NUMERICAL INVESTIGATION OF DAMPED PARALLEL RLC CIRCUIT: ANALYSIS AND INSIGHTS
Abstract
This research addresses the analysis of damped parallel RLC circuits, consisting of resistors (R), inductors (L), and capacitors (C), which are fundamental components in modeling and understanding various electrical systems. The damping effects in these circuits significantly influence their transient behavior, stability, and overall performance. By employing the system of differential equations derived from Kirchhoff's voltage and current laws, this study explores the dynamic properties and responses of these
circuits under damping conditions. The investigation utilizes advanced numerical methods—Euler Method, RK3 Method, and RK5 Method—to approximate solutions for voltage and inductor current in damped parallel RLC circuits. These methods are critically evaluated based on their computational efficiency and accuracy. The Euler Method, known for its simplicity, is suitable for quick estimations but lacks precision compared to higher-order methods. The RK3 Method provides a balance between accuracy and computational effort, making it effective for practical applications. The RK5 Method, a fifth-order technique, stands out for its
exceptional accuracy, proving indispensable in scenarios requiring high precision. This study offers valuable insights into the impact of damping on the transient responses and stability of parallel RLC circuits. Numerical simulations reveal how damping alters the circuit's performance, shedding light on optimization strategies and design considerations. Through detailed
graphical presentations, the research demonstrates the comparative strengths of these numerical methods, highlighting their applicability to solving complex circuit equations. By providing a comprehensive analysis of damping effects and numerical methods, this work contributes to a deeper understanding of the behavior of damped parallel RLC circuits, offering
guidance for efficient and accurate circuit analysis in engineering and applied mathematics.
