Modeling two loops RLC circuit AC power source using symbolic arithmetic differential equations

Abstract

As oscillator applications, resistance-inductor-capacitor (RLC) circuits are employed in a diversity of settings. A low-pass, band-stop, band-pass, or high-pass filters can all be designed using an RLC circuit. A two-loop RLC circuit could not be represented mathematically in prior studies. Laplace transform is one type of integral transformation, which is able to resolve both second order non-uniform and uniform linear differential equations. This work solves the differential equations (DEs) of a two loops RLC circuit of an alternating voltage source by using two alternative approaches, Laplace transform (LT) and deep learning convolutional neural network (DLCNN). Initially, two DE have been declared. Next, Laplace transform is computed to solve these equations with symbolic variables for the first loop current and capacitor charge. Finally, we substitute the numerical values of the circuit elements for the symbolic variables. The charge and current initially decline exponentially. On the other hand, they oscillate over a long period of time. The capacitor charge and current initially decline exponentially and oscillate over a long period of time. The qualities of the result can be examined with a symbolic result, which is not possible with a numeric result.