Matemáticas y Electromagnetismo Aplicados a las Técnicas de Análisis de Circuitos.

Abstract

The proposal is to make a structured monograph in such a way that you can see the techniques of circuit analysis, electromagnetic physics and mathematics as inherent elements. Looking for the generation of a self-study tool for students of medium and low voltage electrical systems. This distribution allows at first to define basic concepts, such as: what is a circuit, what is a node, what is a mesh and explain the fundamental laws from pure resistive circuits. In this first approach the techniques of circuit resolution are explained, which includes: the resistive equivalents, the current divider, the voltage divider, the mesh analysis, the nodal analysis, source transformation, the Thevenin theorem and Norton between others. In the problems worked, the correct development of the analysis leads us to scenarios where the solution focuses on solving systems of linear equations that are developed in detail, using methods such as: Gauss-Jordan, inverse matrix or determinants. In addition, the procedure for raising these equations is step by step, incorporating images that facilitate the understanding and deduction of these. Subsequently, topics such as electric field and magnetic field are explained, which allow understanding the principle of operation of circuit elements such as the capacitor and the inductor. Here the development of the presented examples requires a basic knowledge in the solution of derivatives and integrals, however, in harmony with what is sought, the solutions are given in a detailed manner. Finally, unifying the previous topics and mentioning some important considerations, the techniques of analysis of circuits in alternating current are explained, following the already established guidelines (explicit mathematical solutions and images that allow an easy understanding of the explained topics).