Equivalent resistance of a periodic and asymmetric 2 × n resistor network

• Published in: Results in physics Vol. 60; p. 107683
• Main Authors: Fang, Xin-Yu, Zhang, Zhi-Li, Tan, Zhi-Zhong
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2024; Elsevier
• Subjects: Asymmetric network; Equivalent resistance; Matrix equation; Node voltage; RT-V method; Node voltage; RT-V method; Equivalent resistance; Matrix equation; Asymmetric network
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2024.107683

•A periodic and asymmetric 2 × n resistor network model.•Differential equation and the constraint equations.•The clever and powerful RT-V theory for studying complex networks.•Discovered three new equivalent resistance formulae.•Many interesting results of resistor networks are produced. This article proposes a class of periodic and asymmetric 2 × n resistor network model, and adopts the RT-V theory to conduct in-depth research on this problem, achieving new theoretical breakthroughs. This study derived three original equivalent resistance formulae for this complex circuit network, and also discusses the analytical expressions for equivalent resistance in different special cases, verifying that the conclusions in special cases are completely consistent with the actual circuit or previous existing conclusions, indirectly verifying the correctness of the theoretical results obtained in this article. The resistor network model in this article has multifunctional characteristics, for example, when taking r1→∞, the model degenerates into a cobweb network model. The research methods and results of the article will provide a new theoretical basis for related scientific and engineering research.