TITLE:
Solving Electrical Circuits via Graph Theory
AUTHORS:
Jan Vrbik
KEYWORDS:
Kirchoff’s Laws, Connected Graph, Incidence Matrix, Spanning Tree, Fundamental Cycles
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.1,
January
25,
2022
ABSTRACT: Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution of more complex cases requires good understanding of the relevant part of Graph theory. Even though this is usually not covered by Physics’ curriculum, it may still be of interest to some teachers and their mathematically inclined students, who may want to learn details of the rigorous approach. The purpose of this article is to provide a concise derivation of a linear set of equations leading to a unique solution of the problem at hand. We also present a simple computer program which builds such a solution for circuits of any textbook size.