---
title: "A battery with constant electromotive force \\(\\mathcal{E}\\) and non-negligible internal resistance \\(r\\) is connected in a single-loop circuit to a variable load resistor of resistance \\(R\\).  Which of the following graphs best represents the electrical power \\(P\\) dissipated in the load resistor as a function of the load resistance \\(R\\)?"
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url: "https://nerd-notes.com/ubq/121607/"
date_modified: "2026-08-23T05:24:21+00:00"
---

# A battery with constant electromotive force \(\mathcal{E}\) and non-negligible internal resistance \(r\) is connected in a single-loop circuit to a variable load resistor of resistance \(R\).

Which of the following graphs best represents the electrical power \(P\) dissipated in the load resistor as a function of the load resistance \(R\)?

A battery with constant electromotive force \(\mathcal{E}\) and non-negligible internal resistance \(r\) is connected in a single-loop circuit to a variable load resistor of resistance \(R\).

Which of the following graphs best represents the electrical power \(P\) dissipated in the load resistor as a function of the load resistance \(R\)?

![A single rectangular circuit loop. The top horizontal segment contains a rectangular dashed box representing a non-ideal battery; inside the dashed box are an ideal battery symbol labeled \(\mathcal{E}\) and an adjacent series resistor symbol labeled \(r\). The right vertical branch contains a variable resistor symbol consisting of a zigzag line with a diagonal arrow cutting upward through its center, labeled \(R\). The bottom and left segments are plain straight connecting wires. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1787462659-kNTCq0.jpg)

- **A.** A graph of \(P\) versus \(R\) that starts at a maximum positive value on the vertical axis at \(R = 0\) and decreases monotonically toward zero as \(R \to \infty\).
- **B.** A graph of \(P\) versus \(R\) that starts at \(P = 0\) at \(R = 0\), rises to a single maximum at \(R = r\), and decreases asymptotically toward zero as \(R \to \infty\).
- **C.** A graph of \(P\) versus \(R\) that starts at \(P = 0\) at \(R = 0\) and increases monotonically with decreasing slope, asymptotically approaching a constant maximum value as \(R \to \infty\).
- **D.** A graph of \(P\) versus \(R\) that starts at \(P = 0\) at \(R = 0\), rises to a single maximum at \(R = 2r\), and decreases asymptotically toward zero as \(R \to \infty\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121607/*