---
title: "A battery with electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) is connected in series with a variable load resistor of adjustable resistance \\(R\\). The resistance \\(R\\) is varied until the rate of energy dissipation in the load resistor is maximized. Which of the following expressions represents the maximum electric power dissipated in the load resistor?"
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url: "https://nerd-notes.com/ubq/121543/"
date_modified: "2026-08-23T05:23:55+00:00"
---

# A battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected in series with a variable load resistor of adjustable resistance \(R\). The resistance \(R\) is varied until the rate of energy dissipation in the load resistor is maximized. Which of the following expressions represents the maximum electric power dissipated in the load resistor?

A battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected in series with a variable load resistor of adjustable resistance \(R\). The resistance \(R\) is varied until the rate of energy dissipation in the load resistor is maximized. Which of the following expressions represents the maximum electric power dissipated in the load resistor?

![A single rectangular circuit loop oriented with horizontal top and bottom segments and vertical left and right segments. On the left vertical segment, a nonideal battery is represented within a dashed rectangular box containing an ideal battery symbol with long positive plate above short negative plate labeled \(\mathcal{E}\) in series with a resistor symbol labeled \(r\). The top and bottom horizontal segments are straight solid connecting wires. On the right vertical segment, a variable resistor is shown as a standard zigzag resistor symbol labeled \(R\) with a diagonal arrow pointing upward and to the right across the middle of the zigzag. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462634-uhyHJG.jpg)

- **A.** \(\dfrac{\mathcal{E}^2}{r}\)
- **B.** \(\dfrac{\mathcal{E}^2}{2r}\)
- **C.** \(\dfrac{\mathcal{E}^2}{4r}\)
- **D.** \(\dfrac{\mathcal{E}^2}{8r}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121543/*