A heating element in a toaster consists of a single

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

A heating element in a toaster consists of a single, uniform wire that operates at an average temperature of

350\,^{\circ}\!\text{C}

. The wire has a length of

0.80\,\text{m}

and a diameter of

0.50\,\text{mm}

. When the toaster is on, the resistance of the wire is measured to be

4.5\;\Omega

. Two candidate alloys are being considered by an engineer: (a) Using the operating-temperature measurements, determine the resistivity of the heating-element wire at

350\,^{\circ}\!\text{C}

. (b) For each candidate alloy, estimate its resistivity at

350\,^{\circ}\!\text{C}

and compare the estimates to the value you found in part (a). (c) Identify which alloy the heating element is most likely made of, and justify your answer in terms of the quantitative comparison and the physical suitability of the material for a toaster.

Related theory

Temperature Dependence of Resistivity
Resistance & Resistivity
Resistivity of Materials
Electric Circuits
Electricity
Resistance: geometry and temperature dependence
Current Electricity

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