Application of the recursion‐transform method in calculating the equivalent resistance of two‐dimensional finite resistor network

Abstract

SummaryLooking for a handy and exact calculation for the equivalent resistance of an M × N resistor network is important but difficult, even for the rectangular resistor network. In this paper, we calculate the equivalent resistance of an M × N rectangular resistor network by means of the recursion‐transform method, where the idea of multiple external current sources based on the typical mesh current is used, and find a new formula of equivalent resistance which is different from the result of the other paper. In our scheme, recalculations are not required to obtain the equivalent resistance between different terminals. We further investigate how the order of resistor network and the ratio between two unit resistances affect the equivalent resistance. We find that the equivalent resistance between arbitrary terminals tends to a constant as the order and ratio increase when M is given. Copyright © 2016 John Wiley & Sons, Ltd.