---
title: "A circuit contains three vertical branches connected in parallel by ideal conducting wires at top and bottom junctions, as shown. The left branch contains a battery of emf \\(\\mathcal{E}_1 = 12\\text{ V}\\) oriented with its positive terminal toward the top junction, connected in series with a resistor \\(R_1 = 3.0\\ \\Omega\\). The middle branch contains a resistor \\(R_2 = 6.0\\ \\Omega\\). The right branch contains a battery of emf \\(\\mathcal{E}_2 = 3.0\\text{ V}\\) oriented with its positive terminal toward the top junction, connected in series with a resistor \\(R_3 = 3.0\\ \\Omega\\). What are the magnitude and direction of the electric current passing through resistor \\(R_2\\)?"
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url: "https://nerd-notes.com/ubq/118376/"
date_modified: "2026-08-04T08:09:46+00:00"
---

# A circuit contains three vertical branches connected in parallel by ideal conducting wires at top and bottom junctions, as shown. The left branch contains a battery of emf \(\mathcal{E}_1 = 12\text{ V}\) oriented with its positive terminal toward the top junction, connected in series with a resistor \(R_1 = 3.0\ \Omega\). The middle branch contains a resistor \(R_2 = 6.0\ \Omega\). The right branch contains a battery of emf \(\mathcal{E}_2 = 3.0\text{ V}\) oriented with its positive terminal toward the top junction, connected in series with a resistor \(R_3 = 3.0\ \Omega\). What are the magnitude and direction of the electric current passing through resistor \(R_2\)?

A circuit contains three vertical branches connected in parallel by ideal conducting wires at top and bottom junctions, as shown. The left branch contains a battery of emf \(\mathcal{E}_1 = 12\text{ V}\) oriented with its positive terminal toward the top junction, connected in series with a resistor \(R_1 = 3.0\ \Omega\). The middle branch contains a resistor \(R_2 = 6.0\ \Omega\). The right branch contains a battery of emf \(\mathcal{E}_2 = 3.0\text{ V}\) oriented with its positive terminal toward the top junction, connected in series with a resistor \(R_3 = 3.0\ \Omega\). What are the magnitude and direction of the electric current passing through resistor \(R_2\)?

![A schematic diagram of a two-loop direct current circuit. The circuit consists of three vertical parallel branches connected at top and bottom horizontal wires. The left branch contains an ideal battery labeled \mathcal{E}_1 = 12\text{ V} with its longer positive terminal bar on top, connected in series above a resistor labeled R_1 = 3.0\ \Omega. The middle branch contains a single resistor labeled R_2 = 6.0\ \Omega oriented vertically. The right branch contains an ideal battery labeled \mathcal{E}_2 = 3.0\text{ V} with its longer positive terminal bar on top, connected in series above a resistor labeled R_3 = 3.0\ \Omega. Black lines represent ideal connecting wires joining all three branches at a top junction and a bottom junction. No other labels, arrows, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1785830986-v7vnwh.jpg)

- **A.** \(1.0\text{ A}\), upward
- **B.** \(1.0\text{ A}\), downward
- **C.** \(2.0\text{ A}\), downward
- **D.** \(2.0\text{ A}\), upward

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118376/*