A Nichrome wire is used as a heating element in a toaster. From the moment the toaster is first turned on to the moment the wire reaches it maximum temperature, the current in the wire drops by 20.0% from its initial value. What is the temperature change in the wire? The temperature coefficient of resistivity for Nichrome is 0.000400 (°C)^-1.

Question

Quizplus · Accepted Answer

The resistance of the wire is directly proportional to its temperature. Therefore, we can assume that the resistance of the wire has increased by 20.0% when the current dropped by 20.0%. Let the initial temperature be T1 and the final temperature be T2.
ΔR/R = α ΔT
where ΔR/R is the percentage change in resistance, α is the temperature coefficient of resistivity (0.000400 (°C)-1 for Nichrome wire), and ΔT is the temperature change.
0.200 = 0.000400 ΔT
ΔT = 500 °C
Therefore, the temperature change is 500°C. The correct choice is D.

A Nichrome Wire Is Used as a Heating Element in a Toaster