Eur. Phys. J. Plus (2022) 137: 546
https://doi.org/10.1140/epjp/s13360-022-02750-3

Regular Article

Resistance theory for two classes of n-periodic networks

Department of Physics, Nantong University, 226019, Nantong, China

^a tanz@ntu.edu.cn, tanzzh@163.com

Received: 23 March 2022
Accepted: 21 April 2022
Published online: 4 May 2022

Abstract

Two kinds of n-order periodic resistor networks are considered: one is a standard resistor network with two surfaces; the other is an unconventional resistor network with only one surface (Möbius strip). In this paper, the resistances between arbitrary nodes in these two networks are studied by the recursion-transform theory with voltage parameters (RT-V), and a new theoretical breakthrough is made. The key of RT-V method to solve the problem is matrix transformation, which transforms complex equations into simple ones and can derive relatively simple results. We find four main analytical expressions of equivalent resistance, and find interesting special relations between different resistances. A series of special cases are discussed to verify the correctness of the results, especially compared with other literatures. As a by-product of our research we present two new mathematical identities. The theories and methods proposed in this paper provide a new theoretical basis for related scientific research.