Networks of Identical Capacitors with a Substitutional Capacitor

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.