---
title: "A battery with electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) is connected in series with a variable load resistor of resistance \\(R\\). The graph shows the electric power \\(P\\) dissipated by the load resistor as a function of \\(R\\). Which of the following statements correctly relates features of the graph to the operation of the circuit?"
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url: "https://nerd-notes.com/ubq/124769/"
date_modified: "2026-09-28T14:11:12+00:00"
---

# A battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected in series with a variable load resistor of resistance \(R\). The graph shows the electric power \(P\) dissipated by the load resistor as a function of \(R\). Which of the following statements correctly relates features of the graph to the operation of the circuit?

A battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected in series with a variable load resistor of resistance \(R\). The graph shows the electric power \(P\) dissipated by the load resistor as a function of \(R\). Which of the following statements correctly relates features of the graph to the operation of the circuit?

![A graph with a horizontal axis labeled R and a vertical axis labeled P, intersecting at an origin marked 0. The horizontal axis extends to the right and the vertical axis extends upward, with an arrowhead on each positive axis end. Bare axes with no numerical gridlines. A single smooth solid curve starts at the origin (0, 0), rises smoothly with decreasing slope to reach a rounded local maximum peak at horizontal position labeled r, and then gradually decreases toward the horizontal axis as an asymptote as R increases to the right. A vertical dashed line extends downward from the peak of the curve to a tick mark on the horizontal axis labeled r. A horizontal dashed line extends to the left from the peak of the curve to a tick mark on the vertical axis labeled P_{\text{max}}. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604672-rMukob.jpg)

- **A.** As the load resistance increases beyond the value at the peak of the curve, the electrical efficiency of the circuit decreases because the power delivered to the load decreases.
- **B.** The rate of chemical energy conversion inside the battery is maximized at the peak of the curve, where the load resistance equals the battery internal resistance.
- **C.** At the peak of the curve, the potential difference across the battery terminals is equal to the full electromotive force of the battery because the current through the internal resistance is zero.
- **D.** At the load resistance corresponding to the maximum of the curve, the terminal voltage of the battery is equal to half of its electromotive force, and the power transferred to the load represents half of the total power supplied by the battery.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124769/*