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Subject: Re: Another resistor problem
NNTP-Posting-Date: Thu, 05 Dec 2002 03:36:12 GMT
Organization: AT&T Broadband
Date: Thu, 05 Dec 2002 03:36:12 GMT
> 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.
Er, um 1/2 ohm?
> But what about a pair of diagonally adjacent nodes? That is, what is
> the resistance between nodes (1,1) and (2,2)?
Ok, take a uniform sheet and distort its conductance preferentially
along two orthogonal axes. Let's see, that would be 1/2 ohm times the
non isotropic square lattice conduction factor of 4/Pi. Hmmm...
> Show your work.
Sorry. I never show my work on a first post.
> 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
As I recall, it should be one over one, but I'm only going by fading
memories from double E classes long past, so forgive me if I may have
inadvertently inverted my answer. -- analog