# Power Factor of RL Circuit

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The power factor of an R-L circuit is 12. If the frequency of the AC input source is doubled, what will be the power factor?
A.1/√3
B.1/√7
C.1/√5
D. Remains same
select the correct answer from the above-given options.

## The new power factor of an R-L circuit is 1/√5

Solution:

Power factor of r-L circuit = cosΦ=R/Z=R/[√R2+(XL)2]=1/√2

cosΦ=1/√[1+(XL/R)2]=1/√2

⇒XL/R=1

Here

L is the inductance of RL-circuit,

R is the resistance of RL-circuit,

And f is supply frequency,

If the frequency is doubled, then a new frequency applied to the RL circuit fnew=2f

Then inductive reactance across will become  XL,new=ωL=2(2f)L=2.XL

Then new factor for frequency fnew will be P.Fnew=1/√[1+(2.XL/R)2]=1/√[1+4]=1/√5

## So the new power factor of the RL circuit =1/√5

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