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Sheet Resistance Geometry Problem

  1. Feb 20, 2009 #1
    You have a half sphere with a radius of 1mm made up of an insulating material. This insulator is covered by a thin conductive material 1um thick. (1x10^-6 m) This material has a resistivity of 5x10^-8 ohm m. One electrode has a diameter of .5 mm and is centered at the bottom of the half sphere. The other electrode is around the rim of the sphere and makes contact with the conductive film all the way around the "equator" if you will. What is the effective resistance of this material in this geometry?

    Half sphere with radius 1x10^-3 meters
    Coating Thickness = 1x10^-6 meters
    Resistivity = 5x10^-8 ohm m
    Diameter of one electrode 5x10^-4 meters

    I don't even know where to start. I figure if I knew the resistance of a triangular shape with electrodes on each edge I could break the sphere up into "slices" and integrate treating each slice as a seperate resistor in parallel. 1/Rtotal = 1/R1 + 1/R2 etc... but it would require knowing the resistance of a thin film with a triangle shapped geometry.

    Can anybody help? Or at least start me in the correct direction...

    Thanks!
     
  2. jcsd
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