Electrical properties of a generalized 2 × n resistor network

Abstract

Any changes in resistor conditions will increase the difficulty of resistor network research. This paper considers a new model of a generalized 2 × n resistor network with an arbitrary intermediate axis that was previously unsolved. We investigate the potential function and equivalent resistance of the 2 × n resistor network using the RT-I theory. The RT-I method involves four main steps: (1) establishing difference equations on branch currents, (2) applying a matrix transform to study the general solution of the differential equation, (3) obtaining a current analysis of each branch according to the boundary constraints, and (4) deriving the potential function of any node of the 2 × n resistor network by matrix transformation, and the equivalent resistance formula between any nodes. The article concludes with a discussion of a series of special results, comparing and verifying the correctness of the conclusions. The work establishes a theoretical basis for related scientific research and application.