Thread: I dont even know where to start with this phycis question can anybody pleassee help?

A toaster uses a heating wire. When the toaster is turned on at 18 °C, the initial current is 1.22 A. A few seconds later, the toaster warms up and the current has a value of 0.921 A. The average temperature coefficient of resistivity for this wire is 6.3 x 10-4 (C°)-1. What is the temperature of the heating wire?

Ignoring the change in dimension due to heating we can assume that the resistance of the wire changes linearly with temperature:
R = R??(1 + ??(T - T?) )
where ? is the temperature coefficient of resistivity.

Let R? be the resistance at T?=18°C

The current is given by Ohm's law
V = R?I

Since the the voltage of the power source does not change during the heating process
R?I = R??I?
<=>
R??(1 + ??(T - T?) )?I = R??I?
<=>
(1 + ??(T - T?) )?I = I?
<=>
??(T - T?) = (I?/I) - 1
=>
T = T? + ( (I?/I) - 1)/?
= 20°C + ( (1.22A/0.921A) - 1)/6.3×10??°C?¹
= 533°C