---
title: "A student connects a battery of electromotive force (emf) \\(\\varepsilon\\) and internal resistance \\(r\\) to a variable resistor of resistance \\(R\\), an ammeter, and a voltmeter, as shown in the circuit diagram. By adjusting the resistance \\(R\\), the student measures and records several pairs of the current \\(I\\) through the circuit and the corresponding terminal voltage \\(\\Delta V\\) across the battery. If the student plots \\(\\Delta V\\) on the vertical axis as a function of \\(I\\) on the horizontal axis, which of the following correctly indicates how \\(\\varepsilon\\) and \\(r\\) are determined from the resulting best-fit line?"
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url: "https://nerd-notes.com/ubq/120407/"
date_modified: "2026-08-23T04:34:29+00:00"
---

# A student connects a battery of electromotive force (emf) \(\varepsilon\) and internal resistance \(r\) to a variable resistor of resistance \(R\), an ammeter, and a voltmeter, as shown in the circuit diagram. By adjusting the resistance \(R\), the student measures and records several pairs of the current \(I\) through the circuit and the corresponding terminal voltage \(\Delta V\) across the battery. If the student plots \(\Delta V\) on the vertical axis as a function of \(I\) on the horizontal axis, which of the following correctly indicates how \(\varepsilon\) and \(r\) are determined from the resulting best-fit line?

A student connects a battery of electromotive force (emf) \(\varepsilon\) and internal resistance \(r\) to a variable resistor of resistance \(R\), an ammeter, and a voltmeter, as shown in the circuit diagram. By adjusting the resistance \(R\), the student measures and records several pairs of the current \(I\) through the circuit and the corresponding terminal voltage \(\Delta V\) across the battery. If the student plots \(\Delta V\) on the vertical axis as a function of \(I\) on the horizontal axis, which of the following correctly indicates how \(\varepsilon\) and \(r\) are determined from the resulting best-fit line?

![A rectangular circuit schematic drawn in black lines on a white background. The top horizontal branch contains a dashed rectangular box enclosing a DC voltage source symbol labeled \varepsilon in series with a resistor symbol labeled r. A voltmeter circle containing the letter V is connected in parallel across the two external terminals of the dashed box. The right vertical branch contains an ammeter circle containing the letter A. The bottom horizontal branch contains a variable resistor symbol labeled R, drawn as a resistor with a diagonal arrow through its center. Straight connecting wires complete the closed rectangular loop. No other components, values, arrows, or text appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459669-C7RpZ4.jpg)

- **A.** The emf \(\varepsilon\) equals the vertical intercept, and the internal resistance \(r\) equals the negative of the slope.
- **B.** The emf \(\varepsilon\) equals the vertical intercept, and the internal resistance \(r\) equals the inverse of the slope.
- **C.** The emf \(\varepsilon\) equals the horizontal intercept, and the internal resistance \(r\) equals the slope.
- **D.** The emf \(\varepsilon\) equals the slope, and the internal resistance \(r\) equals the vertical intercept.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120407/*