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Homework Help: Resistance in a wire, sanity check about units.

  1. Sep 16, 2011 #1
    1. The problem statement, all variables and given/known data

    A x cm long wire has a diameter of y mm and a resistivity of 4.0x10-7 ohm-cm. Calculate its resistance.

    2. Relevant equations

    R = p*L/A

    3. The attempt at a solution
    First, I convert the given information into SI units:
    Length = x*10^-2 m
    Diameter = y*10^-3 m
    Resistivity = 4*10^-5 ohm/m

    Next, cross-sectional area of a wire/cylinder is pi*r^2 = pi*(d/2)^2 = (1/4)pi*d^2

    R = p*L/A = p*L/((1/4)pi*d^2) = (4 L p)/(d^2 pi)

    If x = 20 cm and y = 0.3mm,
    R = (4*20*10^-2 *4*10^-5)/((0.3*10^-3)^2*Pi) = 113.177 ohms

    Is this correct? My TA told me that I converted the units wrongly, and that the correct answer is 0.0113177 ohms.
     
  2. jcsd
  3. Sep 16, 2011 #2

    SammyS

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    How did you convert 4.0*10-7 ohm-cm to units of ohm-m ?

    1 cm = 1*10-2m .
     
  4. Sep 16, 2011 #3
    4.0*10-7 ohm-cm * 10^-2 m/cm = 4.0*10^-9 ohm-m

    Oh, that's the mistake, I did it in the opposite direction.
     
  5. Sep 16, 2011 #4

    SammyS

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    And now you should get the accepted answer.
     
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