Power Factor Formula For Single Phase with Sample Sums

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= √[R2 +(xL+ Xc)2]

Where,

R → resistance

X→inductive reactance in ohm

Xc→ 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

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