A certain toaster has a heating element made of Nichrome resistancewire. When th

Question

A certain toaster has a heating element made of Nichrome resistancewire. When the toaster is first connected to a 140 V source of potential difference (and the wire isat a temperature of 20.0°C), the initial current is 1.7 A.However, the current begins to decrease as the resistive elementwarms 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 itis at its operating temperature.
1 W
(b) What is the final temperature of the heating element?
2°C (a) Find the power the toaster converts when itis at its operating temperature.
1 W
(b) What is the final temperature of the heating element?
2°C

Explanation / Answer

   Let the initial resistancebe    R   and final resistancebe   R'.   Then    R   =   V /Iinitial   =   140 /1.7   =   82.35       R'   =   V /Ifinal   =   140 /1.53   =   91.50       a.   Power   P   =   V2/ R   =   1402 /91.50   =   214.21   W    b.   R'   =   R* ( 1 + * T)          =   Temperaturecoefficient of resistance   =   0.40* 10-3   / 0C      T   =   Changein temperature       91.50   =   82.35* ( 1 + 0.40 * 10-3 * T)           1+ 0.40 * 10-3 *T   =   91.50 /82.35   =   1.111            0.40* 10-3 *T   =   1.111   -   1.0   =   0.111          T   =   0.111/ 0.40 * 10-3   =   2.775*102   =   277.50   0C       Finaltemperature   T   =   T   +   initialtemperature   =   277.5 +20   =   297.50   0C

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