Diameter of copper wire to have same resistance as equal length aluminum wire

  1. 1. The problem statement, all variables and given/known data
    What diameter must a copper wire have if its resistance is to be the same as that of an equal length of aluminum wire with diameter 3.94mm?

    Give your answer in mm


    2. Relevant equations

    R = ρL/A

    where A is the cross sectional area, L is the length and ρ resistance of the material

    ρCopper = 1.72x10-8 Ωm
    ρAluminum = 2.82x10-8 Ωm
    3. The attempt at a solution

    So I knew that Rcopper = RAluminum

    (1.72x10-8Ωm)(L)/Acopper = (2.82x10-8Ωm)(L)/(0.00394m)

    A = 0.00240 m
    A = πr2

    r = 0.027657 m

    diameter = 55.31499 mm

    But the system says its wrong and I don't see where I've gone wrong.
     
  2. jcsd
  3. collinsmark

    collinsmark 2,171
    Homework Helper
    Gold Member

    Start with what I've highlighted above in red.

    • What are units for area: meters or square meters?
    • Before calculating the cross section area of the copper wire, first ask, what is the cross sectional area of the aluminum wire? :wink:

    [Edit: On a much lesser note, and I'm not sure if this matters, according to some sources I've looked at on the Internet, 1.72x10-8 Ωm is the resistivity of annealed copper. Plain old copper has a very similar resistivity, but slightly different. Use whatever your course material advises. And again, the difference is small and I'm not sure if copper vs. annealed copper matters.]
     
    Last edited: Oct 2, 2012
  4. I see what you're saying.

    The cross section area od aluminum is π(0.00197m)2

    3.8809x10-6 m2

    Then solving for the cross sectional area of copper I get

    Acopper = 7.4364x10-6 m2

    rcopper wire = sqrt(7.4363x102/π)

    Diameter of copper wire = 2r = 3.077059 mm

    Thanks for your help
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook