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title: "A multi-loop circuit consists of two ideal batteries with electromotive forces \\(\\varepsilon_1\\) and \\(\\varepsilon_2\\), and three resistors with resistances \\(R_1\\), \\(R_2\\), and \\(R_3\\), as shown in the schematic diagram. The currents in the three branches are defined as \\(I_1\\), \\(I_2\\), and \\(I_3\\), with directions indicated by the arrows. Which of the following equations correctly expresses Kirchhoff’s loop rule for the outer loop when traversed in a clockwise direction?"
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url: "https://nerd-notes.com/ubq/116081/"
date_modified: "2026-08-03T10:14:56+00:00"
---

# A multi-loop circuit consists of two ideal batteries with electromotive forces \(\varepsilon_1\) and \(\varepsilon_2\), and three resistors with resistances \(R_1\), \(R_2\), and \(R_3\), as shown in the schematic diagram. The currents in the three branches are defined as \(I_1\), \(I_2\), and \(I_3\), with directions indicated by the arrows. Which of the following equations correctly expresses Kirchhoff’s loop rule for the outer loop when traversed in a clockwise direction?

A multi-loop circuit consists of two ideal batteries with electromotive forces \(\varepsilon_1\) and \(\varepsilon_2\), and three resistors with resistances \(R_1\), \(R_2\), and \(R_3\), as shown in the schematic diagram. The currents in the three branches are defined as \(I_1\), \(I_2\), and \(I_3\), with directions indicated by the arrows. Which of the following equations correctly expresses Kirchhoff's loop rule for the outer loop when traversed in a clockwise direction?

![A circuit schematic displaying a rectangular multi-loop layout with two adjacent loops sharing a central vertical wire. The outer perimeter forms a horizontal rectangle. The left vertical branch contains a battery labeled \(\varepsilon_1\) with its longer positive plate on top and shorter negative plate below, and a resistor labeled \(R_1\) above the battery. An upward arrow beside this branch is labeled \(I_1\). The central vertical branch contains a resistor labeled \(R_2\), with a downward arrow beside it labeled \(I_2\). The right vertical branch contains a resistor labeled \(R_3\) on top and a battery labeled \(\varepsilon_2\) below it with its longer positive plate on top and shorter negative plate below. An upward arrow beside the right branch is labeled \(I_3\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785752095-bFpLrj.jpg)

- **A.** \(\varepsilon_1 - I_1 R_1 - I_3 R_3 - \varepsilon_2 = 0\)
- **B.** \(\varepsilon_1 - I_1 R_1 + I_3 R_3 - \varepsilon_2 = 0\)
- **C.** \(\varepsilon_1 - I_1 R_1 - I_2 R_2 - \varepsilon_2 = 0\)
- **D.** \(\varepsilon_1 + I_1 R_1 - I_3 R_3 - \varepsilon_2 = 0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116081/*