The limb analysis of countably infinite electrical networks

IEEE Circuits Syst. Mag.

1984

What is the driving-point resistance across the diagonal of a square face-or more generally, between any two nodes-of a uniform infinite square grid of 1-[2 resistances? This puzzle has been cropping up in the electrical engineering literature for many decades and reappeared in two recent issues of IEEE Circuits and Systems Magazine. Described herein is an analysis that completely resolves the matter. In fact, it does so for the general case of an n-dimensional resistive grid whose resistors are all the same, or perhaps vary in one direction only.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A classical puzzle: The driving-point resistances of infinite grids

IEEE Circuits Syst. Mag.

1984

A solution for an infinite electrical network arising from various physical phenomena

Subramaniam²

1983

Circuit Theory & Apps

SUMMARYA procedure for determining the currents and voltages in a square or cubic grounded grid, wherein the grounding conductances can differ in quite arbitrary ways, is presented. Such a semi-infinite electrical network is of practical importance, for it arises naturally from the discretization of a number of physical phenomena. There are very few classes of infinite electrical networks for which computational methods of solution exist; the present work adds one more class to that brief list.

A matroid related to finitely chainlike, countably infinite networks

Tucker

1982

Networks

The determination of the currents and voltages in a countably infinite electrical network containing infinite energy requires not only the imposition of Kirchoff's laws and Ohm's laws but also the arbitrary assignment of the current-voltage pairs in certain sets of branches, called joints. For finitely chainlike, countably infinite networks the maximal joint sets satisfy the base axioms of a matroid.