Power factor (PF) is the ratio of real working power (measured in kilowatts, kW) to apparent power (measured in kilovolt-amperes, kVA) in an AC circuit, indicating how effectively current is being converted into useful work. When you ask 'what is pf in physics,' you are looking at the cosine of the phase angle ($\cos \theta$) between voltage and current waveforms. In a purely resistive DC or AC circuit, voltage and current are perfectly in phase, meaning all drawn power performs real work (PF = 1.0). However, in AC circuits containing inductive or capacitive components—like motors, transformers, and switching power supplies—the current waveform shifts out of phase with the voltage. This phase shift creates 'reactive power' (kVAR), which does no actual mechanical or thermal work but still travels through your wires, generating heat and requiring larger infrastructure to support it.
The Core Concept: Real, Reactive, and Apparent Power
To understand power factor, you must separate electrical power into three distinct vector components. All About Circuits defines these using the power triangle:
- Real Power (kW): The actual energy consumed to perform work (turning a motor shaft, heating a coil, emitting light). This is what your residential utility meter measures and bills you for.
- Reactive Power (kVAR): The energy that sloshes back and forth between the source and the load's magnetic or electric fields. It sustains the electromagnetic flux in motors but performs zero net work.
- Apparent Power (kVA): The vector sum of Real and Reactive power. This is the total power the utility must generate and your wires must carry.
Because reactive power still draws physical current (Amps), it directly dictates the physical size of your conductors, breakers, and transformers. Here is how different common loads behave in the real world:
| Load Type | Typical PF Range | Phase Relationship | Primary Reactive Component |
|---|---|---|---|
| Incandescent Bulb / Resistive Heater | 1.00 (Unity) | In-phase | None (Purely Resistive) |
| Uncompensated Fluorescent Lighting | 0.50 - 0.60 | Current Lags Voltage | Magnetic Ballast (Inductive) |
| TEFC Induction Motor (Full Load) | 0.80 - 0.88 | Current Lags Voltage | Stator/Rotor Windings (Inductive) |
| TEFC Induction Motor (No Load) | 0.10 - 0.25 | Current Lags Voltage | Magnetizing Current (Inductive) |
| Modern LED Driver (with Active PFC) | 0.90 - 0.99 | Near Unity | Active Switching Correction Circuitry |
| Arc Welder (Transformer-based) | 0.60 - 0.80 | Current Lags Voltage | High Leakage Reactance (Inductive) |
Worked Numeric Example: Sizing a UPS for an Air Compressor
Let's look at what power factor changes in a real installation. Suppose you need to back up a 5 HP (3.73 kW mechanical output) industrial air compressor with an Uninterruptible Power Supply (UPS). The motor nameplate states an efficiency ($\eta$) of 85% and a Power Factor of 0.75.
Step-by-Step Sizing Calculation
- Calculate Input Real Power (kW): The motor outputs 3.73 kW, but it is only 85% efficient.
Input kW = 3.73 kW / 0.85 = 4.38 kW. - Calculate Apparent Power (kVA): The UPS must supply the total apparent power, not just the real power.
Apparent kVA = Input kW / PF = 4.38 kW / 0.75 = 5.84 kVA. - Calculate Current Draw at 240V AC:
I = (5.84 kVA * 1000) / 240V = 24.3 Amps.
The Trap: If you buy a 5,000W (5 kW) UPS, it will immediately overload and trip its internal breaker when the compressor starts, even though the 'real' work being done is only 4.38 kW. The UPS electronics and internal wiring must handle the 5.84 kVA (24.3A) apparent load. You must specify a UPS rated for at least 6.0 kVA, and your branch circuit wiring must be sized for the 24.3A current (requiring 10 AWG copper wire on a 30A breaker per NEC guidelines), not the 18.2A that a unity PF load would draw.
Where You Meet Power Factor in Practice
Power factor is not just a theoretical physics concept; it has direct financial and physical consequences on the jobsite and in the electrical panel.
- Industrial Utility Penalties: Commercial and industrial facilities are often billed for 'kVA demand' rather than just 'kW usage'. If a factory's PF drops to 0.70, the utility must supply 30% more current than necessary. Utilities install power factor meters and will levy heavy financial penalties (often thousands of dollars a month) on facilities that fail to maintain a PF above 0.90 or 0.95. Facilities correct this by installing automated capacitor banks that inject leading reactive power to cancel out the lagging reactive power of their motors.
- Solar Inverter Clipping: Grid-tied solar inverters are rated in kVA, not just kW. If your home has a heavy inductive load (like a well pump or pool heater) with a low PF, the inverter must supply the reactive current. This eats into the inverter's kVA capacity, causing it to clip (limit) its real kW solar production earlier in the day than expected.
- Wire Sizing and Voltage Drop: According to Fluke's power quality guidelines, low power factor increases the total RMS current flowing through conductors. Higher current means higher $I^2R$ (heat) losses in the wires and a larger voltage drop over long feeder runs. To compensate, engineers must upsize the wire gauge (e.g., moving from 4 AWG to 2 AWG aluminum), increasing material costs.
Common Confusions: Power Factor vs. Efficiency vs. Harmonics
When diagnosing power quality issues, even experienced technicians frequently mix up three distinct concepts:
1. Power Factor vs. Motor Efficiency
Efficiency is the ratio of mechanical power output to electrical real power input. Power factor is the ratio of electrical real power input to electrical apparent power input. A premium-efficiency NEMA motor might be 95% efficient (very little energy lost to heat and friction) but still have a mediocre 0.75 power factor at partial load because it still requires a massive magnetic field to operate. High efficiency does not guarantee high power factor.
2. Displacement PF vs. True PF (Distortion)
The $\cos \theta$ definition applies strictly to linear loads (like standard induction motors), known as Displacement Power Factor. However, modern non-linear loads—such as Variable Frequency Drives (VFDs), cheap LED drivers, and computer switching power supplies—draw current in sharp, non-sinusoidal pulses. This creates harmonic distortion. True Power Factor accounts for both phase displacement and harmonic distortion. A VFD might have a displacement PF of 0.99, but a True PF of 0.65 due to massive 3rd and 5th harmonic currents. You cannot fix distortion PF with standard capacitors; you need active harmonic filters.
Frequently Asked Questions
Can power factor be greater than 1?
No. Because real power (kW) can never exceed apparent power (kVA) in a passive circuit, the maximum theoretical power factor is 1.0 (unity). If your meter reads >1.0, the meter is either miscalibrated, or you have a generating source (like solar) pushing power back into the grid, confusing the meter's directional sensors.
Does a low power factor increase my home electricity bill?
Generally, no. Residential utility meters in the US and UK only measure and bill for Real Power (kWh). The utility absorbs the cost of the reactive power (kVAR) on residential lines. However, low PF in a home can cause localized voltage drops and overheating in your main panel if you are running heavy inductive loads like an oversized well pump on undersized wiring.
How do I measure power factor on a workbench?
Standard digital multimeters (DMMs) cannot measure power factor because they only read RMS voltage and RMS current independently, missing the phase angle. To measure PF, you need a true power quality analyzer (like a Fluke 435) or a wattmeter that samples voltage and current simultaneously to calculate the instantaneous power integral.
