Re: infinite square lattice of resistors

["Prof. John P. Ertel (wizard)" <jpe@NADN.NAVY.MIL>]

I'll bet if I mention the fact that the parallel resistance is always
smaller than the smallest resistance in the "group" you would almost
immediately spot the solution.


On Mon, 11 Oct 1999, Carl E. Mungan wrote:

> > Okay, somebody let me in on the trick for the resistance across a single
> > diagonal of the infinite square lattice of say one-ohm resistors. I'd like
> > both the elegant solution from symmetry which Leigh implied exists, and I'd
> > like to know the formal Fourier method to go between any pair of junctions --
> > or at least a sketch of the basic idea behind the latter if it's very
> > complicated.
> >
> > I can see that the infinite lattice is symmetric across a diagonal and
> > hence if I can find the resistance of one of these half planes, I would
> > just need to need to halve that to get the desired answer. I also remember
> > the trick for the infinite-in-one-dimension ladder of resistors. But
> > neither of these ideas seems to help me make much progress on Leigh's
> > problem.
> >
> > 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?
> >
> > Dr. Carl E. Mungan, Assistant Professor     http://www.uwf.edu/~cmungan/
> > Dept. of Physics, University of West Florida, Pensacola, FL   32514-5751
> > office: 850-474-2645 (secretary -2267, FAX -3323) email: cmungan@uwf.edu

+=================================+=================================+
ERTEL SENDS.
                               /^\-/^\
                              /       \
                             |    *    |
                             |#########|
                     ===========================
                       / Prof. John P. Ertel \
                      / USNA-NESA Faculty Rep \
                     /   veteran Eagle Scout   \
 +==============================================================+
 |     JPE@nadn.navy.mil         or         JPErtel@BigFoot.com |
 |   Physics Department, 9C               Office : 410-293-6657 |
 |     Michelson  Rm-338                     DSN :     281-6657 |
 |      572 Holloway RD                      FAX : 410-293-3729 |
 |    U. S. Naval Academy                                       |
 |   Annapolis, MD 21402-5026          HomeVoice : 410-757-6618 |
 | {Call HomeVoice to activate FAX}      homeFAX : 410-757-6619 |
 +==============================================================+
     http://physics.usna.edu/physics/Faculty/Ertel/ertel.html
            http://physics.usna.edu/ECAs/NESA/nesa.htm