Explanation:
Power factor,
\(\cos \phi=\dfrac{1}{\sqrt{2}}=\dfrac{R}{\sqrt{R^{2}+\omega^{2} L^{2}}}\)
This gives, \(\omega L=R\).
When \(\omega\) is doubled, we find,
\(\cos {\phi ^\prime } = \frac{R}{{\sqrt {{R^2} + 4{\omega ^2}{L^2}} }}\)
\(\,\,\,\,\,\,\,\,\,\,\,\, = \frac{R}{{\sqrt {{R^2} + 4{R^2}} }} = \frac{1}{{\sqrt 5 }}\)