Resistance Theory of General 2 × n Resistor Networks. Issue 2 (14th January 2021) - Zhang, Yi‐Tian; Hu, Xuan; Chen, Hai‐Xiang; Wang, Ming‐Yue; Chen, Wan‐Jiao; Fang, Xin‐Yu; Tan, Zhi‐Zhong
Abstract: Here the problem of equivalent resistance of general 2 × n ‐order resistor networks with four different resistor parameters is investigated, and innovations in theory and method are made. Here, the second‐order matrix equation model and boundary condition equation model are established by the RT‐I technique (recursion–transform theory based on current parameters), and the general solution and the special solution of the matrix equation are given by using the matrix transformation method. The current distribution law in the circuit is obtained, and three equivalent resistance formulas of general 2 × n ‐order resistor networks are obtained. Finally, by analyzing and discussing the special case of the conclusion, the relationship between different resistances is obtained, and the results are compared with those of other literatures. Abstract : A resistance theory for a general 2 × n resistor network is set up. Research is undertaken to establish a matrix equation model and create matrix transformation by Tan's RT‐I theory (recursion‐transform theory based on current parameters). Three equivalent resistance formulas of general 2 × n resistor networks are found. The relationships between the different equivalent resistances are revealed.