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Re: infinite square lattice of resistors



Ludwik,

It seems Carl asked about the edge and diagonal resistances for
an infinite simple cubic *lattice* since he wrote:

For that matter, what's the resistance along a single edge rather than a
diagonal? Or what are the resistances for a simple cubic lattice along an
edge, face diagonal, and body diagonal? ^^^^^^^^^^^^^^^^^^^^

Your solution is a very nice explanation for why the resistance
across the body diagonal of a *single cube* is (5/6)*r. Too bad the
current in the uniform lattice can't be taught to flow only in a single
unit cell of the lattice when it is connected to the rest of the lattice
with finite resistance resistors. Your solution *does* have the virtue
of being an upper bound on the solution for the lattice problem though.
And the single cube is a fun case to consider in its own right.

Let me try the last case (R along the "body diagonal" for a single
cubical cell of identical resistors). Each of the 12 resistors is r.
See below.
<snip solution>

David Bowman
David_Bowman@georgetowncollege.edu