---
title: "A circuit consists of three vertical parallel branches connected at the top by a single horizontal conductor and at the bottom by another horizontal conductor. The left branch contains an ideal battery of emf \\(\\mathcal{E}_1 = 2\\mathcal{E}_0\\) in series with a resistor of resistance \\(R\\), with the battery’s positive terminal pointing toward the top conductor. The middle branch contains a single resistor of resistance \\(2R\\). The right branch contains an ideal battery of emf \\(\\mathcal{E}_2 = \\mathcal{E}_0\\) in series with a resistor of resistance \\(R\\), with this battery’s positive terminal also pointing toward the top conductor. What is the magnitude and direction of the electric current through the rightmost branch?"
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url: "https://nerd-notes.com/ubq/118467/"
date_modified: "2026-08-04T08:10:26+00:00"
---

# A circuit consists of three vertical parallel branches connected at the top by a single horizontal conductor and at the bottom by another horizontal conductor. The left branch contains an ideal battery of emf \(\mathcal{E}_1 = 2\mathcal{E}_0\) in series with a resistor of resistance \(R\), with the battery’s positive terminal pointing toward the top conductor. The middle branch contains a single resistor of resistance \(2R\). The right branch contains an ideal battery of emf \(\mathcal{E}_2 = \mathcal{E}_0\) in series with a resistor of resistance \(R\), with this battery’s positive terminal also pointing toward the top conductor. What is the magnitude and direction of the electric current through the rightmost branch?

A circuit consists of three vertical parallel branches connected at the top by a single horizontal conductor and at the bottom by another horizontal conductor. The left branch contains an ideal battery of emf \(\mathcal{E}_1 = 2\mathcal{E}_0\) in series with a resistor of resistance \(R\), with the battery's positive terminal pointing toward the top conductor. The middle branch contains a single resistor of resistance \(2R\). The right branch contains an ideal battery of emf \(\mathcal{E}_2 = \mathcal{E}_0\) in series with a resistor of resistance \(R\), with this battery's positive terminal also pointing toward the top conductor. What is the magnitude and direction of the electric current through the rightmost branch?

![A rectangular circuit diagram featuring three parallel vertical branches connected by a top horizontal wire and a bottom horizontal wire. The left vertical branch contains a resistor labeled R in series with an ideal battery labeled \mathcal{E}_1 = 2\mathcal{E}_0, where the battery is drawn with its long parallel line above its short parallel line. The middle vertical branch contains a single resistor labeled 2R. The right vertical branch contains a resistor labeled R in series with an ideal battery labeled \mathcal{E}_2 = \mathcal{E}_0, where the battery is drawn with its long parallel line above its short parallel line. Connection nodes are shown at the junctions where the middle vertical branch meets the top and bottom horizontal wires. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/circuit-diagram-1-1785831025-hYIeng.jpg)

- **A.** \(\dfrac{\mathcal{E}_0}{3R}\) directed toward the top conductor
- **B.** \(\dfrac{\mathcal{E}_0}{5R}\) directed toward the bottom conductor
- **C.** \(\dfrac{\mathcal{E}_0}{5R}\) directed toward the top conductor
- **D.** \(\dfrac{3\mathcal{E}_0}{5R}\) directed toward the bottom conductor

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118467/*