---
title: "A student is investigating how the resistance of a metal wire changes with temperature. The relationship between the resistance \\(R\\) of the wire and its temperature \\(T\\) (in \\(^{\\circ}\\text{C}\\)) is modeled by the equation  \\[ R(T) = R_0(1 + \\alpha T) \\]  where \\(R_0\\) is the resistance of the wire at \\(0^{\\circ}\\text{C}\\) and \\(\\alpha\\) is the temperature coefficient of resistivity for the metal.   The student is provided with a sample of the wire coiled around an insulating cylinder, a beaker of water, a hot plate, a thermometer, a variable DC power supply, an ideal ammeter, an ideal voltmeter, and connecting wires."
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url: "https://nerd-notes.com/ubq/117835/"
date_modified: "2026-08-04T07:59:05+00:00"
---

# A student is investigating how the resistance of a metal wire changes with temperature. The relationship between the resistance \(R\) of the wire and its temperature \(T\) (in \(^{\circ}\text{C}\)) is modeled by the equation

\[ R(T) = R_0(1 + \alpha T) \]

where \(R_0\) is the resistance of the wire at \(0^{\circ}\text{C}\) and \(\alpha\) is the temperature coefficient of resistivity for the metal. 

The student is provided with a sample of the wire coiled around an insulating cylinder, a beaker of water, a hot plate, a thermometer, a variable DC power supply, an ideal ammeter, an ideal voltmeter, and connecting wires.

A student is investigating how the resistance of a metal wire changes with temperature. The relationship between the resistance \(R\) of the wire and its temperature \(T\) (in \(^{\circ}\text{C}\)) is modeled by the equation

\[ R(T) = R_0(1 + \alpha T) \]

where \(R_0\) is the resistance of the wire at \(0^{\circ}\text{C}\) and \(\alpha\) is the temperature coefficient of resistivity for the metal. 

The student is provided with a sample of the wire coiled around an insulating cylinder, a beaker of water, a hot plate, a thermometer, a variable DC power supply, an ideal ammeter, an ideal voltmeter, and connecting wires.

**Part a)** The student sets up the equipment so that the wire coil is completely submerged in the water bath on the hot plate. *(4 points)*

**Part b)** The student calculates the resistance \(R\) of the wire at several temperatures and records the data in the table below. | Temperature \(T\) (\(^{\circ}\text{C}\)) | Resistance \(R\) (\(\Omega\)) | |---|---| | 20 | 5.4 | | 40 | 5.9 | | 60 | 6.2 | | 80 | 6.7 | | 100 | 7.0 | **Plot** the data points for resistance \(R\) as a function of temperature \(T\) on the provided grid. **Draw** a best-fit straight line for the data. *(2 points)*

**Part c)** Use the best-fit line to determine the following properties of the wire. *(3 points)*

**Part d)** The wire has a total length of \(2.0 \text{ m}\) and a uniform diameter of \(0.50 \text{ mm}\). **Calculate** the resistivity \(\rho_0\) of the metal at \(0^{\circ}\text{C}\). *(2 points)*

**Part e)** The student realizes that the voltmeter used in the experiment was actually not ideal and has a finite internal resistance. In the student's setup, the ammeter was placed in series with the power supply and measured the total current leaving the power supply, while the voltmeter was placed in parallel with the wire. Does this non-ideal characteristic of the voltmeter cause the calculated value of the wire's resistance to be greater than, less than, or equal to the actual resistance of the wire? - [ ] Greater than - [ ] Less than - [ ] Equal to **Justify** your answer. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117835/*