Resistivity and temperature: 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 change in current can be related to the change in resistance using the formula:

ΔR/R = αΔT

where ΔR is the change in resistance, R is the initial resistance, α is the temperature coefficient of resistivity, and ΔT is the change in temperature.

Since the current drops by 20%, the resistance must increase by 25% (since resistance is proportional to 1/current).

Therefore, ΔR/R = 0.25

Substituting the given value for α, we get:

0.25 = 0.000400 ΔT

Solving for ΔT, we get:

ΔT = 625°C.

Therefore, the temperature change in the wire is 625°C. Answer choice D is correct.

Resistivity and Temperature: a Nichrome Wire Is Used as a Heating