Re: Simple Question
- From: "Bob Myers" <nospamplease@xxxxxxxxxxxxxxx>
- Date: Tue, 26 Sep 2006 20:48:03 GMT
"Leo Meyer" <leomeyer_LIKES_NO_SPAM@xxxxxx> wrote in message
news:efc19b$mct$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxx
My answer would have been zero ohms.
I believe that you are correct.
The theory:
If you connect two resistors in parallel, the resulting resistance is
always lower than the lowest of either's values. So, if you connect an
infinite number of resistors in parallel, the value is infinitely lower,
which is, by definition, 0.
But this wasn't the case here, at least as I understood
the problem. The original post described an infinite
"grid" of resistors - i.e., imagine an infinitely large
grid of squares, with each "node" (every point within
the grid where the corners of the squares meet) connected
to the adjacent nodes by a one-ohm resistor. Now measure
the resistance between any two adjacent nodes, and see
what you get.
The answer clearly can't be zero. The situation is actually
very analogous to determining the resistance between
two points separated by a finite distance, but within an
infinite plane of some conductive (but not perfectly
conductive) material. For instance, imagine a very large
sheet of thin copper; put the probes of your ohmmeter (which
presumably has a scale for sufficiently low resistances)
an inch apart in the middle of the sheet - what should you
read?
Bob M.
.
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