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The Heating of Nichrome Wire in a toaster

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gc33550
#1
Sep24-09, 03:12 PM
P: 23
1. The problem statement, all variables and given/known data

A toaster with a Nichrome heating element has a resistance of 70 ohms at 20oC 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]/(Tf-To)

3. The attempt at a solution
I know that the voltage will remain constant therefore:
Io*Ro=If*Rf
I also know that Nichrome's [tex]\alpha[/tex]=100e-8
but I don't really know where to go from here
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willem2
#2
Sep24-09, 03:39 PM
P: 1,396
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
#3
Sep24-09, 03:43 PM
P: 23
So am I going to be looking at resistivity then? such as [tex]\rho[/tex]=R*A/L ??

willem2
#4
Sep24-09, 04:20 PM
P: 1,396
The Heating of Nichrome Wire in a toaster

Quote Quote by gc33550 View Post
So am I going to be looking at resistivity then? such as [tex]\rho[/tex]=R*A/L ??
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
#5
Sep24-09, 05:17 PM
P: 23
C as in capacitance? How do I find that?
willem2
#6
Sep24-09, 05:31 PM
P: 1,396
Quote Quote by gc33550 View Post
C as in capacitance? How do I find that?
no it's just an arbitrary constant
gc33550
#7
Sep24-09, 05:33 PM
P: 23
would that constant be in my physics book somewhere?


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