Abstract
Traditionally, students are taught to find the equivalent resistance between two arbitrary nodes of an electrical circuit using Kirchhoff’s laws. In this article, we introduce a procedure for finding the equivalent resistance based on a variational principle that is consistent with the Kirchhoff’s laws. This method is easy to track for a nontrivial arrangement of resistors with large numbers of nodes and conceptually straight-forward to implement for a circuit whose components may not be in series or parallel with each other, such as the familiar Wheatstone bridge. Our pedagogical method, with lower computational costs than the Kirchhoff’s laws, is accessible to undergraduates with some background in matrix algebra and calculus.
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Acknowledgement
We thank S. G. Rajeev for useful discussions and M. Bhattacharya for insightful feedback on the article.
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Arnab Kar received his B.Sc. in physics from the Chennai Mathematical Institute and his Ph.D. in physics from the University of Rochester. His diverse research interests are in mathematical physics, quantum chemistry and plasma physics. At present, he is an engineer at the Intel Corporation.
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Kar, A. Equivalent Resistance in a Finite Resistor Network From the Variational Principle. Reson 27, 623–639 (2022). https://doi.org/10.1007/s12045-022-1353-y
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DOI: https://doi.org/10.1007/s12045-022-1353-y