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Need to determine resistance of an object

  1. Feb 12, 2009 #1
    1. The problem statement, all variables and given/known data

    A material of resistivity p is formed into a solid, truncated cone of height
    h and radii r_1 and r_2 at either end. Calculate the resistance of the cone
    between the two flat ends.

    You can find my awful sketch as a thumbnail.

    2. Relevant equations

    R=pL/A ,where p is resistivity.

    3. The attempt at a solution

    I know I need to calculate dR=(p*dy)/(pi*r^2). But I don't know what is r as a function of y.
     

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    Last edited: Feb 12, 2009
  2. jcsd
  3. Feb 12, 2009 #2

    Mapes

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    Your attachment isn't approved yet, but isn't r a linear function of y or, more specifically, h-y? Try to construct a function that varies linearly from r1 to r2.

    Where does the 4 come from in the denominator?
     
  4. Feb 12, 2009 #3
    Thank you. I'll try your tip. And the 4 was just a typing mistake.

    I uploaded the image. It can be found here: http://www.aijaa.com/v.php?i=3584252.jpg
     
    Last edited: Feb 12, 2009
  5. Feb 12, 2009 #4
    This is what I came up with:

    r = r2+y*(r1-r2)/h

    If I integrate dR, it gives me (p*h)/(pi*r1*r2).

    Does that look okay?
     
    Last edited: Feb 12, 2009
  6. Feb 12, 2009 #5

    Mapes

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    Looks good.
     
  7. Feb 12, 2009 #6
    Thanks for the help, Mapes!
     
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