The power factor of LR circuit is `1/sqrt3`. IF the frequency of ac be doubled, what will be the power factor?

Explanation

IF the phase difference between the voltage and the current in the LR circuit is `theta`,
`tantheta=(omegaL)/R`
From the figure , power factor,
`costheta=R/(sqrt(R^2+omega^2L^2))`
In the first case,
`R/(sqrt(R^2+omega^2L^2))=1/sqrt3`or,`R^2/(R^2+omega^2L^2)=1/3`
or,`omega^2L^2=3R^2-R^2=2R^2`
Int he second case , the frequency is doubled. The new frequency is `2omega`.
`therefore` Power factor = `R/sqrt(R^2+4omega^2L^2)=R/(sqrt(R^2+4times2R^2))`
`=R/sqrt(9R^2)=1/3`