Which statement is NOT true about achieving maximum power transfer in an AC circuit?

• A. Load resistance equals source resistance
• B. Load reactance equals the negative of source reactance
• C. Load impedance is the complex conjugate of the source impedance
• D. Load resistance equals zero

Answer: (D)

Maximum real power transfer in an AC network happens when the load impedance matches the source impedance in the complex sense, that is, the load is the complex conjugate of the source. If the source impedance is Z_S = R_s + jX_s, the optimal load becomes Z_L = R_s − jX_s. This arrangement makes the real parts equal (the load resistance equals the source resistance) and cancels the reactive parts (the load reactance is the negative of the source reactance), so the load appears purely resistive to the source and all available power is delivered to it.

This directly corresponds to the statement that the load impedance is the complex conjugate of the source impedance. The idea that the load resistance must be zero would eliminate the delivered real power (P = I^2 R_L, so with R_L = 0 you get zero power), which is why that option is not true for achieving maximum power transfer.