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Resistance versus Temperature

  1. Sep 22, 2005 #1
    A copper wire has a resistance of 0.501 ohms at 20.0 degrees C, and an iron wire has a resistance of 0.487 ohms at the same temperature. At what temperature are their resistances equal?

    Resistivity of Copper: .0039
    Resistivity of Iron: .0005
     
  2. jcsd
  3. Sep 22, 2005 #2
    Try this formula

    [tex]\frac{{\Delta R}}{R_0} = \alpha \Delta T[/tex]


    You need to look up the alpha
     
  4. May 1, 2011 #3
    For pure metals the relationship is (almost) linear and the formula is:
    R=R0[1+[tex]\alpha[/tex](T-T0)

    FYI the figures quote are temperature coefficients measured in K-1 (degrees Celsius to the minus one is also fine, as the increments are the same. Just don't mix the two as values for T and T0 in one calculation):

    Where you want the resistance to be equal, you just back the copper and iron halves of the equation together (copper on the left, iron on the right).

    0.501 [1 + 0.0039 (T - 20)] = 0.487 [1 + 0.0005 (T - 20)]

    Multiply the lot out, so as to separate T
    0.501 + 0.0019539T - 0.039078 = 0.487 + 0.0002435T - 0.00487

    Real numbers on the left, expressions in T on the right
    0.501 - 0.487 - 0.039078 + 0.00487 = (0.0002435 - 0.0019539)T
    -0.020208 = -0.0017104T

    Divide both sides by -0.0017104
    T=11.81478017 degrees Celsius

    It you subs in [T-20] as -8.185 into either equation to double check, at T, the resistance will be about 0.485[tex]\Omega[/tex]

    6 years late, but hope this helps.
     
    Last edited: May 1, 2011
  5. May 3, 2011 #4
    On reflection, I have noticed that Iron has a resistance temperature coefficient of 0.005K-1, not 0.0005K-1. The principle of working through it is still correct, but this answer is only correct for the question asked incorrectly ...if that makes any sense :smile:
     
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