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

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestOh my.

Log in to reply

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.

Log in to reply

Here is the 2-d version of the problem.

Log in to reply

It must be R/3

Log in to reply

Solution ?

Log in to reply

I asked for diagonally opposite points. Not adjacent ones

Log in to reply

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

Log in to reply

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

I can't post a picture of my solution here

Log in to reply

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

Log in to reply

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

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

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

Log in to reply