$................$"Discuss the fundamental principles of electric circuits, including Ohm's law, Kirchhoff's laws, and the concept of electrical impedance. Explain how these principles are applied to analyze DC and AC circuits, considering resistors, capacitors, and inductors. Discuss the significance of circuit analysis techniques such as node voltage and mesh current methods. Illustrate the behavior of circuits under steady$-$state and transient conditions, and analyze the impact of reactive components on circuit performance. Finally, evaluate the practical implications of circuit theory in the design and operation of electronic systems, highlighting key theoretical limitations and current research trends."