The Heating of Nichrome Wire in a toaster

gc33550

1. The problem statement, all variables and given/known data

A toaster with a Nichrome heating element has a resistance of 70 ohms at 20^oC and an initial current of 1.6 A. When the heating element reaches its final temperature, the current is 1.39 A. What is the final temperature of the heating element?

2. Relevant equations

V=IR
[tex]\alpha[/tex]=([tex]\rho[/tex]-[tex]\rho[/tex]_o)/[tex]\rho[/tex]/(T_f-T_o)

3. The attempt at a solution
I know that the voltage will remain constant therefore:
I_o*R_o=I_f*R_f
I also know that Nichrome's [tex]\alpha[/tex]=100e-8
but I don't really know where to go from here

willem2

from [tex]

\alpha = \frac {\rho - \rho_0} {\rho} (T_f - T_0)

[/tex]

try to derive an equation for R as a function of R_0, T_0, T_f and [itex] \alpha [/itex]
you know the new R from ohms law.

The temperature coefficent of nichrome is [itex] 4 *10^{-4} K^{-1} [/itex]

gc33550

So am I going to be looking at resistivity then? such as [tex]\rho[/tex]=R*A/L ??

willem2

yes. Instead of [tex]\rho[/tex]=R*A/L you can use [tex]\rho[/tex]=R*C. You don't know what A and L are anyway, except that they are constant.

gc33550

C as in capacitance? How do I find that?

willem2

no it's just an arbitrary constant

gc33550

would that constant be in my physics book somewhere?