---
title: "A nonideal battery with a constant electromotive force \\(\\mathcal{E}\\) and an internal resistance \\(r\\) is connected across a variable resistor of resistance \\(R\\). The resistance \\(R\\) is decreased, which increases the electric current \\(I\\) in the circuit and decreases the terminal voltage \\(\\Delta V\\) across the battery. Which of the following claims correctly describes what happens to the rate of thermal energy dissipation inside the battery, and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/124824/"
date_modified: "2026-09-28T14:11:35+00:00"
---

# A nonideal battery with a constant electromotive force \(\mathcal{E}\) and an internal resistance \(r\) is connected across a variable resistor of resistance \(R\). The resistance \(R\) is decreased, which increases the electric current \(I\) in the circuit and decreases the terminal voltage \(\Delta V\) across the battery. Which of the following claims correctly describes what happens to the rate of thermal energy dissipation inside the battery, and provides the correct physical justification?

A nonideal battery with a constant electromotive force \(\mathcal{E}\) and an internal resistance \(r\) is connected across a variable resistor of resistance \(R\). The resistance \(R\) is decreased, which increases the electric current \(I\) in the circuit and decreases the terminal voltage \(\Delta V\) across the battery. Which of the following claims correctly describes what happens to the rate of thermal energy dissipation inside the battery, and provides the correct physical justification?

![A single rectangular circuit schematic oriented with two horizontal wires and two vertical wires. On the left vertical branch is a real battery enclosed in a dashed rectangular box. Inside the dashed box, an ideal battery symbol with two parallel plates (longer horizontal plate labeled \(+\) on top, shorter thicker horizontal plate on bottom) is labeled \(\mathcal{E}\), connected in series above a small zig-zag resistor symbol labeled \(r\). Two solid circular dots on the vertical wire just outside the top and bottom edges of the dashed box represent terminals labeled \(a\) and \(b\). On the right vertical branch is a variable resistor represented by a zig-zag resistor symbol labeled \(R\) with a straight diagonal arrow passing through its center pointing toward the upper-right. An arrow on the top horizontal wire points to the right and is labeled \(I\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-diagram-1790604695-1Jl9Hh.jpg)

- **A.** The rate of thermal energy dissipation inside the battery decreases because the terminal voltage \(\Delta V\) decreases, reducing the power dissipated across the internal resistance according to \(P = \dfrac{(\Delta V)^2}{r}\).
- **B.** The rate of thermal energy dissipation inside the battery increases because the larger current causes a greater potential difference across the internal resistance, dissipating power at a rate equal to \(I^2 r\).
- **C.** The rate of thermal energy dissipation inside the battery remains the same because the internal resistance \(r\) is an intrinsic property of the battery that does not depend on the external circuit.
- **D.** The rate of thermal energy dissipation inside the battery increases because the total power generated by the battery \(\mathcal{E} I\) increases, while the fraction of total power dissipated by the internal resistance remains constant.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124824/*