 # What is Power Factor (Cos ϕ) ? Cos fi or P.F Definition & Formulas

## Power Factor Definitions and Formulas

In electrical engineering, power factor is only and only related to AC circuits i.e. there is no power factor (P.f)  in DC circuits due to zero frequency and phase angle difference (Φ) between current and voltage.

### What is Power Factor?

Power factor may be defined by three definitions and formals as follow.

1).  The Cosine of angle between Current and Voltage is called Power Factor.

• P = VI Cosθ OR
• Cosθ = P ÷ V I OR
• Cosθ = kW ÷ kVA OR

Where:

• P = Power in Watts
• V = Voltages in Volts
• I = Current in Amperes
• W = Real Power in Watts
• VA = Apparent Power in Volt-Amperes or kVA
• Cosθ = Power factor

2). The ratio between Resistance and Impedance in AC Circuit is known as Power Factor.

Cosθ = R ÷ Z

Where:

• R = Resistance in Ohms (Ω)
• Z = Impedance (Resistance in AC circuits i.e. XL, XC and R known as Inductive reactance, capacitive reactance and resistance respectively) in Ohms (Ω)
• Cosθ = Power factor

Impedance “Z” is the total resistance of AC Circuit i.e.

Z = √ [R2 + (XL + XC)2]

Where:

• XL = 2πfL   … L is inductance in Henry
• XC = 1 ÷ 2πfC … C is capacitance in Farads

Related Post: Difference Between Active and Reactive Power

3).The ratio between Active Power and Apparent Power in volts-amperes is called power factor.

• Cosθ = Active Power ÷ Apparent Power
• Cosθ = P ÷ S
• Cosθ = kW ÷ kVA

Where

• kW = P = Real Power in kilo-Watts
• kVA = S = Apparent Power in kilo-Volt-Amperes or Watts
• Cosθ = Power factor

Power Factor Formula in Three Phase AC Circuits

Power Factor Cosθ = P ÷ √3 VL × IL     Line Current & Voltage

Power Factor Cosθ = P ÷ √3 VP × IP  Phase Current & Voltage

### Power Factor Triangle and Examples Beer analogy of active or true power, reactive power, apparent power and power factor. Chips bag analogy of true or real power, reactive power, apparent power and power factor. Good to know:

In pure resistive circuit, power factor is 1 due to zero phase angle difference (Φ) between current and voltage.

In pure capacitive circuit, power factor is leading due to the lagging  VARs. i.e. Voltage is lagging 90° behind the current. In other words, Current is leading 90° from voltage (Current and voltage are 90° out of phase with each others, where current is leading and voltage is lagging).

In pure inductive circuit, power factor is lagging due to the leading VARs i.e. Voltage is leading 90° from current. In other words, Current is lagging begging 90° behind the voltage (Current and voltage are 90° out of phase with each, others where voltage is leading and current is lagging).

### Electrical Technology

Simple and easy to understand, thanks

1. Electrical Technology says:

Welcome :)

1. pranava kumar says:

That’s easy to understand!
Now, what analogy can be given to a capacitor to show that even a capacitor is involved in the concept of Power Factor? It will give an even more clear understanding!

1. Electrical Technology says:

You may check the links at the end of the above post :)

2. tharan bugti says:

sir i want to save it..how it is possible?<br />easy to perceive,nice way to demonstrate.thanks

2. Dattatrirao Kulkarni says:

i too expected same example from you<br />

3. Mukund Gawale says:

I want to download free e-books. so plz invite me to do so.

4. kaustubh says:

the total power factor in actual is a product of the displacement power factor(cos[fi]) and the distortion power factor.the distortion power factor is a function of the total harmonic distortion,hence the total power factor of the system decreases on in actual practice on account of the presence of harmonics and other non linearities.

5. CURRLING says:

REALY GOOD EXPLICATION…Thanks!!<br />

its banificial for us that’s why thanks

7. shani says:

sir plz upload 3 phase transformer 25 kva step down oil immresd self cooled core and winding calculation.

sir plz answer the question its about control i know you can answer it …. which transform we use for convergence ? Laplace transform or Fourier transform or Z transform

9. Himanshu verma says:

Its very simple to understand.I never understand about these three power concept.

Thanks sir.

10. chanti says:

plzz tel me how to reduce to kvah

11. Alok Pandey says:

Nice article and well explained!

12. Rajneesh singh says:

tell me why change the pf of d.g and main sub station.

13. gtyui says:

humko pasand aya

14. Ebi says:

Becuse cos& factor is beetween kw and kva.