Homework Help: Resistivity Problem

1. Feb 15, 2008

Sino87

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

2. Relevant 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-?

3. 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.

Last edited: Feb 15, 2008
2. Feb 15, 2008

Astronuc

Staff Emeritus
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 = po(1 + alpha(To-T)), where To = 20°C.

3. Feb 15, 2008

Cynapse

R = po(1 + alpha(To-T))
i dont think thats right becuse po = RA/l

4. Feb 16, 2008

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

5. Feb 16, 2008

Sino87

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

6. Feb 16, 2008

physixguru

yes i did post there....

7. Feb 16, 2008

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.

Last edited: Feb 16, 2008
8. Aug 15, 2011

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.

9. Oct 24, 2011