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Pouillet's law, $R = \rho \frac{\ell}{A}$, is useful when dealing with a "column" (cylinder) of a conducting material, with cross section $A$ and height $\ell$. Using this equation has an underlying assumption: the contribution to the conductance from the surrounding environment of the cylinder is zero.

But how do I calculate the resistance (or conductance) between two given points (electrodes) that are embedded into a general shape object (for example submerged in water), assuming the surrounding environment is infinite in all directions?

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  • $\begingroup$ Is it water that you really care about, or are you more interested in how to compute resistance when you have two electrodes embedded into a 3D object which is not a cylinder? $\endgroup$
    – DanielSank
    Commented Aug 5, 2015 at 16:52
  • $\begingroup$ @DanielSank, water is just one (common) example; I'm more interested in the general case you mentioned. $\endgroup$
    – Sparkler
    Commented Aug 5, 2015 at 16:54
  • $\begingroup$ You may want to edit the question to make it clear that you're asking how to compute resistance through a general shape solid. The title specifically asks about water, so people who don't know about electricity in water, but do know about the methods needed to answer your real question, may not click! $\endgroup$
    – DanielSank
    Commented Aug 5, 2015 at 17:07
  • $\begingroup$ @DanielSank, done :) $\endgroup$
    – Sparkler
    Commented Aug 5, 2015 at 17:11
  • $\begingroup$ Nice! By the way, we have a FAQ about writing good titles. Unfortunately I don't know how to answer this question. I hope someone else does :-) $\endgroup$
    – DanielSank
    Commented Aug 5, 2015 at 17:27

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Pouillet's Law is valid in general, but the specific values of l and A depend in the shape and environment of the resistor. See https://www.academia.edu/1841457/The_Notion_of_Electrical_Resistance

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