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 2.0 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 = current x voltage = 1.53 x 100 = 153 watts

I take it that temperature coefficient of resistivity for nichrome should read: 0.4x10^-3 (degrees C)^-1

Ohm's Law: r = v/i
At 20.0°C:

Rcold = 100 / 2.00 = 50.00 ohms

At operating temperature (T):
r = 100 / 1.53 = 65.36 ohms

Change in resistance (R) = (65.36 - 50.00) = 15.36 ohms

R / Rcold = * T

where is the temp. coeff. of resistance and T is the change in temperature.

Plugging in values:

15.36 / 50.00 = 0.4 * 10^-3 * T

T = 768°C

T = (Operating Temperature - Tcold)

Operating temperature = T + 20.0 = 788°C

T = 768°C

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