Effective resistances of two-dimensional resistor networks

Abstract

Abstract We investigate the behavior of two-dimensional resistor networks, with finite sizes and different kinds (rectangular, hexagonal, and triangular) of lattice geometry. We construct a network by having a network unit repeat itself L x times in the x-direction and L y times in the y-direction. We study the relationship between the effective resistance (R eff) of the network on dimensions L x and L y . The behavior is simple and intuitive for a network with rectangular geometry; however, it becomes non-trivial for other geometries which are solved numerically. We find that R eff depends on the ratio L x /L y in all three studied networks. We also check the consistency of our numerical results experimentally for small network sizes.