we get V_R = E . As time progresses, the capacitor charges up, increasing V_C and decreasing V_R since V_R = E e^ -t/RC . Thus, the maximum potential difference across the resistor occurs at t = 0 and is equal to E .