Question

A certain toaster has a heating element made of Nichrome resistance wire. When the toaster is first connected to a 120 V source of potential difference (and the wire is at a temperature of 20.0°C), the initial current is 1.90 A, but the current begins to decrease as the resistive element warms up. When the toaster reaches its final operating temperature, the current has dropped to 1.5 A. (d) Determine the operating temperature of the heating element.

Answer 1

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Ans:

From Ohm's law:

V = i*R

R0 = resistance at 20 C

R0 = V/I0 = 120/1.90 = 63.16 Ohm

At the operating temperature, suppose resistance is R1

R1 = V/I1 = 120/1.5 = 80 Ohm

Temperature coefficient of Nichrome is = alpha = 0.4*10^-3 (Check this value in your reference book, if it's different let me know)

So we know that

R1 = R0*(1 + alpha*(Tf - Ti))

Ti = 20 C

Tf = operating temperature = ?

Tf = Ti + (R1 - R0)/(R0*alpha)

Tf = 20 + (80 - 63.16)/(63.16*0.4*10^-3)

Tf = 686.6 C

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