Power Factor Formula in AC Circuits with Examples and Solutions
Power factor is a key concept in the study of alternating current (AC) circuits, especially when analyzing how efficiently electric power is used in homes, industries, and commercial setups. It measures how effectively the electrical energy supplied by the source is converted into useful work in an electrical system.
The idea of power factor is based on the relationship between different forms of power in an AC circuit: real power (that performs useful work), reactive power (that sustains electric and magnetic fields), and apparent power (the total power supplied).
Understanding and improving power factor is important for ensuring energy efficiency, reducing electricity costs, and avoiding unnecessary power losses or penalties.
What is Power Factor?
Power factor is defined as the ratio of real (or active) power to apparent power in an AC circuit. Real power (measured in kW) is the energy actually consumed to perform work such as lighting lamps and running motors. Reactive power (measured in kVAR) is needed to create magnetic fields in devices like transformers and motors but does not perform any productive task.
Apparent power (measured in kVA) is the combination of both real and reactive power, representing the total power the system needs to deliver to maintain both real work and energy storage in fields.
A higher power factor means better energy efficiency. The maximum (ideal) power factor value is 1 (unity), meaning all supplied power is converted to useful work, while lower values indicate the presence of wasted (reactive) power.
Power Factor Formula and Explanation
The most common formula for power factor is:
- Power Factor (PF) = Real Power (kW) / Apparent Power (kVA)
- Alternatively, PF = Cos φ, where φ is the phase angle between current and voltage in the circuit.
The value of power factor always ranges from 0 to 1. When all supplied power is used for useful work (no wastage in fields), cos φ = 1 and PF = 1.
Practical Analogy: The Beer Glass
A simple analogy helps clarify power factor: imagine ordering a glass of beer. The drinkable part (beer) represents real power, while the foam represents reactive power. The total contents (beer plus foam) is the apparent power.
A glass with less foam gives a higher ratio of beer to total volume—just like a system with a higher power factor uses energy more efficiently. If foam is minimized (reactive power is low), power factor approaches 1, and almost all supplied power is used productively.
Step-by-Step Example: Calculating Power Factor
Suppose an AC motor draws a real power of 500 kW while receiving an apparent power of 625 kVA from the source.
- PF = Real Power ÷ Apparent Power = 500 ÷ 625 = 0.8
- This means the system uses 80% of supplied power for actual work, and the rest is used to sustain electric and magnetic fields (not performing any useful work).
A power factor of 0.8 is typical in many industrial environments, but power suppliers may require higher values to avoid penalties and reduce losses.
Key Power Factor Formulas and Applications
| Formula | Interpretation & Use | Values/Units |
|---|---|---|
| Power Factor = kW / kVA | Efficiency of converting supplied power to usable power | 0 to 1 (unitless) |
| PF = Cos φ | Cosine of phase angle between voltage and current | – |
| Apparent Power = Voltage × Current | Total power drawn (including losses) | kVA |
Why is Power Factor Important?
Low power factor means the system must deliver more current to supply the same amount of real power, increasing electrical losses and raising electricity costs.
Electric utilities may charge additional fees or require businesses to install power factor correction equipment to keep power factor above a specified level. Efficient power factor also helps prevent voltage drops and equipment overheating.
Power Factor Correction Explained
To improve (correct) a low power factor, devices called power factor correction (PFC) units are installed. The most common method involves using capacitor banks, which supply reactive power locally and reduce the total current drawn from the power source.
In modern setups with complex electronic devices switching rapidly, advanced PFC solutions like Static Var Generators (SVG) offer more precise, dynamic compensation—helping maintain a consistently high power factor and maximizing overall efficiency.
Comparison Table: Types of Power in AC Circuits
| Type of Power | Meaning | Unit |
|---|---|---|
| Real Power | Does actual work (motors, lights) | kW |
| Reactive Power | Supports fields in coils/capacitors, doesn't do work | kVAR |
| Apparent Power | Total supplied power (vector sum) | kVA |
Practice Problem
A factory uses 1,000 kW of real power with a power factor of 0.75. Calculate its apparent power drawn from the supply.
- Apparent Power (kVA) = Real Power (kW) / Power Factor
- = 1,000 ÷ 0.75 = 1,333.3 kVA
So, the factory draws 1,333.3 kVA total despite only consuming 1,000 kW for productive work. Improving the power factor would reduce the apparent power needed and save on electricity costs.
How Power Factor Correction Saves Money
When power factor is low, utilities may bill based on the higher apparent power (kVA), not just what is actually used (kW). By improving your power factor, you can reduce both your monthly demand and the size or capacity upgrades of electrical equipment.
Most correction investments recover costs quickly, and modern PFC solutions adapt to changing electrical loads for sustained savings.
Next Steps and Resources
Explore detailed lessons, solved examples, and downloadable notes on power factor and related AC circuit topics at Vedantu's Power Factor Physics page.
- Attempt topic-specific practice questions on power factor and AC circuits.
- Review key Physics concepts such as real, apparent, and reactive power.
- Explore more on Physics topics for complete exam coverage and doubt clearing.
FAQs on Power Factor Explained for Class 12 & Competitive Exams
1. What is power factor in simple terms?
Power factor is a measure of how effectively electrical power is converted into useful work output. It is defined as the ratio of true power (watts) to apparent power (volt-amperes) in an AC circuit. A higher power factor means more efficient utilization of electrical power.
2. What does a 0.8 power factor mean?
A power factor of 0.8 means that only 80% of the supplied apparent power is being used as true power to do useful work, and the remaining 20% is wasted as reactive power. This indicates lower efficiency in the electrical system.
3. Why is power factor important?
Power factor is important because it determines the efficiency of power usage in AC circuits. A low power factor leads to higher losses, voltage drops, and increased electricity bills. Improving power factor increases energy efficiency and can save on demand charges.
4. What is the power factor formula?
The power factor (PF) formula is given by:
PF = Cos φ = True Power (W) / Apparent Power (VA)
where φ is the phase angle between the circuit's voltage and current.
5. How to improve power factor?
To improve power factor, you can:
• Install capacitors in parallel with the load to add leading reactive power.
• Use power factor correction (PFC) equipment.
• Replace low power factor devices with efficient equipment.
• Operate electrical systems at their rated capacity.
6. What is the unit for power factor?
Power factor is a dimensionless quantity and has no unit. It is always expressed as a number between 0 and 1.
7. What is the difference between true power, apparent power, and reactive power?
True Power (P): Actual power consumed; measured in Watts (W).
Apparent Power (S): Total power supplied; measured in Volt-Amperes (VA).
Reactive Power (Q): Power used for creating magnetic and electric fields; measured in Volt-Amperes Reactive (VAR).
The relation is: S² = P² + Q².
8. How does power factor affect electricity bills?
A lower power factor increases the apparent power demand, which can raise maximum demand charges and overall electricity bills. Utility companies may add penalty charges if power factor is below a set threshold. Improving power factor helps reduce such costs.
9. What are leading and lagging power factors?
Leading power factor occurs when the current leads the voltage (common with capacitive loads).
Lagging power factor happens when current lags behind voltage (typical for inductive loads like motors and transformers).
10. Can power factor be negative?
Generally, power factor is a positive value between 0 and 1, representing the cosine of the phase angle. However, the sign indicates whether the load is leading or lagging. A negative result can occur in metering when the load is capacitive (leading), but in most practical calculations, only the magnitude is considered.
11. What is a power factor correction capacitor?
A power factor correction capacitor is a device installed in parallel with inductive loads to supply leading reactive power. This helps neutralize the lagging reactive power from inductive devices, thus improving the overall power factor of the electrical system.
12. Is power factor and efficiency the same thing?
No, power factor and efficiency are different concepts.
• Power factor measures how much of the supplied power is used for useful work as opposed to being wasted as reactive power.
• Efficiency measures how much input energy is converted into output work or useful energy by a device.
Both are important for effective use of electrical power but are not interchangeable.
