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Reactive power and power phasor diagram

Short answer

Reactive power Q = VI sin φ (VAR) is the power oscillating between source and load without net work. In the phasor diagram, I is resolved into an active component I cos φ aligned with V and a reactive component I sin φ at 90°, multiplying by V gives the power triangle P–Q–S with S² = P² + Q².

What do you mean by reactive power in AC circuit? Explain it by constructing phasor diagram for real power, reactive power and apparent power.

Reactive power (Q) is the power that is alternately stored and returned by the inductors and capacitors in an AC circuit. It does no useful work, and its average over a cycle is zero, but it is needed to set up the magnetic and electric fields. It is the product of voltage, current and sin φ:

Q = V I sin φ (unit: volt-ampere reactive, VAR)

Equivalent forms: Q = I²X = V²/X, where X = X_L − X_C. Q is positive for a lagging (inductive) load and negative for a leading (capacitive) load.

Phasor diagram

Take V as reference along the horizontal axis. The current I lags V by φ. Resolve I into two components:

   O ───── I cos φ ─────┬──────────► V (reference)
     ╲  φ               ┆
        ╲               ┆  I sin φ
           ╲            ┆  (reactive component, 90° behind V)
              ╲         ┆
                 ↘      ┆
                    ↘   ▼
                       I (lags V by φ)
  • I cos φ is in phase with V, and produces the active power.
  • I sin φ is at 90° to V, and produces the reactive power.

Power triangle

Multiplying each current component by V:

  • Active power P = V I cos φ (W)
  • Reactive power Q = V I sin φ (VAR)
  • Apparent power S = V I (VA)
          /|
     S   / |  Q = VI sin φ
        /  |
       / φ |
      /____|
      P = VI cos φ

S² = P² + Q², and power factor cos φ = P/S.

Example: V = 230 V and I = 10 A at φ = 60°: S = 2300 VA, P = 1150 W, Q = 1992 VAR.

✓ Answer checked by Claude Opus 5.5 (high effort)

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