Can we find net resistance between the body diagonal points of a infinite cubic lattice

?The objective is to find net resistance between A & B of the given cube which is part of infinite grid. Let the resistance between any two adjacent vertices is R

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TopNewestOh my.

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Yes, I know about 2 d version for resistors and fourier series for getting across square diagonal 2r/pi.[you know that Ishan :D ] But this is quite different fom those, much more difficult in getting the approach. You should share this so that someone reaches at the final ansWeR.

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Here is the 2-d version of the problem.

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It must be R/3

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Solution ?

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I asked for diagonally opposite points. Not adjacent ones

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A simpler version would be two find the equivalent resistance between two diagonally opposite points in an infinite grid of resistors, which is still quite difficult. See the page I have linked Infinite grid of resistors

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Total resistance (across points A and B) = ( 5/6 ) * R

I can't post a picture of my solution here

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Incorrect, This answer holds if there was a single cube of resistances rather than an infinite one.

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but infinite series of resistors just push the "single cube value" to an exact number so my idea is that effective resistance is near (5/6)

R (like 0.85R or 0.9R max but not less than (5/6)R). Please notify me if there is a mistake in my assumption.Log in to reply

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Yes it is haha, I considered only a 'cube'.

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