Which expression correctly computes active power P in a balanced AC circuit?

• A. P = VI
• B. P = VI cos φ
• C. P = V^2 / R
• D. P = I^2 R

Answer: (B)

Active power is the portion of electrical power that actually does work, and it depends on how in phase the voltage and current are. The real power you get from an AC circuit is the product of the RMS voltage, the RMS current, and the cosine of the phase angle between them: P = V I cos φ. The cos φ factor represents how much of the current is in step with the voltage; only that in-phase portion contributes to real work. If the circuit is purely resistive, φ = 0 and cos φ = 1, so P = VI. If the circuit is purely reactive, cos φ = 0 and P = 0, even though VI can be large.

In a general balanced AC circuit with impedance that has both resistive and reactive parts, P = VI cos φ remains the correct expression for active power. The other forms would only be correct in special cases: P = VI is the apparent power when phase is ignored; P = V^2 / R or P = I^2 R assume a purely resistive load with no phase difference.