From: Robert Baer
X-Mailer: Mozilla 4.75 [en] (Win98; U)
Subject: Re: Another resistor problem
Date: Wed, 04 Dec 2002 09:21:08 GMT
NNTP-Posting-Date: Wed, 04 Dec 2002 01:21:08 PST
Organization: EarthLink Inc. -- http://www.EarthLink.net
> 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
Extra credit: how many bytes in an Apple?