Question

Determine the temperature at which the resistance of an aluminum wire will be twice its value at $20.0^{\circ} \mathrm{C}$ . Assume its coefficient of resistivity remains constant.

Name: Problem 48, Chapter 27: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2020-06-15T18:38:18-08:00
Duration: 1 min 20 s
Channel: Kayla Gephart
Description: Determine the temperature at which the resistance of an aluminum wire will be twice its value at 20.0^∘ C . Assume its coefficient of resistivity remains constant.

   Determine the temperature at which the resistance of an aluminum wire will be twice its value at $20.0^{\circ} \mathrm{C}$ . Assume its coefficient of resistivity remains constant.

Physics for Scientists and Engineers with Modern Physics

Raymond A. Serway,… 8th Edition

Chapter 27, Problem 48

Instant Answer

Solved by Expert Kayla Gephart

06/15/2020

Step 1

Step 1: We start with the formula for the change in resistance due to temperature change: \[R_f = R_i(1 + \alpha \Delta T)\] where $R_f$ is the final resistance, $R_i$ is the initial resistance, $\alpha$ is the temperature coefficient of resistivity, and Show more…

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Determine the temperature at which the resistance of an aluminum wire will be twice its value at $20.0^{\circ} \mathrm{C}$ . Assume its coefficient of resistivity remains constant.

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Key Concepts

Temperature Dependence of Electrical Resistance

This concept explains that the resistance of a conductor changes as its temperature changes. The most common model for this behavior is given by the linear relationship R = R0[1 + ?(T - T0)], where R0 is the original resistance at reference temperature T0, ? is the temperature coefficient of resistivity, and T is the new temperature. This relationship allows for determining a new resistance value when the temperature is changed, assuming ? is constant.

Temperature Coefficient of Resistivity

This is a material-specific constant (typically represented by ?) that indicates how much the resistivity, and hence the resistance, of the material changes per degree change in temperature. For conductive materials like aluminum, this coefficient is crucial in calculating how its resistance will double at a certain increased temperature based on the linear approximation.

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