QPages 165-170: Q46: HC Verma: Concepts of Physics - Volume 2 Capacitors Pages 165-170: Q46 Solution: Consider the situation shown in the figure. The switch S is…
Students often assume the battery remains connected to the circuit after the switch is closed, leading to an overestimation of the charge that flows through it. In this problem the battery only charged the 2 F capacitor initially; when the switch closes the 3 F capacitor is connected to the 2 F, but the battery is effectively disconnected. The correct approach is to apply conservation of charge to the two capacitors alone, find the final common voltage (V_f= rac{C_1V_0}{C_1+C_2}), and then compute the charge that actually flows between the capacitors. The battery does not supply additional charge, so the charge flown through the battery is zero, and the work done by the battery is zero. This careful bookkeeping prevents the common mistake of using (Q_{ ext{battery}}=C_2V_f) or (W=Q_{ ext{battery}}V_{ ext{battery}}) incorrectly.