Estudo de circuitos RL e RC: comparação entre valores experimentais, analíticos e numéricos

• Main Author: Martelo, Leicam Feroldi
• Publication Date: 2025
• Format: Bachelor thesis
• Language: por
• Source: Repositório Institucional da UTFPR (da Universidade Tecnológica Federal do Paraná (RIUT))
• Download full: http://repositorio.utfpr.edu.br/jspui/handle/1/36505
• topic: Circuitos elétricos; Equações diferenciais; Runge-Kutta, Fórmulas de; Electric circuits; Differential equations; Runge-Kutta formulas; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This study analyzes the behavior of Resistor-Inductor (RL) and Resistor-Capacitor (RC) circuits, focusing on a comparison between analytical and numerical methods. For the RL circuit, the results obtained through the analytical solution were compared with experimentally measured values. In the case of the RC circuit, analytical values were compared with results obtained using two widely used numerical methods: Finite Differences and Runge-Kutta. Initially, a detailed literature review was conducted, utilizing articles, theses, and other relevant academic works to support the analysis. In the analytical calculations, the integrating factor method was employed for both circuits. For the RL circuit, the analytical calculations resulted in a constant that closely matched the experimentally measured values. In the RC circuit, the resulting equation is time-dependent, which required the application of numerical methods for a more detailed analysis. Python software was chosen for implementing the calculations due to its popularity, ease of use, and accessibility. By comparing the three methods using graphs with 0.05-second steps, it was observed that the Runge-Kutta method aligns perfectly with the analytical values. In contrast, the Finite Differences method exhibited a slight deviation in the middle of the curve but coincided with the results at the beginning and end. This observation indicates the higher accuracy of the Runge-Kutta method, although it is more complex. On the other hand, the Finite Differences method also produced results close to the analytical ones, especially when used with smaller step sizes. It is concluded that both methods are effective and accurate: the Runge-Kutta method provides higher precision even with larger steps, whereas the Finite Differences method requires smaller steps to achieve the same level of accuracy while maintaining its simplicity.