Exact asymptotic expansion for the resistance between center node and a node on the cobweb network boundary

TL;DR

This paper derives exact asymptotic expansions for the electrical resistance between the center and boundary nodes in a cobweb resistor network, providing detailed analytical expressions for large network sizes.

Contribution

It introduces a precise asymptotic expansion for resistance in cobweb networks, with all coefficients expressed analytically, advancing understanding of resistor network behavior.

Findings

Asymptotic resistance formulas for large networks

Analytical expressions for all expansion coefficients

Enhanced understanding of resistor network asymptotics

Abstract

We analyze the resistance between two notes in a cobweb network of resistors. Based on an exact expression, we derive the asymptotic expansions for the resistance between the center node and a node on the boundary of the M by N cobweb network of resistors with resistors r and s in the two spatial directions. All coefficients in this expansion are expressed through analytical functions.