---
title: "A real battery with electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) is connected in a complete circuit with a variable load resistor. When the current in the circuit is \\(1.5\\text{ A}\\), the terminal potential difference across the battery is \\(11.4\\text{ V}\\). When the load resistance is decreased such that the current increases to \\(4.0\\text{ A}\\), the terminal potential difference decreases to \\(10.4\\text{ V}\\). What is the internal resistance \\(r\\) of the battery?"
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url: "https://nerd-notes.com/ubq/121549/"
date_modified: "2026-08-23T05:23:58+00:00"
---

# A real battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected in a complete circuit with a variable load resistor. When the current in the circuit is \(1.5\text{ A}\), the terminal potential difference across the battery is \(11.4\text{ V}\). When the load resistance is decreased such that the current increases to \(4.0\text{ A}\), the terminal potential difference decreases to \(10.4\text{ V}\). What is the internal resistance \(r\) of the battery?

A real battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected in a complete circuit with a variable load resistor. When the current in the circuit is \(1.5\text{ A}\), the terminal potential difference across the battery is \(11.4\text{ V}\). When the load resistance is decreased such that the current increases to \(4.0\text{ A}\), the terminal potential difference decreases to \(10.4\text{ V}\). What is the internal resistance \(r\) of the battery?

![A single rectangular circuit loop. On the left vertical branch is a non-ideal battery outlined by a light-gray dashed rectangular box; inside this box, an ideal DC voltage source symbol labeled \(\mathcal{E}\) is connected in series with a resistor zigzag symbol labeled \(r\). On the right vertical branch is a variable load resistor represented by a resistor zigzag labeled \(R\) with a diagonal arrow crossing through it pointing toward the upper-right. Solid connecting wires form the top and bottom horizontal segments of the loop. A current arrow labeled \(I\) along the top horizontal wire points to the right. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-diagram-1787462638-LaKLH8.jpg)

- **A.** \(0.25\text{ }\Omega\)
- **B.** \(0.40\text{ }\Omega\)
- **C.** \(0.60\text{ }\Omega\)
- **D.** \(0.67\text{ }\Omega\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121549/*