Final answer:
The potential difference across the terminals while charging is 9 V. The thermal energy dissipation rate is 180 W, and the rate of electric energy conversion to chemical energy is 540 W. When discharging to a motor, the potential difference remains 12 V.
Step-by-step explanation:
The question is about the electrical characteristics of a car battery being charged. When a current is passed through a battery to charge it, the potential difference across the terminals can be different from the battery's electromotive force (emf) due to the internal resistance of the battery.
For part (a), the potential difference (V) across the terminals of the battery is calculated using Ohm's Law for the internal circuit, which is V = emf - I*r, where I is the current and r is the internal resistance. Substituting in the values:
V = 12 V - (60 A * 0.050 Ω) = 12 V - 3 V = 9 V.
For part (b), the rate at which thermal energy is being dissipated in the battery is found using the power formula P = I^2*r. The thermal power dissipated is:
P = (60 A)^2 * 0.050 Ω = 3600 A^2 * 0.050 Ω = 180 W.
For part (c), the rate at which electric energy is being converted to chemical energy (charging power) in the battery is the total power minus the power lost as heat:
P_total = emf * I = 12 V * 60 A = 720 W
Charging Power = P_total - P_thermal = 720 W - 180 W = 540 W.
For part (d), when the battery is used to supply 60 A to the starter motor, the terminal voltage is the same as the emf since the battery is assumed to be ideal and supplying power, so V_terminal = emf = 12 V. The rate of thermal energy dissipation will be the same 180 W as when charging.