## Power Factor Formula For Single Phase :

Power Factor Formula For Single Phase P_{(w)} in watts is equal to product of voltage V _{(m/s)} in meter per second and multiply the current I_{(a) } in amperes and multiply the cos θ.Hence the Power Factor Formula for single phase can be written as

P_{(w)}=V _{(m/s)} *I_{(a) }* cos θ

Rearranging the above formula we get

cos θ= P_{(w)}/ V _{(m/s)} *I_{(a)}

Therefore

cos θ= true power/ apparent power

where

cos θ→ power factor

P→ Power in Watts

V→ Voltages in Volts (m/s)

I→ Current in Amperes

The true power is given in terms of Watts and the Apparent power is given in terms of Volt-Amperes or Watts

The power factor in an AC circuit is also given by the ratio of Resistance and Impedance

cos θ =R_{(ohm)}/z

Where,

R → Resistance in ohms

Z → Impedance

Impedance (Z) is the total resistance in the AC circuit and is given by

Z= √[R^{2 }+(x_{L}+ X_{c})^{2}]

Where,

R → resistance

X_{L }→inductive reactance in ohm

X_{c}→ capacitive reactance in ohm

Here, it is noted that single-phase power factor is less than 1.

## Sample Problems :

### Example 1 :

Calculate the power factor ? In a 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_{(w)}/ V _{(v)} *I_{(a)}

=100/(200 × 4 )

=100/800

=1/8

=1.25

### Example 2 :

Calculate the power ? In a 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