Use of Reversion Method to Solve Mathematical Models on Series Electrical Circuits (Rl) with Nonlinear Inductors

. Forming a mathematical model of a series electrical circuit with a nonlinear inductor obtained based on Kirchoff's laws one and two takes the form of a nonlinear differential equation. Approach methods are used to determine the electric current in the circuit, including the Reversion Method, namely by converting nonlinear differential equations into a system of linear differential equations.


INTRODUCTION
In today's rapid development of science, especially in technological advances, scientists are required to be able to solve problems arising from these technological advances.Applications of mathematics, especially differential equations, are widely used in almost all fields of science, such as engineering and industry, physics, management, astronomy, psychology, economics, engineering, and many others, because mathematics is the basis of science to solve problems arising from the rapid progress of science and technology today.
The application of mathematics in the field of electrical engineering is the application of the reversion method in series electrical circuits with nonlinear inductors where the mathematical model of the electric circuit is in the form of a nonlinear differential equation whose online is caused by changes in magnetically induced flux F (t) in the coil so that at both ends of the coil there will be an induced or impacted electromotive force (gg).
The reversion method is used to solve the mathematical model of the electrical circuit, which is an approach method that converts nonlinear differential equations into a system of linear differential equations.In solving the system of linear differential equations obtained, the Laplace transformation method should be used because it saves much numerical work.

METHOD
This method is based on an algebraic procedure that converts a nonlinear differential equation into a system of linear differential equations.
Suppose that the desired differential equation for the solution takes the form : a1y + a2y 2 + a3y 3 + a4y 4 + ...... + a7y 7 + ...... = k(t) where ai is usually a function of the operator D with D = d/s and a1 0 and it is assumed that a solution takes the form : to determine the coefficients Ai that is, by substituting equation ( 2) into (1) and equating the power coefficients k In the same way, if this is done, then coefficients are obtained A1, A2, A3, A4, ......... and so on.
In this writing only displays seven coefficients Ai The first is : Defined self-inductance as : the unit for self-inductance is Hendry (H).
A coil that is made to have a certain price is called an inductor.
If the equation ( 14) substituted into equations ( 13) then obtained Here L is an inductance inductance, according to Lenz's law the direction of electromotive force (ggl) this induction will counteract the cause.
To determine the current equation in the above electrical circuit can be used Kirchoff's law as follows : with the switch assumed closed on t = 0 so that i = 0 at t = 0 where (t) is the total flux connection of a nonlinear inductor and is generally a function of i depending on the material of the inductor.A typical form of analytics assumed for functional relationships between fluxes (t) and the current i is : with c1 and c2 is the specified setting of the nutility curve of the core ferromagnetic material.
The above electrical circuit can be developed for a general circuit in series with a nonlinear inductor, as in figure 2 below : with Es(t) is the electromotive force (ggl) which is imposed as a function of time.
It is assumed that the switch closes on t = 0 so that i = 0 at t = 0 , and generally flux (t) be GASAL's function with a series is as follows: :