Efficient Methods for Calculating Equivalent Resistance Between Nodes of a Highly Symmetric Resistor Network
Jeremy Thomas Moody · Digital WPI · 2013
Classic Kirchhoff methods for solving resistor network problems rapidly become unwieldy as the network size grows. For all but trivial networks, the number of equations to be solved makes the task tedious and error-prone. We present an algorithm for generating and solving the Kirchhoff equations for an arbitrary N-node network, given an NxN matrix representation of the network. Using the algorithm and van Steenwijk's symmetry method, we replicated his solutions for the effective resistance between nodes of Platonic polyhedral networks. We derived new solutions for Archimedean and Catalan polyhedral networks, 4D polytopes, and N-dimensional hypercubes. Finally, we constructed physical models of several networks and measured the resistance between nodes, validating our calculated results.