The third theory of m×n cylindrical resistor network

The resistor network model has been applied in many disciplinary fields and can be used for solving complex problems. The solution to its problems mainly lies in the innovation of methods. This article considers an arbitrary m × n-order cylindrical resistance network model (CRNM), and the study of their electrical characteristic analytical expressions is challenging. This article establishes new research techniques and methods, using node voltage parameters to establish matrix equations (including master matrix equations and boundary condition equations), and cleverly transforms 2D equations into 1D difference equations using matrix transformation techniques. The potential function and equivalent resistance formula of any m × n-order CRNM are derived. Visual exploration was conducted on CRNM, revealing the basic characteristics of the potential function and equivalent resistance as they vary with node position. Further discussed some results of special cases, while analyzing other related results. Due to the two different theories previously proposed regarding the equivalent resistance of CRNM, the theoretical formula in this article is completely different from the previous theory. Therefore, the electrical characteristic analysis formula obtained in this study can be referred to as the third theory of CRNM.