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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Top NewestOh 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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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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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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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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Yes it is haha, I considered only a 'cube'.
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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.
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π
NO, IT IS NOT SO. In the fourier series , steps of integration are nasty, but answer is simply 2r/Log in to reply
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see 2nd answer to the question in the link https://physics.stackexchange.com/questions/2072/on-this-infinite-grid-of-resistors-whats-the-equivalent-resistance It's for n dimensional grid
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