An innovative method is applied to solve the equivalent resistance between any nodes of a 2 × 4 × n tower‐shaped cascaded resistive network

Abstract

AbstractIn previous methods for solving the equivalent resistance of large‐scale complex resistive networks, abstract Green's functions or complex matrix transformations were often involved, which brought more difficulties to the readers' understanding. For this reason, this study proposed an innovative method based entirely on simple algebraic operations. This method combined the equivalent decomposition method with the improved recursion‐transform (IRT) method. It was divided into three steps: Firstly, by introducing the concept of “negative resistance,” one of the resistors of the network to be solved was equivalently decomposed into the parallel connection of three resistors, so that the whole resistive network was equivalently decomposed into three parts, namely, a left network, a middle network, and a right network. Then, the equivalent resistances of the left network and the right network were calculated using the IRT method, respectively. Finally, the equivalent resistance between any nodes was solved according to the parallel relationship of the equivalent resistances of the left network, the middle network, and the right network. The equivalent resistance between any nodes in the 2 × 4 × n tower‐shaped cascaded resistive network was successfully solved using this method. The calculation showed that because the concept of negative resistance was introduced in this method, the equivalent resistance problem of any nodes in the network was changed into the equivalent resistance problem of the initial nodes of the network, which made the equivalent resistance problem of any nodes simple, convenient, fast and easy to understand.