Elementary Methods for Infinite Resistive Networks with Complex Topologies

TL;DR

This paper extends elementary methods to compute the equivalent resistance of infinite resistive networks with complex, entangled topologies, broadening the scope of classical physics puzzles for educational purposes.

Contribution

It introduces a novel approach to analyze complex infinite resistor networks using elementary techniques, expanding beyond traditional ladder circuits.

Findings

Exact analytical solutions for new complex topologies

Elementary methods remain effective for intricate network structures

Enhanced educational tools for physics and engineering students

Abstract

Finding the equivalent resistance of an infinite ladder circuit is a classical problem in physics. We expand this well-known challenge to new classes of network topologies, in which the unit cells are much more entangled together. The exact analytical results there can still be obtained with elementary methods. These topology classes will add layers of complexity and much more diversity to a very popular kind of physics puzzles for teachers and students.