The behavior of resistive circuits

Abstract

We apply the modeling methodology of tearing, zooming, and linking to passive linear resistive circuits. The purpose of the article is to present necessary and sufficient conditions that govern the terminal voltage/current behavior of such a circuit. In its simplest form, these conditions require the matrix that relates the voltage vector to the current vector to be symmetric hyperdominant with zero excess. We also discuss the decomposition of a resistive circuit into a set of indecomposable components.