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Question

Physics Question on Alternating current

The power factor of an R−LR-L circuit is 12\frac{ 1}{ \sqrt 2} . If the frequency of AC is doubled, what will be the power factor?

A

13\frac{ 1}{ \sqrt 3 }

B

15\frac{ 1}{ \sqrt 5 }

C

17\frac{ 1}{ \sqrt 7 }

D

111\frac{ 1}{ \sqrt {11}}

Answer

15\frac{ 1}{ \sqrt 5 }

Explanation

Solution

Power factor cos⁡ϕ=12=RR2+ω2 L2\cos \phi = \frac{ 1}{ \sqrt 2} = \frac{ R}{ \sqrt{ R^2 + \omega^2 \, L^2 }} This gives, ωL=R \omega L = R when ω\omega is doubled, we find cos⁡ϕ′=RR2+4ω2 L2\cos \phi' = \frac{ R}{ \sqrt{ R^2 + 4 \omega^2 \, L^2 }} = RR2+4R2=15\frac{ R}{ \sqrt{ R^2 + 4 R^2}} = \frac{ 1}{ \sqrt 5 }