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AP Physics C: E&M
11.6 Kirchhoff’s Loop Rule
11.4 Electric Power
IntermediateMCQMathematical14.7k
Circuit loop containing two opposing batteries and resistance.
Circuit loop containing two opposing batteries and resistance.
Two batteries with emfs \(3\mathcal{E}_0\) and \(\mathcal{E}_0\) are connected in a single closed loop with an external resistor, as shown. The total resistance of the circuit, including internal resistances of both batteries and the external resistor, is \(R\). Battery 1 (emf \(3\mathcal{E}_0\)) forces current through Battery 2 (emf \(\mathcal{E}_0\)) in the reverse direction, charging it.

RowRate Chemical Energy Stored in Battery 2Total Rate Thermal Energy Dissipated
A\(\dfrac{\mathcal{E}_0^2}{R}\)\(\dfrac{4\mathcal{E}_0^2}{R}\)
B\(\dfrac{2\mathcal{E}_0^2}{R}\)\(\dfrac{4\mathcal{E}_0^2}{R}\)
C\(\dfrac{2\mathcal{E}_0^2}{R}\)\(\dfrac{2\mathcal{E}_0^2}{R}\)
D\(\dfrac{6\mathcal{E}_0^2}{R}\)\(\dfrac{4\mathcal{E}_0^2}{R}\)

Which row correctly identifies the rate at which chemical energy is stored in Battery 2 and the total rate at which thermal energy is dissipated in the circuit?

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