Re: infinite square lattice of resistors

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

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