Posted by **rick** on Wednesday, January 30, 2008 at 9:16pm.

A toaster uses a Nichrome heating wire. When the toaster is turned on at 20°C, the initial current is 1.50 A. A few seconds later, the toaster warms up and the current has a value of 1.22 A. The average temperature coefficient of resistivity for Nichrome wire is 4.5 10-4 (C°)-1. What is the temperature of the heating wire?

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**drwls**, Wednesday, January 30, 2008 at 9:25pm
The relative change in resistivity as the wire heats up is 1.50/1.22 = 1.2295. That is a 22.95% INCREASE.

(delta T)* coefficient of resistivity = 0.2295

delta T = 0.2295/4.5*10^-4 = 510 C

T = 510 + 23 = 533 C

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**Damon**, Wednesday, January 30, 2008 at 9:37pm
R = V/i , V is constant here

V/i2 = V/i1 (T2-T1)k

i1 = i2 (T2 - 20) k

1.5 = 1.22 (T2 - 20)(4.5 * 10^-4)

15000 = 5.49 T2 - 110

You can get it from there

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**Damon**, Wednesday, January 30, 2008 at 9:43pm
Whoa - I forgot the definition. dr wls did it right !

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**drwls**, Wednesday, January 30, 2008 at 11:47pm
In answer to your followup questions: delta T is the increase in temperature. The 22.95% resistance increase was explained in my first calculation. 1.2295 is the inverse of the current decrease factor, 1.22/1.50. Since I = V/R, the current varies inversely with the resistance at constant voltage

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**anonymous**, Tuesday, July 17, 2012 at 12:02pm
drwls is correct. To get the percentage subtract 1.22 from 1.5, then divide by 1.22

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