(a) What is the resistance of a Nichrome wire at 0.0^∘ C if its resistance is 180.0 Ωat 11.5^∘ C

Name: Problem 23, Chapter 25: University Physics with Modern Physics In SI Units
Uploaded: 2022-11-22T21:29:11-08:00
Duration: 2 min 45 s
Channel: Melissa Walsh
Description: (a) What is the resistance of a Nichrome wire at 0.0^∘ C if its resistance is 180.0 Ωat 11.5^∘ C ? (b) What is the resistance of a carbon rod at 25.8^∘ C if its resistance is 0.0140 Ωat 0.0^∘ C ?

step 1 We have a nicrome wire, which we know the coefficient of resistivity at a temperature of this is

Question

(a) What is the resistance of a Nichrome wire at $0.0^{\circ} \mathrm{C}$ if its resistance is $180.0 \Omega$ at $11.5^{\circ} \mathrm{C} ?$ (b) What is the resistance of a carbon rod at $25.8^{\circ} \mathrm{C}$ if its resistance is $0.0140 \Omega$ at $0.0^{\circ} \mathrm{C} ?$

   (a) What is the resistance of a Nichrome wire at $0.0^{\circ} \mathrm{C}$ if its resistance is $180.0 \Omega$ at $11.5^{\circ} \mathrm{C} ?$ (b) What is the resistance of a carbon rod at $25.8^{\circ} \mathrm{C}$ if its resistance is $0.0140 \Omega$ at $0.0^{\circ} \mathrm{C} ?$

University Physics with Modern Physics In SI Units

Hugh D Young; Roger… 15th Edition

Chapter 25, Problem 23

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Solved by Expert Melissa Walsh

11/22/2022

Step 1

Step 1: We know that the resistance of a material at a certain temperature can be calculated using the formula: \[R_T = R_0(1 + \alpha \Delta T)\] where $R_T$ is the resistance at temperature $T$, $R_0$ is the resistance at 0 degrees Celsius, $\alpha$ is Show more…

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(a) What is the resistance of a Nichrome wire at $0.0^{\circ} \mathrm{C}$ if its resistance is $180.0 \Omega$ at $11.5^{\circ} \mathrm{C} ?$ (b) What is the resistance of a carbon rod at $25.8^{\circ} \mathrm{C}$ if its resistance is $0.0140 \Omega$ at $0.0^{\circ} \mathrm{C} ?$

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Key Concepts

Temperature Coefficient of Resistance

This concept describes how the resistance of a material changes with temperature. It is expressed as a constant, ?, which quantifies the fractional change in resistance per degree change in temperature. The temperature coefficient is fundamental in understanding the thermal behavior of conductors and semiconductors since it directly affects the performance of electrical components as temperatures vary.

Linear Temperature Dependence of Resistance

Resistance in many materials changes approximately linearly with temperature over a limited range. This relationship is commonly given by the equation R = R0 (1 + ? (T - T0)), where R0 is the resistance at a reference temperature T0, and R is the resistance at temperature T. Understanding this linear dependency is crucial for designing circuits and systems that must operate reliably over varying temperatures.

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