Minimum Power Transfer Theorem?

📌 CONCEPT: The Minimum Power Transfer Theorem states that in a circuit containing a resistor and an inductor with a capacitor in parallel, the power consumed by the inductor is minimum when the capacitive reactance is equal to the inductive reactance.

📐 RULE / FORMULA: To apply the Minimum Power Transfer Theorem, we use the condition Xc = Xl, where Xc is the capacitive reactance and Xl is the inductive reactance.

💡 WORKED EXAMPLE: Consider a circuit with a resistor (R = 10 Ω), an inductor (L = 2 H) and a capacitor in parallel. Initially, the capacitance (C) is 100 μF. As C reduces to 10 μF, we find that the capacitive reactance Xc = 1/2πfC is equal to the inductive reactance Xl = 2πfL. Therefore, power consumption by the inductor is minimum at this value of capacitance.

⚠️ COMMON MISTAKE: Students often confuse the condition for minimum power transfer with the condition for resonance in an LC circuit, which is ω = 1/√(LC).