CONSTRUCTION OF AN RL CIRCUIT, MODELING THE GOVERNING DIFFERENTIAL EQUATION AND COMPARISON BETWEEN THE ANALYTICAL SOLUTION AND EXPERIMENTAL DATA

• DOI: https://doi.org/10.22533/at.ed.1317412415019

• Palavras-chave: Mathematical modeling. Ordinary Differential Equation. RL Circuit. Teaching and learning.

• Keywords: Mathematical modeling. Ordinary Differential Equation. RL Circuit. Teaching and learning.

• Abstract:

  This article proposes the modeling of the ordinary differential equation referring to a resistor-inductor (RL) electrical circuit, obtaining the analytical solution and comparison with experimental data (charge and electrical current) obtained from an electrical circuit that It was built with recyclable materials. This practical approach aims to sharpen the student's interest in the discipline and the undergraduate course, offering them another incentive for your stay at the university. As in other disciplines, teaching the theory of ordinary differential equations (ODE) can be associated with practical experiments, allowing the connection between theory and practice, providing opportunities for efficient learning of the content covered and the perception of how mathematics is embedded in various events around us. Furthermore, mathematical modeling is an interesting, powerful and enlightening artifice, as it allows a better visualization of the laws and properties that govern the studied event. Following this path, this work contemplates the modeling of the ordinary differential equation that governs the movement of charge and current in an RL electrical circuit, its analytical resolution and the comparison between the analytical results and experimental data obtained from the electrical circuit. This way, Kirchoff's second law and concepts from the theory of electricity were used to model the ordinary differential equation that governs the RL circuit. The analytical solution of this problem was obtained by the integrating factor method, as the ordinary differential equation governing the electrical circuit has the characteristics of being linear and first order. The construction of a circuit was carried out using recyclable materials that can be found in homes, schools, universities or in places that receive electronic waste. The construction of the circuit made it possible to obtain experimental data (charge and electric current), which were measured using a multimeter. Subsequently, these data were compared with those obtained by the analytical solution. The relative error obtained shows the compatibility between the data obtained by the experiment and the analytical solution. The objective of this work is to bridge the gap between theory and practice. This way, the text has a practical educational teaching and learning nature, bringing to the public the importance of associating concepts and properties with problem solving.