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Homework Help: Changes in Resistance due to Temperature

  1. Apr 7, 2008 #1
    1. The problem statement, all variables and given/known data

    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.


    2. Relevant equations

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

    R = density L/A

    3. 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%
     
  2. jcsd
  3. Apr 7, 2008 #2

    Mapes

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    Science Advisor
    Homework Helper
    Gold Member

    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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