Consider the circuit shown in the figure. The switch S is open for a long time and subsequently closed. Determine the charge that flows through the battery when the switch S is closed.

Step-by-step solution

When the switch S is open, the two capacitors are connected in series across the battery. The equivalent capacitance is C_ eq = C C C + C = C 2 . The initial charge supplied by the battery is Q_i = C_ eq E = C E 2 . When the switch S is closed, the right capacitor is short-circuited and the left capacitor is connected directly across the battery. The new equivalent capacitance is C_ eq ' = C . The final charge supplied by the battery is Q_f = C E . The charge that flows through the battery after closing the switch