---
title: "A real battery with electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) is connected to an ideal high-resistance digital voltmeter. When only the voltmeter is connected across the battery terminals, the reading is \\(12\\text{ V}\\). When a resistor with resistance \\(R = 5.0\\text{ }\\Omega\\) is connected in parallel across the terminals, the voltmeter reading drops to \\(10\\text{ V}\\). What is the internal resistance \\(r\\) of the battery?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118348/"
date_modified: "2026-08-04T08:09:39+00:00"
---

# A real battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected to an ideal high-resistance digital voltmeter. When only the voltmeter is connected across the battery terminals, the reading is \(12\text{ V}\). When a resistor with resistance \(R = 5.0\text{ }\Omega\) is connected in parallel across the terminals, the voltmeter reading drops to \(10\text{ V}\). What is the internal resistance \(r\) of the battery?

A real battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected to an ideal high-resistance digital voltmeter. When only the voltmeter is connected across the battery terminals, the reading is \(12\text{ V}\). When a resistor with resistance \(R = 5.0\text{ }\Omega\) is connected in parallel across the terminals, the voltmeter reading drops to \(10\text{ V}\). What is the internal resistance \(r\) of the battery?

![A schematic diagram of a circuit. On the left, a dashed rectangular box encloses an ideal DC voltage source labeled \mathcal{E} connected in series with an internal resistor labeled r. Wire leads extend from the top and bottom of the dashed box to two terminal nodes. Connected across the terminal nodes in parallel are two branches: the middle branch contains a switch S in series with a resistor labeled R = 5.0\text{ }\Omega, and the rightmost branch contains a circle labeled V representing a voltmeter. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830979-Uy4J5D.jpg)

- **A.** \(0.83\text{ }\Omega\)
- **B.** \(1.0\text{ }\Omega\)
- **C.** \(2.5\text{ }\Omega\)
- **D.** \(6.0\text{ }\Omega\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118348/*