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% from its initial value. What is the temperature change in the wire? The temperature coefficient for Nichrome is α = 0.0004 (°C) - 1.

Temperature change in the wire is 625°C

Explanation:

Let the initial current in the wire be I₀

Thus,

the final current in the wire will be, I = (1 - 0.20) * I₀ = 0.80I₀

Given α = 0.0004 1/°C

Now,

Resistance = (potential difference (E)) / current (I)

also

R = R₀ [1 + αΔT]

Where ΔT is the increase in temperature, thus

E/I = E/I₀ [1 + α * ΔT)

on substituting the values in the above equation, we get

1 / (0.80I₀) = 1 / (I₀) * [1 + 0.0004 * ΔT]

or

1 / (0.80) = [1 + 0.0004 * ΔT) ]

or

ΔT = 625°C