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Resistivity of Cylinder

  1. Aug 5, 2010 #1
    1. The problem statement, all variables and given/known data
    A cylinder of radius a with a hole through it (of radius a/2) is filled with a material of resistivity p_2. Show that the total resistivity is now 4*(pL / pi*a²) (p_2 / 3p_2 + p)

    2. Relevant equations

    3. The attempt at a solution
    I started with a full cylinder and a single value of p:

    Then worked my way to a cylinder with a hole in it (empty):
    A_full - A_hole = pi*a² - pi*(a/2)² and found A= (3/4)*pi*a² so:
    R = (4/3) * pL / pi*a²

    Now I know that I need to add both values of p somehow, but I'm unsure of the relation between 2 materials with different values of p.
  2. jcsd
  3. Aug 5, 2010 #2


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    Think of it as two resistors in parallel.
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