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. Identify whether work is done by the battery or on the battery, and determine its magnitude.

Step-by-step solution

Initial charge on the capacitor, Q_i = CV_i = 100 10⁻⁶ 24 = 2400 C Final charge on the capacitor, Q_f = CV_f = 100 10⁻⁶ 12 = 1200 C Change in charge on the positive plate of the capacitor, Q = Q_f - Q_i = 1200 C - 2400 C = -1200 C Since the final charge is less than the initial charge, a positive charge of 1200 C flows from the positive plate of the capacitor into the positive terminal of the 12 V battery. When positive charge enters the positive terminal of a battery, work is done on the battery. Magnitude of work