Power factor of an LR circuit is `1/sqrt2`. If the frequency of ac is doubled, what will be the power factor?

Explanation

Power factor, `costheta=R/Z=1/sqrt2`
`thereforeZ^2=2R^2`or,`R^2+(omegaL)^2=2R^2`or,`(omegaL)^2=R^2`
Now if the angular frequency `omega` is doubled,
`(omega'L)^2=(2omegaL)^2=4(omegaL)^3=4R^2`
So, impedance, `Z'=sqrt(R^2+(omega'L)^2)=sqrt(R^2+4R^2)=Rsqrt5`
Hence , power factor, `R/(Z')=R/(Rsqrt5)=1/sqrt5`