Networks of Identical Capacitors with a Substitutional Capacitor

Abstract

The effective capacitance between two arbitrary lattice points in a finite or infinite network of identical capacitors is investigated for a perturbed lattice, by substituting a single capacitor, using lattice Green's function. The relation between the capacitance and the lattice Green's function for the perturbed lattice is derived. Solving Dyson's equation, the Green's function and the capacitance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical results for a square lattice are presented.

Keywords: Capacitance; Substitutional; Lattice Green's Function.

PACS (2003): 61.50.Ah, 63.20.-e, 71.15.-m, 84.37.+q.