Which condition yields maximum power transfer from a source to a load in an AC circuit?

Which condition yields maximum power transfer from a source to a load in an AC circuit?

• A. Load resistance equals source resistance and load reactance equals source reactance
• B. Load resistance equals source resistance and load reactance equals negative of source reactance
• C. Load resistance equals zero and load reactance equals the source reactance
• D. Load resistance equals twice the source resistance and load reactance equals negative of source reactance

Answer: (B)

Maximum power transfer in AC occurs when the load impedance is the complex conjugate of the source impedance. If the source is Zs = Rs + jXs, the optimal load is ZL = RL + jXL = Rs - jXs. This makes the load cancel the source’s reactive part, so the total impedance becomes purely real (Zt = Zs + ZL = 2Rs). The current is then I = Vs / (2Rs) and the power delivered to the load is maximized because all the power goes into the resistive part, not into storing and returning energy via reactance. In this matched condition, RL equals Rs and XL equals -Xs, which is exactly the conjugate match. Any deviation leaves a net reactive component, which wastes energy by circulating it back and forth and reduces the real power delivered to the load. In the special case of zero source reactance, this reduces to simply RL = Rs.

Maximum power transfer in AC occurs when the load impedance is the complex conjugate of the source impedance. If the source is Zs = Rs + jXs, the optimal load is ZL = RL + jXL = Rs - jXs. This makes the load cancel the source’s reactive part, so the total impedance becomes purely real (Zt = Zs + ZL = 2Rs). The current is then I = Vs / (2Rs) and the power delivered to the load is maximized because all the power goes into the resistive part, not into storing and returning energy via reactance. In this matched condition, RL equals Rs and XL equals -Xs, which is exactly the conjugate match. Any deviation leaves a net reactive component, which wastes energy by circulating it back and forth and reduces the real power delivered to the load. In the special case of zero source reactance, this reduces to simply RL = Rs.