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📘 Maximum Power Transfer Theorem | Derivation & Proof (RL = RS, ZL = Z*) In this video, we derive and prove the Maximum Power Transfer Theorem for both DC and AC circuits in a clear, step-by-step manner. 🔹 DC Case: We mathematically prove that maximum power is transferred to the load when 👉 Load resistance equals source (Thevenin) resistance 𝑅𝐿=𝑅𝑆 RL=RS 🔹 AC Case: For AC circuits, where impedance is complex, we derive the condition for maximum power transfer and show that: 𝑍𝐿=𝑍∗(complex conjugate of source impedance) ZL=Z∗(complex conjugate of source impedance) i.e. 𝑅𝐿=𝑅 and 𝑋𝐿=−𝑋 📐 The derivation is carried out using: Thevenin equivalent circuit Power equation in terms of load resistance / impedance Differentiation to find maximum power condition 🎯 This video is useful for: VTU examinations Network Analysis / Electric Circuits GATE & competitive exams Conceptual understanding with proof 📌 Topics covered: ✔ Statement of Maximum Power Transfer Theorem ✔ DC derivation (RL = RS) ✔ AC derivation (ZL = Z*) ✔ Physical interpretation ✔ Exam-oriented explanation 📚 Subject: Electric Circuit Analysis / Network Theory 📘 Level: Undergraduate (VTU / B.E / B.Tech) 👉 Like, Share & Subscribe for more VTU-focused, exam-ready explanations.