---
title: "The circuit shown consists of an ideal battery of electromotive force \\(\\mathcal{E}\\), three identical resistors each of resistance \\(R\\), and an open switch \\(S\\). Resistor \\(R_1\\) is connected in series with the parallel combination of resistor \\(R_2\\) and the branch containing switch \\(S\\) and resistor \\(R_3\\). When switch \\(S\\) is closed, what is the current passing through resistor \\(R_2\\)?"
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url: "https://nerd-notes.com/ubq/121553/"
date_modified: "2026-08-23T05:23:59+00:00"
---

# The circuit shown consists of an ideal battery of electromotive force \(\mathcal{E}\), three identical resistors each of resistance \(R\), and an open switch \(S\). Resistor \(R_1\) is connected in series with the parallel combination of resistor \(R_2\) and the branch containing switch \(S\) and resistor \(R_3\). When switch \(S\) is closed, what is the current passing through resistor \(R_2\)?

The circuit shown consists of an ideal battery of electromotive force \(\mathcal{E}\), three identical resistors each of resistance \(R\), and an open switch \(S\). Resistor \(R_1\) is connected in series with the parallel combination of resistor \(R_2\) and the branch containing switch \(S\) and resistor \(R_3\). When switch \(S\) is closed, what is the current passing through resistor \(R_2\)?

![A schematic diagram of a direct current circuit. On the left vertical wire is an ideal battery labeled \(\mathcal{E}\), with its longer positive plate on top and shorter negative plate on the bottom. The top wire extends horizontally to the right from the battery's positive terminal, containing a resistor labeled \(R_1\). To the right of \(R_1\), the wire splits at a junction into two parallel vertical branches that rejoin at a lower junction before returning horizontally along the bottom wire to the negative terminal of the battery. The left parallel branch contains a resistor labeled \(R_2\). The right parallel branch contains an open switch labeled \(S\) in series with a resistor labeled \(R_3\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462639-BxrbDq.jpg)

- **A.** \(\dfrac{\mathcal{E}}{6R}\)
- **B.** \(\dfrac{\mathcal{E}}{4R}\)
- **C.** \(\dfrac{\mathcal{E}}{3R}\)
- **D.** \(\dfrac{2\mathcal{E}}{3R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121553/*