Question

Is work done by a battery always equal to the thermal energy developed in electrical circuit? What happens if a capacitor is connected in the circuit?

Answer 1

No, the work done by a battery is not always equal to the thermal energy developed in the electrical circuit. In case of a non-ideal battery, the work done by the battery is the sum of the thermal energy developed in the electric circuit and the thermal energy developed in the internal resistance of the battery. In case of a capacitor, the work done by the battery is equal to C V². An amount of energy equal to $\frac{1}{2}$ C V² is stored in it when it is fully charged, which is a form of electrical energy and not a form of thermal energy. During the charging of the capacitor, $\frac{1}{2}$ C V² of energy is lost in the form of heat and electromagnetic radiation.