---
title: "A circuit consists of an ideal battery with electromotive force \\(\\varepsilon\\) connected in series with a resistor of resistance \\(R\\). This series combination is connected across a multi-way junction that divides current among three parallel branches with resistances \\(R\\), \\(2R\\), and \\(3R\\), as shown in the diagram. Which of the following expressions represents the electric current \\(I_2\\) flowing through the branch with resistance \\(2R\\)?"
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url: "https://nerd-notes.com/ubq/120422/"
date_modified: "2026-08-23T04:34:33+00:00"
---

# A circuit consists of an ideal battery with electromotive force \(\varepsilon\) connected in series with a resistor of resistance \(R\). This series combination is connected across a multi-way junction that divides current among three parallel branches with resistances \(R\), \(2R\), and \(3R\), as shown in the diagram. Which of the following expressions represents the electric current \(I_2\) flowing through the branch with resistance \(2R\)?

A circuit consists of an ideal battery with electromotive force \(\varepsilon\) connected in series with a resistor of resistance \(R\). This series combination is connected across a multi-way junction that divides current among three parallel branches with resistances \(R\), \(2R\), and \(3R\), as shown in the diagram. Which of the following expressions represents the electric current \(I_2\) flowing through the branch with resistance \(2R\)?

![A rectangular schematic circuit diagram. On the left vertical wire is an ideal battery of emf \varepsilon with the longer horizontal positive plate on top and the shorter negative plate on bottom. The top wire extends horizontally to the right through a single resistor labeled R. Past this resistor, the wire reaches a junction that splits vertically into three parallel horizontal branches. The top branch contains a resistor labeled R, the middle branch contains a resistor labeled 2R, and the bottom branch contains a resistor labeled 3R. The three branches reconnect at a common junction on the right. A single return wire extends from this junction down and to the left, forming a closed loop with the negative terminal of the battery. No other labels, lines, meters, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459673-lrvDNf.jpg)

- **A.** \(\dfrac{11\varepsilon}{51R}\)
- **B.** \(\dfrac{2\varepsilon}{17R}\)
- **C.** \(\dfrac{6\varepsilon}{17R}\)
- **D.** \(\dfrac{3\varepsilon}{17R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120422/*