---
title: "A student investigates the electrical properties of a thin cylindrical metal wire of fixed length and cross-sectional area. The student measures the potential difference \\(\\Delta V\\) across the wire for various values of the current \\(I\\) and generates the graph shown. As the current increases, the graph curves upward with an increasing slope. Which of the following statements correctly interprets the graph in terms of the wire’s resistance and physical properties?"
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url: "https://nerd-notes.com/ubq/120394/"
date_modified: "2026-08-23T04:34:27+00:00"
---

# A student investigates the electrical properties of a thin cylindrical metal wire of fixed length and cross-sectional area. The student measures the potential difference \(\Delta V\) across the wire for various values of the current \(I\) and generates the graph shown. As the current increases, the graph curves upward with an increasing slope. Which of the following statements correctly interprets the graph in terms of the wire’s resistance and physical properties?

A student investigates the electrical properties of a thin cylindrical metal wire of fixed length and cross-sectional area. The student measures the potential difference \(\Delta V\) across the wire for various values of the current \(I\) and generates the graph shown. As the current increases, the graph curves upward with an increasing slope. Which of the following statements correctly interprets the graph in terms of the wire's resistance and physical properties?

![A 2D Cartesian graph with a horizontal axis labeled Current, I and a vertical axis labeled Potential Difference, \Delta V. The origin is labeled 0. There are no gridlines. A single solid curve begins at the origin with a moderate positive slope and smoothly curves upward with increasing positive slope (concave up) as current I increases. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459666-OzZ4ZF.jpg)

- **A.** The increasing slope indicates that the wire's resistance decreases as current increases, because resistance is represented by the reciprocal of the slope on a \(\Delta V\) versus \(I\) graph.
- **B.** The increasing slope indicates that the wire's resistivity decreases as current increases, because higher electron drift speeds reduce the frequency of collisions within the metal lattice.
- **C.** The increasing slope indicates that the wire's resistance remains constant, because the total thermal energy dissipated is proportional to the area under the \(\Delta V\) versus \(I\) curve.
- **D.** The increasing slope indicates that the wire's resistance increases as current increases, because greater rate of thermal energy dissipation raises the wire's temperature, which increases its resistivity.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120394/*