Power Factor of RL Circuit

Answer: C.1/√5

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

Solution:

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

cosΦ=1/√[1+(X_L/R)²]=1/√2

⇒X_L/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 f_new=2f

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

Then new factor for frequency f_new will be P.F_new=1/√[1+(2.X_L/R)²]=1/√[1+4]=1/√5

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

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