TITLE:
3D_Multi Resistor Electric Circuit
AUTHORS:
Haiduke Sarafian
KEYWORDS:
3D Electric Circuit, Equivalent Resistor, Computer Algebra System, Mathematica
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.2,
June
26,
2023
ABSTRACT: This report addresses the issues concerning the analysis of an electric circuit
composed of multiple resistors configured in a 3-Dimension structure. Noting, all the standard textbooks of physics and engineering irrespective of the used
components are circuits assembled in two dimensions. Here, by deviating from
the “norm” we consider a case where
the resistors are arranged in a 3D structure; e.g., a cube. Although,
independent of the dimension of the design the same physics principles apply,
transitioning from a 2D to a 3D makes the corresponding analysis considerably
challenging. In general, with no exception, depending on the used components
the analysis faces with solving a set of either algebraic or
differential-algebraic equations. Practically, this interfaces with a Computer
Algebra System (CAS). The main objective is symbolically to identify the
current distributions and the equivalent resistor (s) of cubically assembled
resistors.