Changes in Resistance due to Temperature

  • Thread starter dari09
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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%
 

Answers and Replies

  • #2
Mapes
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Hi dari09, welcome to PF. Unfortunately, [itex]\rho[/itex] is used to mean multiple things in engineering, including density and (in this case) resistivity, which is a material property with units [itex]\Omega\cdot m[/itex]. You can see how that correctly makes ohms the unit of resistance.

You need to find the resistivity [itex]\rho[/itex] of copper at the two different temperatures.
 

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