---
title: "A student connects a real battery of unknown electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) to a variable resistor of calibrated resistance \\(R\\). An ideal voltmeter connected across the battery terminals measures the terminal voltage \\(\\Delta V\\) for several different values of \\(R\\). Which of the following pairs of quantities should be plotted on the vertical and horizontal axes to produce a linear graph, and what is the correct expression for \\(r\\) in terms of the slope \\(m\\) and vertical intercept \\(b\\) of the resulting best-fit line?"
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url: "https://nerd-notes.com/ubq/121593/"
date_modified: "2026-08-23T05:24:12+00:00"
---

# A student connects a real battery of unknown electromotive force \(\mathcal{E}\) and internal resistance \(r\) to a variable resistor of calibrated resistance \(R\). An ideal voltmeter connected across the battery terminals measures the terminal voltage \(\Delta V\) for several different values of \(R\). Which of the following pairs of quantities should be plotted on the vertical and horizontal axes to produce a linear graph, and what is the correct expression for \(r\) in terms of the slope \(m\) and vertical intercept \(b\) of the resulting best-fit line?

A student connects a real battery of unknown electromotive force \(\mathcal{E}\) and internal resistance \(r\) to a variable resistor of calibrated resistance \(R\). An ideal voltmeter connected across the battery terminals measures the terminal voltage \(\Delta V\) for several different values of \(R\). Which of the following pairs of quantities should be plotted on the vertical and horizontal axes to produce a linear graph, and what is the correct expression for \(r\) in terms of the slope \(m\) and vertical intercept \(b\) of the resulting best-fit line?

![A single rectangular circuit loop drawn with solid black lines. The left vertical branch contains a DC source symbol labeled \(\mathcal{E}\) in series with a small resistor symbol labeled \(r\), enclosed by a dashed gray box representing the battery. The right vertical branch contains a variable resistor symbol labeled \(R\) with an arrow drawn diagonally across it. Two wire leads extend from the top and bottom terminals of the dashed box to an ideal voltmeter symbol labeled V in parallel with the battery. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462651-8ROFiO.jpg)

- **A.** Vertical axis: \(\dfrac{R}{\Delta V}\) Horizontal axis: \(R\) Internal resistance: \(r = \dfrac{m}{b}\)
- **B.** Vertical axis: \(\Delta V\) Horizontal axis: \(\dfrac{1}{R}\) Internal resistance: \(r = -m\)
- **C.** Vertical axis: \(\dfrac{1}{\Delta V}\) Horizontal axis: \(\dfrac{1}{R}\) Internal resistance: \(r = \dfrac{b}{m}\)
- **D.** Vertical axis: \(\dfrac{1}{\Delta V}\) Horizontal axis: \(\dfrac{1}{R}\) Internal resistance: \(r = \dfrac{m}{b}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121593/*