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Suppose you have a thin sheet of a material of size say (1mtr X 2mtr X 1mm). You do not know what material it is. How to find its resistivity? One way I can think of is to measure resistance across smallest cross section i.e. 1mtr X 1mm, and then using $\rho = R\frac{A}{l}$, one can calculate the resistivity. However, in case of metal alloys, resistivity can be very low resulting in very low values of resistance which may not be picked by general multimeter and one may have to use micro ohm meter. Will this method work given the unusual shape of the conductor? Is there any other way to calculate the resistivity?

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Generally, for thin sheets, we measure sheet resistance by using a three point or four point probe method. Then, you can find the resistivity of the material by using a relation between sheet resistance, resistivity and thickness of the sheet.

Sheet Resistance and the Calculation of Resistivity or Thickness Relative to Semiconductor Applications

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No it will not work for unusual shape. Because resistance varies as area of the conductor varies. So to calculate resistivity you must pick a part of your sample whose area remains same between the two point at which you connected the multi-meter and then calculate the area and length between those two points to find the resistivity.

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  • $\begingroup$ By unusual shape I meant the sheet described in the question. Unlike a wire it has large cross section. Will the method work for a sheet? $\endgroup$ – akm Nov 26 '16 at 14:33
  • $\begingroup$ Yes It will work. $\endgroup$ – Taha Nov 27 '16 at 12:26
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Given a homogenous Material with only scalar resistivity like in ordinary metals, you can derive the resistivity for any given shape by integration, after you have acquired one measurement of resistance between two planar contacts. This can be tedious with pen and paper, but it is at least possible. Depending on the complexity if the shape you can go straight ahead with integration or you have to make some assumptions and simplifications.

For inhomogenous and/or non-scalar resistivity as in crystals, it is very difficult. I think software like Ansys or Comsol will supply a sufficiently practical numerical algorithm.

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  • $\begingroup$ How will you derive resistivity when you dont know the material? $\endgroup$ – akm Nov 28 '16 at 23:45
  • $\begingroup$ @AmitMaurva I forgot to write, that you need one well defined measurement between two planar contacts. $\endgroup$ – Ariser Nov 29 '16 at 9:24

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