From: snyder@henry.ece.cmu.edu (John Snyder)
Newsgroups: sci.physics
Subject: Re: ... an infinite mesh of 1ohm resistors ...
Date: 28 Jul 92 09:32:01 GMT
Article-I.D.: fs7.1992Jul28.093201.10671
Organization: Physics Department, Carnegie Mellon University

In article <1992Jul28.000844.27051@mixcom.com> ttyytt@mixcom.com (Adam Costello) writes:
>In article <1992Jul27.210947.5820@fs7.ece.cmu.edu> snyder@henry.ece.cmu.edu (John Snyder) writes:
>>
>>I believe that you are missing the point of the previous post here.
>
>But I think you are missing the point of the second post.  The "solution"
>involved imagining that you could inject an amp of current into a network
>of resistors.  No capacitors!  Where is the charge supposed to go?
                ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Hunh?  What do capacitors have to do with it?
Surely, you can pass 1 amp through a network of resistors with
no capacitors present.  We solved *MANY* such problems in Electrical
Engineering 101 (groan! (:^)).  The current goes in at terminal A, and 
out at terminal B.  I cannot seem to locate the original problem, but my 
recollection is that there were 2 terminals involved.

>Regardless of whether this can be done in the laboratory, there's still
>the question of whether it can be done in the mind.  Certainly, if the
>network were finite, it would make no sense.  Does the infinitude of the
>network allow a source with no sink?  We can argue that it does this way:
>
>Consider this sequence of networks:
>
>+-----+-----+     +-----+-----+-----+-----+
>|     |     |     |     |     |     |     |
>|     /     |     |     /     /     /     |
>|     \     |     |     \     \     \     |
>|     /     |     |     /     /     /     |
>|     |A    |     |     |     |     |     |
>+-/\/-+-/\/-+     +-/\/-+-/\/-+-/\/-+-/\/-+
>|     |     |     |     |     |     |     |
>|     /     |     |     /     /     /     |
>|     \     |     |     \     \     \     |
>|     /     |     |     /     /     /     |
>|     |     |B    |     |     |A    |     |
>+-----+-----+     +-/\/-+-/\/-+-/\/-+-/\/-+     And so on...
>                  |     |     |     |     |
>                  |     /     /     /     |
>                  |     \     \     \     |
>                  |     /     /     /     |
>                  |     |     |     |     |
>                  +-/\/-+-/\/-+-/\/-+-/\/-+
>                  |     |     |     |     |
>                  |     /     /     /     |
>                  |     \     \     \     |
>                  |     /     /     /     |
>                  |     |     |     |     |B
>                  +-----+-----+-----+-----+
>
>In each network, connect a 1 amp current source from B to A.  In the
>limit, we have the infinite network with a source and no sink.  I'm
>still not convinced, because I'm not sure "limit" makes sense here.
>Any comments?
>
>AMC


Just because the network is infinite does *NOT* mean that the resistance
is infinite.  Consider the following simple example:  A parallel circuit,
one leg has 1 ohm resistance, the other has near-infinite (or infinite)
resistance.  What is the equivalent resistance?  (surely not infinite)  
Can you pass current through it? (of course).  Now consider that near-
infinite resistor to be a huge network of resistors.  The solution is still
the same.  How much current flows thru that huge network leg?  (Almost none)
I believe that the original post had 2 terminals.  One does not 
talk about the resistance at a point, only the equivalent resistance between 
2 terminals.

John
snyder@henry.ece.cmu.edu
Newsgroups: sci.physics