Solve Nichrome Wire Resistivity Problem

[Sino87]

Homework Statement

A toaster uses a Nichrome heating wire. When the toaster is turned on at 27 deg C, the initial current is 1.50A. A few seconds later, the toaster warms up and the current is now 1.30A. The avg. temp coefficient of resistivity for Nichrome wire is 4.5 x 10 ^ -4 (degree C) ^-1. What is the temperature of the heating wire?

Homework Equations

Nichrome(alloy) p=100 x 10^-8 ohm*m.
p = po [1 + alpha(T - To)]
To=20 deg C.
alpha=4.5x10^-4 (deg C)^-1
Io=1.50A
I=1.30A
T-?

The Attempt at a Solution

My attempt.

R = Ro [1 + alpha(T - To)]

R - Ro = alpha(T-To)

R=V/I

T= V(1/I - 1/Io)/alpha + 20

T = 20 + V(227.72)

V = (T-20)/227.92

T = 20 + (T-20/227.12) (227.12)

The answer is 360 deg C btw.

 

[Astronuc]

The voltage across the toaster must be constant, and the current changes (decreases) as the resistance increases with temperature. One knows the initial temperature and current, and final current, so use these to solve for the unknown temperature.

V = IR = I₁R₁ = I₂R₂, and then write R from R = p_o(1 + alpha(T_o-T)), where T_o = 20°C.

 

[Cynapse]

R = po(1 + alpha(To-T))
i don't think that's right becuse po = RA/l

 

[physixguru]

Actually (I think you know what you have done wrong by now)...

R=R0( 1+ a(T-T0))

T= T0 + (R - R0 )/a
R = V/I
R0=V/I0
T= 20 + V(1/I - 1/I0)/a

what was the voltage?

T= 20 + V( 1/1.30 - 1/1.5)/ 4.5x10^-4=
T= 20 + V(227.92)

for 12 V we have plenty...

T= 20 + 12(227.92)=2760 C

 

[Sino87]

^Did you post on yahoo answers? Well anyways, no voltage was given and the answer is 360 degrees.

 

[physixguru]

yes i did post there...

 

[Sino87]

Ok lol. Yeah, I thought your posts was familiar. Thanks for the help, but the Voltage wasn't given in the problem. Your method totally makes sense, but when I solve for V and replug it into the original equation I get 20 deg C, when it should be 360 deg C.

 

[solas99]

Given the following data on copper, how do i calculate the resistivity?

Relaxation time: 2.50e10-14s
Density: 8940Kgm-3
molar mass: 63.5g

is there an equation for it.

 

[sec8]

i have a question on resistivity which i can't do, anyone please help me.
Question: Calculate the resistance of a rectangular strip of copper length 0.08m, thickness 15mm and width 0.80mm. The resistivity of of copper = 1.7 x 10^-7. Equations that are relevant:
Resistance= resitivity x length/Area. Resistance measured in ohms of course.
for a conductor with a circular cross section of diameter,d = pi(3.142) x d squared/4.
pleaseee help