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AP Physics C: E&M
11.8 Resistor Capacitor (RC) Circuits
11.6 Kirchhoff’s Loop Rule
11.5 Compound Direct Current Circuits
AdvancedMCQProportional AnalysisConceptual15.8k
A rectangular circuit diagram oriented horizontally. On the left vertical segment, an ideal battery symbol is drawn with a long line on top and a short line on bottom, labeled \(\mathcal{E}\), in series with a small zig-zag resistor labeled \(r\) immediately above it; a dashed box encloses both elements to represent the non-ideal battery. The top and bottom wires extend horizontally to the right. A first vertical branch connects the top and bottom wires, containing a zig-zag resistor labeled \(R_1\). Further to the right, the top wire continues to a second vertical branch. This second branch contains a zig-zag resistor labeled \(R_2\) on its upper portion, which then splits into two parallel vertical sub-paths: the left sub-path contains a zig-zag resistor with an arrow drawn diagonally across it labeled \(R\), and the right sub-path contains two equal-length parallel horizontal plates labeled \(C\). These two sub-paths rejoin before connecting to the bottom horizontal wire. No other labels, lines, text, or axes appear.
Circuit schematic with a non-ideal battery, two parallel branches, and an adjustable resistor.
A circuit consists of a battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) connected to two parallel branches: one branch contains a fixed resistor of resistance \(R_1\), and the second branch contains a fixed resistor of resistance \(R_2\) in series with a parallel combination of a capacitor of capacitance \(C\) and a variable resistor of resistance \(R\).

The circuit is allowed to reach steady state.

Which of the following correctly describes the behavior of the current \(I_{\text{bat}}\) through the battery and the current \(I_1\) through resistor \(R_1\) in the limit as \(R \to \infty\)?

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