Thevenin Equivalent for Circuits with Capacitors, Inductors, and AC Sources?

Thevenin's theorem traditionally states that any linear circuit with voltage sources, current sources, and resistors can be reduced to a single voltage source and series resistor at two terminals. However, for AC circuits involving capacitors and inductors, the theorem extends to include general impedances, which are complex and frequency-dependent. Thevenin equivalents can be applied to linear AC networks at a single frequency by representing reactive components as impedances and combining them algebraically. When multiple AC sources with different frequencies and phases are present, the equivalent circuit must consider the frequency components separately, often using techniques like Laplace transforms or trigonometric identities to analyze the combined effect. Thevenin equivalents are not limited to purely resistive circuits or DC sources but are applicable to linear circuits with reactive elements and AC sources under appropriate conditions.
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