Continuing from the previous scenario, what is the electric potential energy gained by the charges that passed through the battery?

• A. 159.0 J
• B. 359.1 J
• C. 718.2 J
• D. 71.9 J

Answer: (B)

Charges gain electric potential energy when a battery pushes them from the negative to the positive terminal, doing work on the charges as they move through the battery. The amount of energy transferred to the charges is the product of how much charge passes through the battery and the potential difference they experience. If the battery has emf ε and a total charge Q moves through it, the energy gained is εQ. If you know the current I and the time t that the charges pass, Q = It, so the energy is εIt. This is why the value 359.1 J is the correct amount: it matches the emf times the total charge moved through the battery in the given scenario. The energy is positive because the battery increases the charges’ potential energy.