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AP Physics 2
11.7 Kirchhoff’s Junction Rule
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current (DC) Circuits
11.3 Resistance, Resistivity, and Ohm’s Law
AdvancedMCQMathematicalConceptual18.6k
Parallel battery circuit with a load resistor.
Parallel battery circuit with a load resistor.
Two nonideal batteries, Battery 1 with emf \(\mathcal{E}_1 = 2\mathcal{E}_0\) and internal resistance \(r_1 = r\), and Battery 2 with emf \(\mathcal{E}_2 = \mathcal{E}_0\) and internal resistance \(r_2 = r\), are connected in parallel with their positive terminals connected to the same upper conductor wire. A load resistor of resistance \(R = 2r\) is connected in parallel across the two batteries. Let \(V_{T1}\) and \(V_{T2}\) represent the terminal voltages of Battery 1 and Battery 2, respectively, and let \(I_1\), \(I_2\), and \(I_3\) represent the magnitudes of the currents through Battery 1, Battery 2, and resistor \(R\), respectively.

OptionTerminal Voltage \(V_{T1}\)Terminal Voltage \(V_{T2}\)Current Magnitudes
(A)\(V_{T1} < \mathcal{E}_1\)\(V_{T2} < \mathcal{E}_2\)\(I_1 > I_2 > I_3\)
(B)\(V_{T1} > \mathcal{E}_1\)\(V_{T2} < \mathcal{E}_2\)\(I_1 > I_3 > I_2\)
(C)\(V_{T1} < \mathcal{E}_1\)\(V_{T2} < \mathcal{E}_2\)\(I_1 > I_3 > I_2\)
(D)\(V_{T1} < \mathcal{E}_1\)\(V_{T2} > \mathcal{E}_2\)\(I_1 > I_3 > I_2\)

Which row in the table correctly compares the terminal voltages \(V_{T1}\) and \(V_{T2}\) to their respective emfs and correctly ranks the magnitudes of the branch currents \(I_1\), \(I_2\), and \(I_3\)?

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