2014/12/23 by Mikhail Kagan · 25 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Electrical network #Electronic circuit #Equivalent circuit #Graph theory #Graph theory and applications #Low-power high-performance VLSI design #Mathematical proof #Matrix (chemical analysis) #Network analysis #Quantum Computing Algorithms and Architecture #Wheatstone bridge #physics.class-ph
paper · pdf · doi:10.1119/1.4900918
published in American Journal of Physics 83(1), 53-63 (American Institute of Physics) · 27 pages, 5 figures
openalex publication_date 2014/12/23 · arxiv created 2015/06/26 · arxiv updated 2015/07/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
While the standard (introductory physics) way of computing the equivalent resistance of nontrivial electrical circuits is based on Kirchhoff's rules, there is a mathematically and conceptually simpler approach, called the method of nodal potentials, whose basic variables are the values of the electric potential at the circuit's nodes. In this paper, we review the method of nodal potentials and illustrate it using the Wheatstone bridge as an example. We then derive a closed-form expression for the equivalent resistance of a generic circuit, which we apply to a few sample circuits. The result unveils a curious interplay between electrical circuits, matrix algebra, and graph theory and its applications to computer science. The paper is written at a level accessible by undergraduate students who are familiar with matrix arithmetic. Additional proofs and technical details are provided in appendices.