---
title: "A student conducts an experiment to determine the resistivity \\(\\rho\\) of a metallic alloy using several cylindrical wire samples that vary in both length \\(L\\) and circular cross-sectional radius \\(r\\). For each wire sample, the student measures \\(L\\), \\(r\\), and the electrical resistance \\(R\\). Which of the following quantities, when plotted on the vertical and horizontal axes, will produce a linear graph whose best-fit line has a slope directly equal to \\(\\rho\\)?"
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url: "https://nerd-notes.com/ubq/124775/"
date_modified: "2026-09-28T14:11:12+00:00"
---

# A student conducts an experiment to determine the resistivity \(\rho\) of a metallic alloy using several cylindrical wire samples that vary in both length \(L\) and circular cross-sectional radius \(r\). For each wire sample, the student measures \(L\), \(r\), and the electrical resistance \(R\). Which of the following quantities, when plotted on the vertical and horizontal axes, will produce a linear graph whose best-fit line has a slope directly equal to \(\rho\)?

A student conducts an experiment to determine the resistivity \(\rho\) of a metallic alloy using several cylindrical wire samples that vary in both length \(L\) and circular cross-sectional radius \(r\). For each wire sample, the student measures \(L\), \(r\), and the electrical resistance \(R\). Which of the following quantities, when plotted on the vertical and horizontal axes, will produce a linear graph whose best-fit line has a slope directly equal to \(\rho\)?

![A single horizontal cylindrical wire viewed in perspective from the front and slightly above. The left end is drawn as a complete vertical ellipse representing the circular cross-sectional face of the wire, with light gray shading. From the center of this left elliptical face, a single solid straight arrow points vertically upward to the top edge of the ellipse, labeled r. The cylindrical body extends horizontally to the right, terminating at a parallel elliptical curved edge. Directly beneath the cylinder, two vertical dashed extension lines drop from the left and right endpoints. A horizontal line with arrowheads at both ends spans between these extension lines and is labeled L. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604672-Ju8iUp.jpg)

- **A.** \(R\) on the vertical axis and \(\dfrac{L}{r}\) on the horizontal axis
- **B.** \(R\) on the vertical axis and \(\dfrac{r^2}{L}\) on the horizontal axis
- **C.** \(R\) on the vertical axis and \(\dfrac{L}{r^2}\) on the horizontal axis
- **D.** \(R\) on the vertical axis and \(\dfrac{L}{\pi r^2}\) on the horizontal axis

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124775/*