Power Factor Formula for Single Phase

Power factor for a single-phase in an alternating current circuit is defined as a measure of energy efficiency. It is usually expressed as a number ranging from 0 to 1. It is the ratio of working power (or actual power) to apparent power. The actual power is expressed in watts while the apparent power is expressed in volt-amperes. The most important concept here is that the power factor is only applicable to alternating current circuits. As there is no frequency or phase angle difference between current and voltage, the DC circuit can’t have a power factor. The power factor of a circuit is denoted by the symbol P. It is a unitless quantity which has no dimensional formula. The value of the power factor for a single-phase is always less than 1. While for a pure resistance circuit, its value is 1.

Formula

P = W/A

where,

P is the power factor,

W is the working power,

A is the apparent power.

The power factor is also given by the cosine of the angle between voltage and current.

cos θ = P/VI

where,

cos θ is the power factor,

P is the power of circuit,

V is the voltage,

I is the current value.

The power factor can also be expressed as the ratio of resistance to the impedance.

cos θ = R/Z

or

cos θ = R/√[R² + (X_L + X_C)²]

where,

R is the resistance of the circuit,

Z = √[R² + (X_L + X_C)²] is the impedance of the current,

X_L is the inductive reactance,

X_C is the capacitive reactance.

Sample Problems

Problem 1. Calculate the power factor of an AC circuit for working power of 20 W and apparent power of 40 W.

Solution:

We have,

W = 20

A = 40

Using the formula we get,

P = W/A

= 20/40

= 1/2

= 0.5

Problem 2. Calculate the power factor of an AC circuit for working power of 50 W and apparent power of 200 W.

Solution:

We have,

W = 50

A = 200

Using the formula we get,

P = W/A

= 50/200

= 1/4

= 0.25

Problem 3. Calculate the working power of an AC circuit for power factor 0.6 and apparent power of 150 W.

Solution:

We have,

P = 0.6

A = 150

Using the formula we get,

P = W/A

=> W = PA

=> W = 0.6 (150)

=> W = 90 W

Problem 4. Calculate the power factor of an AC circuit for the power of 100 W, current of 4 A and voltage of 200 V.

Solution:

We have,

P = 100

I = 4

V = 200

Using the formula we get,

cos θ = P/VI

= 100/(200 × 4)

= 100/800

= 1/8

= 0.125

Problem 5. Calculate the power of an AC circuit for power factor 0.2, current 5 A and voltage 100 V.

Solution:

We have,

cos θ = 0.2

I = 5

V = 100

Using the formula we get,

cos θ = P/VI

=> P = VI cos θ

=> P = 100 (5) (0.2)

=> P = 250 W

Problem 6. Calculate the power factor of an AC circuit for resistance of 10 ohms and impedance of 40 ohms.

Solution:

We have,

R = 10

Z = 40

Using the formula we get,

cos θ = R/Z

= 10/40

= 1/4

= 0.25

Problem 7. Calculate the resistance of an AC circuit for a power factor of 0.4 and impedance of 60 ohms.

Solution:

We have,

cos θ = 0.4

Z = 60

Using the formula we get,

cos θ = R/Z

=> R = Z cos θ

=> R = 60 (0.4)

=> R = 24 ohms