---
title: "A circuit contains two loops connected by a top junction and a bottom junction, as shown in the schematic. The left branch contains an ideal battery of emf \\(\\mathcal{E}_1 = 16\\text{ V}\\) in series with resistor \\(R_1 = 4\\ \\Omega\\). The middle branch contains resistor \\(R_2 = 4\\ \\Omega\\). The right branch contains resistor \\(R_3 = 2\\ \\Omega\\) in series with an ideal battery of emf \\(\\mathcal{E}_2 = 4\\text{ V}\\) directed upward. What is the potential difference across resistor \\(R_3\\), and what is the direction of the current through the right-hand branch?"
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url: "https://nerd-notes.com/ubq/117428/"
date_modified: "2026-08-04T06:52:06+00:00"
---

# A circuit contains two loops connected by a top junction and a bottom junction, as shown in the schematic. The left branch contains an ideal battery of emf \(\mathcal{E}_1 = 16\text{ V}\) in series with resistor \(R_1 = 4\ \Omega\). The middle branch contains resistor \(R_2 = 4\ \Omega\). The right branch contains resistor \(R_3 = 2\ \Omega\) in series with an ideal battery of emf \(\mathcal{E}_2 = 4\text{ V}\) directed upward. What is the potential difference across resistor \(R_3\), and what is the direction of the current through the right-hand branch?

A circuit contains two loops connected by a top junction and a bottom junction, as shown in the schematic. The left branch contains an ideal battery of emf \(\mathcal{E}_1 = 16\text{ V}\) in series with resistor \(R_1 = 4\ \Omega\). The middle branch contains resistor \(R_2 = 4\ \Omega\). The right branch contains resistor \(R_3 = 2\ \Omega\) in series with an ideal battery of emf \(\mathcal{E}_2 = 4\text{ V}\) directed upward. What is the potential difference across resistor \(R_3\), and what is the direction of the current through the right-hand branch?

![A schematic diagram of a two-loop direct current circuit on a plain white background. The circuit features three vertical parallel branches connected at top and bottom horizontal wires. The left branch contains an ideal DC battery labeled \(\mathcal{E}_1 = 16\text{ V}\) with its longer positive terminal on top, connected in series below a resistor labeled \(R_1 = 4\ \Omega\). The middle branch contains a single vertical resistor labeled \(R_2 = 4\ \Omega\). The right branch contains a resistor labeled \(R_3 = 2\ \Omega\) connected in series above an ideal DC battery labeled \(\mathcal{E}_2 = 4\text{ V}\), which has its longer positive terminal on top. Black dots mark the top and bottom junction nodes. No other text, lines, arrows, or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1785826326-aXyUwh.jpg)

- **A.** The potential difference is \(4\text{ V}\), and the current flows upward.
- **B.** The potential difference is \(2\text{ V}\), and the current flows downward.
- **C.** The potential difference is \(2\text{ V}\), and the current flows upward.
- **D.** The potential difference is \(6\text{ V}\), and the current flows downward.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117428/*