---
title: "A battery having an electromotive force \\(\\varepsilon\\) and an internal resistance \\(r > 0\\) is connected to three identical resistors, each of resistance \\(R\\), which are arranged in series as shown. Let \\(\\Delta V_{\\text{term}}\\) represent the magnitude of the terminal voltage across the battery, and let \\(\\Delta V_1\\), \\(\\Delta V_2\\), and \\(\\Delta V_3\\) represent the magnitudes of the potential differences across each of the three resistors, respectively. Which of the following correctly ranks the electromotive force and the potential differences?"
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url: "https://nerd-notes.com/ubq/121545/"
date_modified: "2026-08-23T05:23:56+00:00"
---

# A battery having an electromotive force \(\varepsilon\) and an internal resistance \(r > 0\) is connected to three identical resistors, each of resistance \(R\), which are arranged in series as shown. Let \(\Delta V_{\text{term}}\) represent the magnitude of the terminal voltage across the battery, and let \(\Delta V_1\), \(\Delta V_2\), and \(\Delta V_3\) represent the magnitudes of the potential differences across each of the three resistors, respectively. Which of the following correctly ranks the electromotive force and the potential differences?

A battery having an electromotive force \(\varepsilon\) and an internal resistance \(r > 0\) is connected to three identical resistors, each of resistance \(R\), which are arranged in series as shown. Let \(\Delta V_{\text{term}}\) represent the magnitude of the terminal voltage across the battery, and let \(\Delta V_1\), \(\Delta V_2\), and \(\Delta V_3\) represent the magnitudes of the potential differences across each of the three resistors, respectively. Which of the following correctly ranks the electromotive force and the potential differences?

![A single-loop rectangular circuit diagram with four labeled components. Along the top horizontal segment, a dashed rectangle encloses a DC voltage source labeled \(\varepsilon\) on the left and a small resistor labeled \(r\) on the right; two connection points on either side of the dashed box are labeled with terminals for \(\Delta V_{\text{term}}\). Along the bottom horizontal segment, three identical zigzag resistor symbols labeled \(R\), \(R\), and \(R\) are connected in series from left to right. Solid black lines form the closed rectangular loop connecting the top and bottom branches on the left and right vertical segments. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462635-qLoP0A.jpg)

- **A.** \(\varepsilon > \Delta V_{\text{term}} > \Delta V_1 = \Delta V_2 = \Delta V_3\)
- **B.** \(\varepsilon = \Delta V_{\text{term}} > \Delta V_1 = \Delta V_2 = \Delta V_3\)
- **C.** \(\Delta V_{\text{term}} > \varepsilon > \Delta V_1 = \Delta V_2 = \Delta V_3\)
- **D.** \(\varepsilon > \Delta V_{\text{term}} > \Delta V_1 > \Delta V_2 > \Delta V_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121545/*