Potential formula of an m × n globe network and its application

Abstract

Searching for the explicit solutions of the potential function in an arbitrary resistor network is important but difficult in physics. We investigate the problem of potential formula in an arbitrary m × n globe network of resistors, which has not been resolved before (the previous study only calculated the resistance). In this paper, an exact potential formula of an arbitrary m × n globe network is discovered by means of the Recursion-Transform method with current parameters (RT-I). The key process of RT method is to set up matrix equation and to transform two-dimensional matrix equation into one-dimensional matrix equation. In order to facilitate practical application, we deduced a series of interesting results of potential by means of the general formula, and the effective resistance between two nodes in the m × n globe network is derived naturally by making use of potential formula.