The Heating of Nichrome Wire in a toaster


by gc33550
Tags: circuit, current, nichrome, ohm's law, resistance
gc33550
gc33550 is offline
#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
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#2
Sep24-09, 03:39 PM
P: 1,351
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
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#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
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#4
Sep24-09, 04:20 PM
P: 1,351

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
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#5
Sep24-09, 05:17 PM
P: 23
C as in capacitance? How do I find that?
willem2
willem2 is offline
#6
Sep24-09, 05:31 PM
P: 1,351
Quote Quote by gc33550 View Post
C as in capacitance? How do I find that?
no it's just an arbitrary constant
gc33550
gc33550 is offline
#7
Sep24-09, 05:33 PM
P: 23
would that constant be in my physics book somewhere?


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