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

## Comments

Sort by:

TopNewestOh my. – Josh Silverman Staff · 1 year, 1 month ago

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. – Pranjal Prashant · 1 year, 1 month ago

Log in to reply

Here is the 2-d version of the problem. – Calvin Lin Staff · 1 year, 1 month ago

Log in to reply

It must be R/3 – Jatin Chauhan · 6 months, 3 weeks ago

Log in to reply

– Rajdeep Dhingra · 6 months, 3 weeks ago

Solution ?Log in to reply

– Pranjal Prashant · 6 months ago

I asked for diagonally opposite points. Not adjacent onesLog 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 – Ishan Tarunesh · 1 year, 1 month ago

Log in to reply

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

I can't post a picture of my solution here – Vincent Miller Moral · 1 year, 1 month ago

Log in to reply

– Ishan Tarunesh · 1 year, 1 month ago

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

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. – Yeshas Bharadwaj · 1 year, 1 month agoLog in to reply

– Pranjal Prashant · 1 year, 1 month ago

Now what significance pushing values is of, the question is not an mcq, I want to know how it can be done, and I am sure that it is solvable. {although answer would not be beautiful perhaps}.Log in to reply

– Yeshas Bharadwaj · 1 year, 1 month ago

got it but I dont know how to solve the way you told and yes the answer sure will be weirdLog in to reply

– Pranjal Prashant · 1 year, 1 month ago

NO, IT IS NOT SO. In the fourier series , steps of integration are nasty, but answer is simply 2r/ \(\pi\)Log in to reply

– Yeshas Bharadwaj · 1 year, 1 month ago

thanks for the info I will surely try to get the steps for your answer.Log in to reply

– Ishan Tarunesh · 1 year, 1 month ago

I could not understand "push the single cube value to an exact number". Also think of 2-D grid of infinite resistors in which we have to find the equivalent resistance between adjacent points which everyone knows to be R/2. What will be your argument in this one? Just because other resistances are present does not mean that the net would be greater than 5R/6 because resistances in parallel decrease the valueLog in to reply

– Vincent Miller Moral · 1 year, 1 month ago

Yes it is haha, I considered only a 'cube'.Log in to reply