**Understanding Resistivity and Temperature**The resistivity of a metal increases slightly with increased temperature. This relationship can be expressed using the formula:\[\rho = \rho_0 [1 + \alpha (T - T_0)]\]- \(\rho\) is the resistivity at temperature \(T\).- \(\rho_0\) is the resistivity at a reference temperature \(T_0\), usually 20°C.- \(\alpha\) is the temperature coefficient of resistivity.For copper, \(\alpha = 3.9 \times 10^{-3} \, ^\circ \text{C}^{-1}\).**Example Problem**Suppose a long, thin copper wire has a resistance of 0.25 Ω at 20°C.**Part A***Question:* At what temperature, in °C, will its resistance be 0.25 Ω?To solve this, you would set up the equation using the given resistance and solve for \(T\).*Interactive Tools*- There is an input box for entering the temperature value in °C.- Options for submitting your answer and requesting additional help are provided.

Given data, Final resistance R=0.25 Ω Initial resistance R0=0.25 Ω Constant α=3.9×10-3 °C-1…

The resistivity of a metal increases slightly with increased temperature. This can be expressed as p = po[1+ a(T-To)], where To is a reference temperature, usually 20° C, and a is the temperature coefficient of resistivity. For copper, a = 3.9x 10-3 °C-1. Suppose a long, thin copper wire has a resistance of 0.25 at 20°C. Part A At what temperature, in °C, will its resistance be 0.25 ? T= Submit | ΑΣΦ Request Answer wood ? °C

The resistivity of a metal increases slightly with increased temperature. This can be expressed as p = po[1+ a(T-To)], where To is a reference temperature, usually 20° C, and a is the temperature coefficient of resistivity. For copper, a = 3.9x 10-3 °C-1. Suppose a long, thin copper wire has a resistance of 0.25 at 20°C. Part A At what temperature, in °C, will its resistance be 0.25 ? T= Submit | ΑΣΦ Request Answer wood ? °C

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Resistivity

Resistivity is a characteristic property of the conductor’s material that measures the extent to which the material opposes the flow of current. It is denoted by the Greek letter “rho”. Electrical resistivity, also known as specific resistance, depends on the nature of the material of the conductor and is unaffected by its dimensions.

Question

**Understanding Resistivity and Temperature**

The resistivity of a metal increases slightly with increased temperature. This relationship can be expressed using the formula:

\[
\rho = \rho_0 [1 + \alpha (T - T_0)]
\]

- \(\rho\) is the resistivity at temperature \(T\).
- \(\rho_0\) is the resistivity at a reference temperature \(T_0\), usually 20°C.
- \(\alpha\) is the temperature coefficient of resistivity.

For copper, \(\alpha = 3.9 \times 10^{-3} \, ^\circ \text{C}^{-1}\).

**Example Problem**

Suppose a long, thin copper wire has a resistance of 0.25 Ω at 20°C.

**Part A**

*Question:* At what temperature, in °C, will its resistance be 0.25 Ω?

To solve this, you would set up the equation using the given resistance and solve for \(T\).

*Interactive Tools*

- There is an input box for entering the temperature value in °C.
- Options for submitting your answer and requesting additional help are provided.

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