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?

Question

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?

drwls · Accepted Answer

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

rick · Answer

where are you getting 22.95% and what is delta T

Damon · Answer

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

Damon · Answer

Whoa - I forgot the definition. dr wls did it right !

drwls · Answer

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

anonymous · Answer

drwls is correct. To get the percentage subtract 1.22 from 1.5, then divide by 1.22