Mikhail Kagan. On Equivalent Resistance of Electrical Circuits
Natural Sciences / Physics / General Physics
Submitted on: Nov 11, 2013, 22:43:52
Description: One of the basic tasks related to electrical circuits is computing equivalent resistance. In some simple cases, this task can be handled by combining resistors connected either in series or in parallel, until the original circuit reduces to a single element. When this is not possible, one resorts to the Eheavy artilleryE of Kirchhoff's rules or method of nodal potentials. In this paper, we apply the latter method to derive - in a closed form - the equivalent resistance of a generic circuit. This result unveils a curious interplay between electrical circuits, matrix algebra, graph theory and its applications to computer science.