Back
 AM  Vol.13 No.1 , January 2022
Solving Electrical Circuits via Graph Theory
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.
Cite this paper: Vrbik, J. (2022) Solving Electrical Circuits via Graph Theory. Applied Mathematics, 13, 77-86. doi: 10.4236/am.2022.131007.
References

[1]   Halliday, D. Resnick, R. and Walker, J. (2008) Fundamentals of Physics (Vol. 2). 8th Edition, John Wiley & Sons, Hoboken.

[2]   Deo, N. (1974) Graph Theory with Applications to Engineering & Computer Science. Dover Publications, New York.

[3]   Chen, W.-K. (1976) Applied Graph Theory: Graphs and Electrical Networks. 2nd Edition, Elsevier Science, Amsterdam.

[4]   Khalifa, W.R. and Jasim, T.H. (2021) On Study of Some Concepts in Nano Continuity via Graph Theory. Open Access Library Journal, 8, 1-9.
https://doi.org/10.4236/oalib.1107568

[5]   Kalil, C., de Castro, M., Silva, D. and Cortez, C. (2021) Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit. Open Journal of Modelling and Simulation, 9, 159-171.
https://doi.org/10.4236/ojmsi.2021.92011

[6]   Bondy, J.A. and Murty, U.S.R (2008) Graph Theory. Springer, Berlin.
https://doi.org/10.1007/978-1-84628-970-5

[7]   https://math.stackexchange.com/q/3952813

[8]   https://mathoverflow.net/q/385726

[9]   https://math.stackexchange.com/q/4355930

 
 
Top