---
title: "A student designs an experiment to determine the electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) of a battery using a decade resistance box and a voltmeter.  The decade resistance box, set to resistance \\(R\\), is connected across the terminals of the battery, and the voltmeter, which has a finite internal resistance \\(R_V\\), is connected in parallel with the resistance box. Assuming the voltmeter is ideal, the student records the potential difference \\(V\\) across the box for several values of \\(R\\), plots \\(\\dfrac{1}{V}\\) as a function of \\(\\dfrac{1}{R}\\), and uses the slope and vertical intercept of the best-fit line to calculate experimental values \\(\\mathcal{E}_{\\text{exp}}\\) and \\(r_{\\text{exp}}\\). Which of the following correctly compares the experimental values \\(\\mathcal{E}_{\\text{exp}}\\) and \\(r_{\\text{exp}}\\) to the true values \\(\\mathcal{E}\\) and \\(r\\), respectively?"
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url: "https://nerd-notes.com/ubq/124898/"
date_modified: "2026-09-28T14:11:51+00:00"
---

# A student designs an experiment to determine the electromotive force \(\mathcal{E}\) and internal resistance \(r\) of a battery using a decade resistance box and a voltmeter.

The decade resistance box, set to resistance \(R\), is connected across the terminals of the battery, and the voltmeter, which has a finite internal resistance \(R_V\), is connected in parallel with the resistance box. Assuming the voltmeter is ideal, the student records the potential difference \(V\) across the box for several values of \(R\), plots \(\dfrac{1}{V}\) as a function of \(\dfrac{1}{R}\), and uses the slope and vertical intercept of the best-fit line to calculate experimental values \(\mathcal{E}_{\text{exp}}\) and \(r_{\text{exp}}\). Which of the following correctly compares the experimental values \(\mathcal{E}_{\text{exp}}\) and \(r_{\text{exp}}\) to the true values \(\mathcal{E}\) and \(r\), respectively?

A student designs an experiment to determine the electromotive force \(\mathcal{E}\) and internal resistance \(r\) of a battery using a decade resistance box and a voltmeter.

The decade resistance box, set to resistance \(R\), is connected across the terminals of the battery, and the voltmeter, which has a finite internal resistance \(R_V\), is connected in parallel with the resistance box. Assuming the voltmeter is ideal, the student records the potential difference \(V\) across the box for several values of \(R\), plots \(\dfrac{1}{V}\) as a function of \(\dfrac{1}{R}\), and uses the slope and vertical intercept of the best-fit line to calculate experimental values \(\mathcal{E}_{\text{exp}}\) and \(r_{\text{exp}}\). Which of the following correctly compares the experimental values \(\mathcal{E}_{\text{exp}}\) and \(r_{\text{exp}}\) to the true values \(\mathcal{E}\) and \(r\), respectively?

![A rectangular circuit schematic in grayscale. On the left vertical branch is a real battery drawn inside a dashed rectangular box, consisting of a DC voltage source symbol labeled \(\mathcal{E}\) in series with an internal resistor labeled \(r\). Solid wires extend horizontally to the right from the top and bottom terminals of the battery box. Connected between the top and bottom wires is a decade resistance box depicted as a standard resistor symbol with a diagonal arrow through its center, labeled \(R\). Further to the right, connected in parallel across the resistance box, is a circle containing the letter V, labeled with internal resistance \(R_V\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1790604711-b3WF42.jpg)

- **A.** \(\mathcal{E}_{\text{exp}} > \mathcal{E}\) and \(r_{\text{exp}} > r\)
- **B.** \(\mathcal{E}_{\text{exp}} < \mathcal{E}\) and \(r_{\text{exp}} > r\)
- **C.** \(\mathcal{E}_{\text{exp}} < \mathcal{E}\) and \(r_{\text{exp}} < r\)
- **D.** \(\mathcal{E}_{\text{exp}} > \mathcal{E}\) and \(r_{\text{exp}} < r\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124898/*