Application of the recursion-transform method in calculating the resistance of an M×N cobweb resistor network with an arbitrary boundary

Abstract

Looking for a handy and exact calculation for the equivalent resistance of an M[Formula: see text]×[Formula: see text]N resistor network is important, but difficult. In this paper, we present a standard and convenient approach to calculate the equivalent resistance of an M[Formula: see text]×[Formula: see text]N cobweb resistor network by applying multiple external current sources based on the nodal analysis in circuit theory and the recursion-transform (R-T) method. The test current source acts on different nodes in radial direction to obtain an analytical expression for the equivalent resistance between nodes of an M[Formula: see text]×[Formula: see text]N cobweb resistor network in radial direction. In our scheme, recalculations are not required to obtain the equivalent resistance between different radial nodes. We also discuss the influence of polygon sides of cobweb network and the ratio between two unit resistances on the equivalent resistance. The results show that, when the number of similar polygons M is given, with the increasing of the polygon sides and the ratio between two unit resistance, the equivalent resistances between two arbitrary radial nodes tend to a constant.