A capacitor with a capacitance of 100 F is charged to a potential difference of 24 V . After disconnecting the charging battery, the capacitor is connected to a different battery of emf 12 V such that the positive plate of the capacitor is attached to the positive terminal of the battery. Evaluate the heat developed during the flow of charge following the reconnection.

Step-by-step solution

Initial charge on the capacitor, Q_i = C V_i = 100 10⁻⁶ 24 = 2400 C Initial energy stored in the capacitor, U_i = 1 2 C V_i^2 = 1 2 100 10⁻⁶ (24)^2 = 28.8 mJ When connected to the 12 V battery with the positive plate to the positive terminal, the final charge on the capacitor is Q_f = C V_f = 100 10⁻⁶ 12 = 1200 C Final energy stored in the capacitor, U_f = 1 2 C V_f^2 = 1 2 100 10⁻⁶ (12)^2 = 7.2 mJ Charge flown through the battery is Q = Q_f - Q_i = 1200 C - 2400 C = -1200 C Work done by the battery, W = Q V_f = -1