Changes in Resistance due to Temperature

[dari09]

Homework Statement

When a metal rod is heated, not only its resistance but also its length and its cross-sectional area change. The relation R = L/A suggests that all three factors should be taken into account in measuring at various temperatures.
(a) If the temperature changes by 5.0 C°, what percentage changes in R, L, and A occur for a copper conductor? The coefficient of linear expansion is 1.7 10-5/K.

Homework Equations

delta L = L initial (delta T) (alpha)

R = density L/A

The Attempt at a Solution

I got the answer to the percentage changes of L and A using the equation
L = L initial (delta T) alpha.
I tried to plug those answers into the equation R = density L/A which gives the answer.5
Unfortunately that answer is wrong and and now I am currently lost.

The percent changes of L and A are:
delta L / L initial = .0085%
delta A / A initial = .017%

 

[Mapes]

Hi dari09, welcome to PF. Unfortunately, $\rho$ is used to mean multiple things in engineering, including density and (in this case) resistivity, which is a material property with units $\Omega\cdot m$. You can see how that correctly makes ohms the unit of resistance.

You need to find the resistivity $\rho$ of copper at the two different temperatures.

 

[Moetasim]

To find the percentage change in R, you can use the formula:

delta R / R initial = (delta L / L initial) + (delta A / A initial)

Substituting the values we found earlier, we get:

delta R / R initial = .0085% + .017% = 0.0255%

This means that for every 1% change in temperature, there will be a 0.0255% change in resistance for a copper conductor. It is important to take into account all three factors (length, cross-sectional area, and temperature) when measuring resistance at different temperatures to get an accurate measurement.