From: Chris Carlen
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Subject: Re: Another resistor problem
References: <firstname.lastname@example.org> <3DEDC939.32BEA236@earthlink.net>
Date: Thu, 05 Dec 2002 04:58:21 GMT
NNTP-Posting-Date: Wed, 04 Dec 2002 20:58:21 PST
Robert Baer wrote:
> Phantom wrote:
>>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)?
>>Show your work.
>>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
> Those are rather ohmly problems; try converting a resistive "wye"
> network to a resistive "delta" network, and vice versa; give equations
> for the general case and explain how the equations were derived, step by
That's a bit simpler that what Phantom is proposing, it seems to me.
Christopher R. Carlen
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