Impact of a Non-Concentric Cylindrical Capacitor on the Characteristics of an RC DC-Driven Circuit

Abstract

This report is a follow-up to the previously published article. The scope of the purely numeric study of the previous report is augmented and formulated analytically. The main objective is to analytically formulate the capacitance of a non-concentric, asymmetric, long cylindrical capacitor. It is proven that the capacitance is a function of the radii of the cylinders and the separation distance between the circular centers. It is also shown that the numeric conformal mapping of the previous work is closely related to the bipolar coordinate system. To accomplish the set goal, we utilized one of the popular Computer Algebra Systems (CAS), especially Mathematica . To underline the usefulness of the CAS, the analytic formulation, its associated numeric and graphical outputs are bundled into one file. It is shown under special conditions that the presented format approaches the well-known characteristic of the symmetric capacitor. Application-wise, the impact of the non-concentric cylindrical capacitor in an RC DC-driven electric circuit is reported. The report embodies the essential Mathematica codes, readily making the reproduction of the results attainable.