A certain toaster has a heating element made of Nichrome resistance wire. When t

Question

A certain toaster has a heating element made of Nichrome resistance wire. When the toaster is first connected to a 100 V source of potential difference (and the wire is at a temperature of 20.0°C), the initial current is 1.9 A. However, the current begins to decrease as the resistive element warms up. When the toaster reaches its final operating temperature, the current has dropped to 1.53 A.

(a) Find the power the toaster converts when it is at its operating temperature.
W
(b) What is the final temperature of the heating element?
°C

Explanation / Answer

(a) Power is simply I*V = 1.53*100 = 153 Watts.

(b) At 20 degrees the resistance is V/I = 100/1.9 = 52.63 Ohms. At operating temperature the resistance is V/I = 100/1.53 = 65.35 Ohms.

Resitivity depends on temperature via rho0(1 + alpha (t - t0)), and resistance is simple resitivity times some geometric factor that does not change as the wires heat up.

Thus we can write 65.35= 52.63(1 + alpha(Nichrome)(t - 20)) with alpha(Nichrome) = 0.4 x 10-3, and solve for t. We get t = 22 degrees C.

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