Reactive power expression.

Reactive power expression.

• A. Q = V I cos φ
• B. Q = V I sin φ
• C. Q = V I
• D. Q = V^2 / (ω L)

Answer: (B)

Reactive power measures the energy that alternates between the source and the reactive elements (inductors and capacitors) each cycle. It depends on how far voltage and current are out of phase. The general expression is Q = V I sin φ, where φ is the phase angle between voltage and current. This comes from the complex power concept S = V I*, which splits into P = V I cos φ (real power) and Q = V I sin φ (reactive power). The sine factor tells you how much of the apparent power VI is actually stored and returned by the reactive elements. If φ is 90 degrees, as with a pure inductor, Q = VI, and you can also write Q = I^2 X_L = V^2 / X_L with X_L = ωL. The other forms are either real power (Q = VI cos φ) or special-case expressions for a purely reactive element (Q = V^2 / (ωL) applies only to a pure inductor).

Reactive power measures the energy that alternates between the source and the reactive elements (inductors and capacitors) each cycle. It depends on how far voltage and current are out of phase. The general expression is Q = V I sin φ, where φ is the phase angle between voltage and current. This comes from the complex power concept S = V I*, which splits into P = V I cos φ (real power) and Q = V I sin φ (reactive power). The sine factor tells you how much of the apparent power VI is actually stored and returned by the reactive elements.

If φ is 90 degrees, as with a pure inductor, Q = VI, and you can also write Q = I^2 X_L = V^2 / X_L with X_L = ωL. The other forms are either real power (Q = VI cos φ) or special-case expressions for a purely reactive element (Q = V^2 / (ωL) applies only to a pure inductor).