On the resistance of an Infinite Square Network of Identical Resistors- Theoretical and Experimental Comparison

TL;DR

This paper compares theoretical calculations using Lattice Green's Functions with experimental measurements of resistance in a finite 30x30 resistor network, enhancing understanding of resistance in infinite and perturbed square lattices.

Contribution

It provides a detailed theoretical method for calculating lattice resistances and validates it through experimental measurements on a finite resistor network.

Findings

Theoretical resistance calculations match experimental results closely.

Lattice Green's Function effectively predicts resistance between lattice points.

Experimental data confirms the theoretical approach for finite networks.

Abstract

A review of the theoretical approach for calculating the resistance between two arbitrary lattice points in an infinite square lattice (perfect and perturbed cases)is carried out using the Lattice Green's Function. We show how to calculate the resistance between the origin and any other site using the Lattice Green's Function at the origin, and its derivatives. Experimental results are obtained for a finite square network consisting 30x30 identical resistors, and a comparison with those obtained theoretically is presented.