Modeling electric circuit dynamics: an approach via first-order ordinary differential equations

This study explores the dynamics of electric circuits using first-order ordinary differential equations (ODEs) as a foundational framework. It begins with an introduction to the fundamental principles of electric current, progressing to the formulation and solution of first-order ODEs that characterize circuit behaviour, particularly in RL circuits. The analytical solutions reveal both transient and steady state responses, enhanced by practical examples and graphical illustrations. These representations offer tangible insights into the real-world applications of theoretical concepts. By seamlessly integrating theoretical frameworks with practical scenarios, this research provides a holistic understanding of how first-order ODEs serve as predictive tools in analyzing electrical circuits. This study not only bridges the gap between theory and practice but also lays a crucial foundation for complex circuit analysis, underpinned by Kirchhoff's Second Law, thereby enhancing the predictive analysis of dynamic electrical behaviour.