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Homework Help: Stuck-Resistivity problem

  1. Mar 29, 2010 #1
    1. The problem statement, all variables and given/known data

    A transmission line is made of aluminum wire 1 inch in diameter. What is the resistance of 20 miles of this wire?

    2. Relevant equations

    Resistance varies directly with the length of a wire and inversely with its cross-sectional area.
    Resistivity of aluminum = 2.8 x 10-8
    R=pl/A
    Where l=32,186.88 meters
    Find cross-sectional area.

    R= 2.8 x 10-8 (31,186.88)/A =


    3. The attempt at a solution

    I'm stuck trying to find the cross-sectional area, A.

    Also, the answer has to be in the same units as the problem, so does that mean I have to convert to inches and miles? The answer should be in ohms correct?
     
  2. jcsd
  3. Mar 29, 2010 #2

    rock.freak667

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    The wire is like a long shaft or a long cylinder, so the cross-sectional area is?

    Also, you need to convert everything to same set of units. What is the resistivity measured in?
     
  4. Mar 29, 2010 #3
    The cross-sectional area would be the diamter then? Converted to meters, we get


    R= 2.8 x 10-8 (32,186.88)/0.0254 = .0354816 ohm-metres

    correct?
     
  5. Mar 29, 2010 #4

    rock.freak667

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    No, the cross-section of the wire is just a circle with diameter 'd'. So the area of a circle is ?
     
  6. Mar 30, 2010 #5
    SO - Cross-Sectional Area= = Area: (pi)(.0127) ² = 5.067E-4

    R= 2.8 x 10-8 (32,186.88)/ 5.067E-4 = 1.79 ohm-metres
     
  7. Mar 30, 2010 #6

    rock.freak667

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    Yes that should be correct now.
     
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