A car battery that is initially fully charged has an emf of 12.0 V and an internal resistance of 0.30 Ω. After prolonged use, its emf falls to 11.0 V and its internal resistance rises to 0.60 Ω. The battery supplies a headlamp rated at 24 Ω.
(i) For the fully charged battery, calculate the current drawn by the lamp and the power delivered to the lamp.
(ii) For the discharged battery, calculate the current and lamp power.
(iii) For each of the two cases, determine the rate at which energy is dissipated as heat inside the battery.
(iv) Compare the ratios of useful lamp power to total power supplied by the battery in the two cases and comment briefly on the efficiency change as the battery discharges.