Here is the problem. You need to model the resistance across a circular sheet of polypropylene (plastic). The resistivity of polypropylene is 1E15 Ohms per meter. The expression for resistance on a wire is:
But, this expression does not help with a sheet of plastic. The geometry of the sheet is shown below. It runs from a 6 mm diameter (along the edge of the anode) to 2 mm inner diameter (along the edge of the cathode).
Here is what I tried. I modeled the sheet like a series of tiny wires. I said each wire was 1E-8 meters wide. Doing this gave me a cross section area for my little wires. Then I multiplied by length and got the resistance along my small wire. Then I multiplied by the number of wires, which was the average diameter divided by 1E-8 meters.
I thought I was pretty clever.
But, this did not work, because the system should converge to a final solution. As the small wires got thinner and thinner, the solution should reach some final number… but it does not.
How do you model the resistance across a symmetric sheet of plastic, streched (think ceran wrap) between a circular anode and cathode?