What is the correct expression for complex power S in terms of voltage and current?

What is the correct expression for complex power S in terms of voltage and current?

• A. S = V × I
• B. S = V × I*
• C. S = V / I
• D. S = I^2 × R

Answer: (B)

Complex power uses the complex conjugate of current when expressed with phasors, so it correctly captures both real and reactive power. If V is the voltage phasor and I is the current phasor, the proper expression is S = V times the complex conjugate of I. This conjugation ensures the real part of S equals the active power P and the imaginary part equals the reactive power Q, since P = Re(S) and Q = Im(S). The magnitude is |S| = |V||I| and the angle is ∠S = ∠V − ∠I. Using S = V × I would mix the phases incorrectly and not separate P and Q. S = V / I isn’t a power expression. S = I^2 × R represents real power dissipated in a resistor, not the complex power.

Complex power uses the complex conjugate of current when expressed with phasors, so it correctly captures both real and reactive power. If V is the voltage phasor and I is the current phasor, the proper expression is S = V times the complex conjugate of I. This conjugation ensures the real part of S equals the active power P and the imaginary part equals the reactive power Q, since P = Re(S) and Q = Im(S). The magnitude is |S| = |V||I| and the angle is ∠S = ∠V − ∠I.

Using S = V × I would mix the phases incorrectly and not separate P and Q. S = V / I isn’t a power expression. S = I^2 × R represents real power dissipated in a resistor, not the complex power.