Subject: Re: Another resistor problem--answer?
Date: 5 Dec 2002 03:36:11 -0600
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On Thu, 05 Dec 2002 05:25:47 GMT, Chris Carlen
>I have begun an attempt at an answer to the second pert, see below...
>> Many of us have seen the old problem of the infinite planar lattice of
>> 1 ohm resistors, the nodes being arranged in a square array. Assume
>> that the nodes are the points whose coordinates are the integers on
>> the plane. Then it's easy to find the resistance between nodes (1,1)
>> and (2,1), or any other adjacent nodes where either the ordinate or
>> abscissa is constant. But what about a pair of diagonally adjacent
>> nodes? That is, what is the resistance between nodes (1,1) and (2,2)?
>I'm more comfortable with integral vector calculus than with summing
>series, so I'll skip to the next part...
>> Extra credit: If we have a sheet of isotropic resistive material,
>> infinite in extent, and using circular contacts (use silver paint on
>> teledeltos paper), measure the resistance between the contacts with
>> the distance between contacts 1000 times the diameter of the contacts.
>> Now move the contacts sqrt(2) times as far apart as they were. What
>> is the ratio of the resistance between the contacts now to what it was
>I have done some computations on this, coming to the conclusion that
>this question can't be answered as stated. Perhaps you can take a look
>at my result and point out what might have gone wrong.
Since I postulated that the sheet was infinite in extent, and I
meant in both x and y dimension, your dimensions labelled w and l
should be infinite. Your final expression would suggest that if w is
unbounded, then the resistance doesn't vary with the position of the
contacts, which is what you said. Does anybody else think this is the
>Until then, perhaps I'll get another chance to play with this in a few days.