---
title: "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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url: "https://nerd-notes.com/ubq/124914/"
date_modified: "2026-09-28T14:11:56+00:00"
---

# 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 \(R \to \infty\)?

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 \(R \to \infty\)?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604716-4iSKuk.jpg)

- **A.** \(I_{\text{bat}}\) decreases toward \(0\), and \(I_1\) decreases toward \(0\).
- **B.** \(I_{\text{bat}}\) decreases toward \(\dfrac{\mathcal{E}}{r + R_1}\), and \(I_1\) remains constant at \(\dfrac{\mathcal{E}}{R_1}\).
- **C.** \(I_{\text{bat}}\) decreases toward \(\dfrac{\mathcal{E}}{r + R_1}\), and \(I_1\) increases toward \(\dfrac{\mathcal{E}}{r + R_1}\).
- **D.** \(I_{\text{bat}}\) decreases toward \(\dfrac{\mathcal{E}}{r + R_1}\), and \(I_1\) decreases toward \(\dfrac{\mathcal{E}}{r + R_1}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124914/*