---
title: "A student performs an experiment to characterize a nonideal battery with electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) by connecting it across a variable load resistor. The student measures the battery’s terminal voltage \\(\\Delta V\\) as a function of the output current \\(I\\) delivered to the load, obtaining a linear best-fit line with vertical intercept \\(V_0\\) and slope \\(-s\\), where \\(s > 0\\). Which of the following expressions correctly gives the internal resistance \\(r\\) of the battery and the maximum power \\(P_{\\text{max}}\\) that the battery can deliver to the load resistor?"
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url: "https://nerd-notes.com/ubq/124842/"
date_modified: "2026-09-28T14:11:39+00:00"
---

# A student performs an experiment to characterize a nonideal battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) by connecting it across a variable load resistor. The student measures the battery’s terminal voltage \(\Delta V\) as a function of the output current \(I\) delivered to the load, obtaining a linear best-fit line with vertical intercept \(V_0\) and slope \(-s\), where \(s > 0\). Which of the following expressions correctly gives the internal resistance \(r\) of the battery and the maximum power \(P_{\text{max}}\) that the battery can deliver to the load resistor?

A student performs an experiment to characterize a nonideal battery with electromotive force \(\mathcal{E}\) and internal resistance \(r\) by connecting it across a variable load resistor. The student measures the battery's terminal voltage \(\Delta V\) as a function of the output current \(I\) delivered to the load, obtaining a linear best-fit line with vertical intercept \(V_0\) and slope \(-s\), where \(s > 0\). Which of the following expressions correctly gives the internal resistance \(r\) of the battery and the maximum power \(P_{\text{max}}\) that the battery can deliver to the load resistor?

![A Cartesian coordinate system with a horizontal axis labeled \(I\) and a vertical axis labeled \(\Delta V\). The origin is at the intersection of the two perpendicular axes. A single straight solid line with a negative slope starts on the vertical axis at a tick mark labeled \(V_0\) and extends downward and to the right into the first quadrant. An annotation next to the line indicates a slope of \(-s\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604698-RcYzKJ.jpg)

- **A.** \(r = s\) and \(P_{\text{max}} = \dfrac{V_0^2}{4s}\)
- **B.** \(r = s\) and \(P_{\text{max}} = \dfrac{V_0^2}{2s}\)
- **C.** \(r = \dfrac{1}{s}\) and \(P_{\text{max}} = \dfrac{V_0^2 s}{4}\)
- **D.** \(r = \dfrac{1}{s}\) and \(P_{\text{max}} = \dfrac{V_0^2 s}{2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124842/*