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What is Reactive power?

In an AC circuit, power that only shuttles back and forth between source and load and is not consumed on average. With a phase difference φ between voltage and current it is Q = VI sin φ [var], related to the active power P = VI cos φ [W] and the apparent power S = VI [VA] by S² = P² + Q² (the power triangle). The complex power is S = V × (conjugate of I) = P + jQ; for example, P = 800 W and Q = 600 var give S = 1,000 VA and a power factor of 0.8. Because it increases the current in the wires and causes losses, it is cancelled with capacitors in power-factor correction.

Japanese name: 無効電力

Reactive power appears in 8 practice questions across 3 topics, including Circuit Analysis: AC, Linear Circuits and Transients, Circuit and electromagnetism basics, Power Electronics Circuits.

Power-factor correction of an inductive load with a capacitor V C R L Load I IC IL
Power-factor correction of an inductive load with a capacitor · View in diagrams

Field: Circuit Analysis: AC, Linear Circuits and Transients

Try it: questions about Reactive power

In an AC circuit, with active power P [W] and apparent power S [VA], which expression gives the power factor?

  1. AP / S
  2. BS / P
  3. CP × S
Show answer and explanation

Answer: A. P / S

The power factor is the ratio P/S of active power P to apparent power S (RMS voltage × RMS current). For sinusoids it can be written cos φ, where φ is the phase difference between voltage and current. For example, S = 2000 VA and P = 1800 W give a power factor of 0.9. A low power factor means more current is needed to deliver the same active power, increasing losses in wiring and transformers.

An AC load has an active power of 800 W and an apparent power of 1000 VA. What is its reactive power? (Sinusoidal voltage and current.)

  1. A600 var
  2. B200 var
  3. C1800 var
Show answer and explanation

Answer: A. 600 var

Apparent power S, active power P and reactive power Q satisfy S² = P² + Q² (the power triangle). Q = √(1000² − 800²) = √360000 = 600 var, and the power factor is P/S = 0.8. Reactive power only shuttles back and forth between source and load and is not consumed on average, but it increases the current and therefore the losses in wiring and transformers.

Reactive power in the explanations

Questions that mention Reactive power (8)

  1. In an AC circuit, with active power P [W] and apparent power S [VA], which expression gives the power factor?
  2. An AC load has an active power of 800 W and an apparent power of 1000 VA. What is its reactive power? (Sinusoidal voltage and current.)
  3. The voltage and current phasors (RMS) of a load are V = 100∠0° V and I = 5∠−30° A. Which of the following is the magnitude of the reactive power of this load?
  4. As in the figure, a capacitor C is connected in parallel with an inductive load of 8 kW active power and a power factor of 0.8 (lagging) so that the power factor seen from the source becomes 1. Which of the following is the reactive power the capacitor must supply?
  5. As in the figure, a capacitor C is connected in parallel with an inductive load of 8 kW active power and a power factor of 0.8 (lagging) to improve the power factor seen from the source to 0.96 (lagging). Which of the following is closest to the reactive power the capacitor must supply?
  6. What is generally done to improve the power factor of a circuit containing an inductive load such as a motor?
  7. A sinusoidal voltage of 100 V RMS is applied to a load consisting of a resistor R = 8 Ω in series with a coil of reactance X = 6 Ω. Which of the following is the active power of the load?
  8. In a power supply whose input current is not sinusoidal but contains many harmonics, which of the following correctly explains why the power factor is not 1 even if the fundamental of the current is in phase with the voltage?

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Related terms

Power factor Phasor Reactance Power factor correction Admittance Impedance Mesh analysis Nodal analysis Norton's theorem Partial fraction decomposition

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