From: Chris Carlen
User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.1) Gecko/20020826
X-Accept-Language: en-us, en
Subject: Re: Another resistor problem--answer?
Date: Thu, 05 Dec 2002 05:25:47 GMT
NNTP-Posting-Date: Wed, 04 Dec 2002 21:25:47 PST
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.
Until then, perhaps I'll get another chance to play with this in a few days.
Christopher R. Carlen
Suse 8.1 Linux 2.4.19