Application of mathematical methods of engineering to transient analysis of r-l-c series circuit with sinusoidal voltage

Abstract

The paper has made an attempt to obtain transient response of an AC series circuit by mathematical methods of engineering namely classical method and Laplace transform method. The equations developed are differential equations of second order. The solution is obtained by classical method with initialization condition and Laplace transform method. A comparative study is done in analyzing the transient response of an R-L-C series circuit connected to sinusoidal source of voltage by the two methods. The derived equations of transient response by two methods are similar although Laplace transform method is better tool with respect to initialization conditions in a circuit. Proposed work has established similarity of transient response of all the three conditions of under and over damped, as well as critically damped case by two different methods.

Keywords: Classical Method, Differential Equation, Initialization, Laplace Transforms Transient Response.