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What is Power factor?

In an AC circuit, the ratio of the active power (the power actually consumed) to the apparent power (RMS voltage × RMS current). It lies between 0 and 1, and when the voltage and current are sinusoidal it equals cos φ of their phase difference φ. A low power factor means a larger current is needed to deliver the same active power, increasing the losses in wiring and transformers.

Read the beginner explainer: AC vs DC Explained: Impedance, Phase and Power Factor

Japanese name: 力率

Power factor appears in 11 practice questions across 4 topics, including Circuit and electromagnetism basics, Circuit Analysis: AC, Linear Circuits and Transients, 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: Power Electronics Circuits

Power factor from phase difference

With an inductive load such as a motor, the current lags the voltage and the power factor falls. For example, a load with an apparent power of 1 kVA and a power factor of 0.8 consumes 800 W of active power, and reactive power also flows back and forth between the source and the load. Connecting a capacitor in parallel with the load cancels the lagging reactive power and brings the power factor closer to 1.

Power factor from waveform distortion

When the current is not sinusoidal, harmonic currents at frequencies different from the voltage carry no average power but still increase the RMS current. The power factor is then the product of cos φ, from the phase difference of the fundamental, and the RMS fundamental current ÷ the total RMS current. A rectifier with capacitor smoothing has a low power factor because its current flows in pulses, even though the phase shift of the current is small.

Why raise the power factor

A load using 800 W at 100 V draws 10 A at a power factor of 0.8 but only 8 A at a power factor of 1. Wiring loss is proportional to the square of the current, so at 0.8 it is about 1.56 times the loss at 1. Standards such as IEC 61000-3-2 set limits on the harmonic currents drawn by equipment, which is another reason power supplies correct their power factor.

Try it: questions about Power factor

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.

What is generally done to improve the power factor of a circuit containing an inductive load such as a motor?

  1. AConnect a capacitor in parallel with the load
  2. BConnect an inductor in parallel with the load
  3. CRaise the supply frequency
Show answer and explanation

Answer: A. Connect a capacitor in parallel with the load

In an inductive load the current lags the voltage, producing lagging reactive power. A capacitor produces reactive power of the opposite (leading) sign, so placing one in parallel with the load cancels reactive power, reduces the current drawn from the supply and brings the power factor closer to 1. The voltage across the load and the active power it consumes are unchanged. Such power-factor-correction capacitors are used in factory power-receiving equipment, but overcompensation makes the power factor leading and can raise the voltage.

FAQ

Are power factor and efficiency the same thing?

No. Efficiency is output power ÷ input power and expresses the fraction lost. Power factor is input active power ÷ apparent power and expresses how much of the current flowing actually helps deliver power. Equipment can have a high efficiency and still a low power factor.

Can the power factor exceed 1?

No. Active power never exceeds apparent power, so the power factor lies between 0 and 1. Whether the current lags or leads the voltage is described as a lagging or leading power factor.

Power factor in the explanations

Questions that mention Power factor (11)

  1. In an AC circuit, with active power P [W] and apparent power S [VA], which expression gives the power factor?
  2. What is generally done to improve the power factor of a circuit containing an inductive load such as a motor?
  3. For a balanced three-phase load with a line voltage of 200 V, a line current of 10 A and a power factor of 0.8, which is closest to the load's active power (total of all three phases)?
  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. 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?
  7. What is the magnitude of the impedance of a circuit with a resistor R = 30 Ω in series with a coil of reactance XL = 40 Ω? (Ignore the coil's resistance.)
  8. 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.)
  9. 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?
  10. A Y-connected load with an impedance of Z = 8 + j6 Ω per phase, as in figure (a), is connected to a balanced three-phase source with a line voltage of 200 V RMS. Which of the following is closest to the total three-phase active power?
  11. What is the purpose of a power factor correction (PFC) circuit used in power supplies?

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Related terms

Reactive power Three-phase AC Power factor correction Impedance Reactance Boost converter Back EMF Buck converter Buck-boost converter Continuous conduction mode

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