Engineering and Scientific International Journal (ESIJ) ISSN 2394-7187(Online) Volume 8, Issue 2, April – June 2021 ISSN 2394 - 7179 (Print) 45 DOI: 10.30726/esij/v8.i2.2021.82011 Gupta Transform Approach to the Series RL and RC Networks with Steady Excitation Sources Rahul Gupta *1 , Rohit Gupta #2 , Loveneesh Talwar #3 1,2 Lecturer of Physics, Department of Applied Sciences, Yogananda College of Engineering and Technology, Jammu, J&K, India 3 Assistant Professor, Department of Electrical Engineering, Yogananda College of Engineering and Technology, Jammu, J&K, India Abstract— The analysis of electric networks circuits is an essential course in engineering. The response of such networks is usually obtained by mathematical approaches such as Laplace Transform, Calculus Approach, Convolution Theorem Approach, Residue Theorem Approach. This paper presents a new integral transform called Gupta Transform for obtaining the complete response of the series RL and RC networks circuits with a steady voltage source. The response obtained will provide electric current or charge flowing through series RL and RC networks circuits with a steady voltage source. In this paper, the response of the series RL and RC networks circuits with steady excitation source is provided as a demonstration of the application of the new integral transform called Gupta Transform. Keywords — Gupta Transform; Series RL and RC Networks circuits; Response . 1. Introduction The electric circuit of the series RL network consists of two passive electric elements: an inductor Ł and a resistor Ɍ, connected in series with asteady voltage source and theelectric circuit of the series RC network consists of two passive electric elements: a capacitor C and a resistor R, connected in series with a steady current source. Such networks are used as a tuning or resonant circuit in the radio and television set to a particular frequency band from the wide range of frequency components, or in the chokes of luminescent tubes [1-4]. The Gupta Transform has been proposed recently by the authors Rahul Gupta and Rohit Gupta and generally, it has been applied in different areas of science and engineering [5, 6].The response of electrical networks is generally obtained by the different mathematical approaches like the calculus approach [1-3], convolution theorem approach [7], or by various integral transforms like Laplace Transform [1-3], Mohand Transform [8, 9], Aboodh Transform [10], Elzaki Transform [11], residue theorem approach [12], Rohit Transform [13]. This paper presents the use of a new integral transform called Gupta Transform for obtaining the complete response of the series RL and RC networks circuits with a steady voltage source and brings up the Gupta Transform as a new successful powerful tool for determining the response of network circuits. 2. Gupta Transform Let g(y) is a continuous function on any interval for y ≥ 0. The Gupta Transform of g(y) is as [5, 6] Ṙ { g ( y )} = 1 3 ∫ − ∞ 0 ( ) = () , provided that the integral is convergent, where, may be a real or complex parameter and Ṙ is the Gupta Transform operator. The Gupta Transform of elementary functions are given in [5, 6, 15]. The inverse Gupta Transform of the function G(r) is denoted by Ṙ -1 {G (r)} or g (y). If we write Ṙ {g (y)} = G (r), then Ṙ - 1 {G (r)} = g (y), where Ṙ -1 is called the inverse Gupta Transform operator. The Inverse Gupta Transform of elementary functions are given in [5, 6]. The Gupta Transform of some derivatives [5, 6, 15] of g(y) are, Ṙ { ′ ( )} = Ṙ { ( )} − 1 3 ( 0 ) , Ṙ { ′′ ( )} = 2 Ṙ { ( )} − 1 2 ( 0 ) − 1 3 ′ ( 0 ) . 2.1 Series Rl Network Circuit with Steady Voltage Source We will take a series RL network circuit to which a steady voltage source of potential V 0 is applied through a key K as shown in figure 1. Fig.1: Series RL network with steady voltage source