This project report delves into the application of complex variables in the analysis of AC RLC circuits. It begins with an introduction to RLC circuits, their components (resistors, capacitors, and inductors), and the use of AC sources. The report then explains the advantages of using complex variables in solving for the current and voltage in these circuits. It presents the mathematical framework, including the representation of voltage and current using complex notation, and the application of Kirchhoff's Voltage Law. The core of the report details the step-by-step procedure for solving the circuit problem using complex variables, including the derivation of the current equation. The solution is compared with the traditional trigonometric approach. Finally, the report provides a detailed example with numerical values, demonstrating how to calculate the current in a series RLC circuit driven by an AC source, and concludes by emphasizing the simplicity and efficiency of the complex variable method for solving AC RLC circuit problems, especially for more complex circuit configurations. The document includes references to relevant sources.
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