Exact Evaluation of The Resistance in an Infinite Face- Centered Cubic Network

TL;DR

This paper derives an exact formula for the electrical resistance between two points in an infinite face-centered cubic resistor network, using elliptic integrals, and explores its asymptotic behavior with numerical examples.

Contribution

It provides the first exact analytical expression for resistance in an infinite FCC network using elliptic integrals, advancing theoretical understanding.

Findings

Exact resistance formula in terms of elliptic integrals

Asymptotic resistance behavior analyzed

Numerical resistance values presented

Abstract

The equivalent resistance between the origin and the lattice site (2n,0,0), in an infinite Face Centered Cubic network consisting from identical resistors each of resistance R, has been expressed in terms of the complete elliptic integral of the first kind, and . The asymptotic behavior is investigated, and some numerical values for the equivalent resistance are presented.