Choose correct option(s) regarding the AC circuit given in the figure: (Symbols have their usual meaning)

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Power factor of the circuit is $\frac{\sqrt{3}}{2}$

Equivalent impedance of the circuit is $\frac{2 R}{\sqrt{3}}$

Effective reactance of the circuit is $\frac{R}{3}$

Average power for complete cycle is $\frac{3 E_{0}^{2}}{8 R}$

answer is A, B, C.

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Detailed Solution

$I_{1} = \frac{E_{0}}{2 R} \sin (ω t + \frac{π}{3}) I_{2} = \frac{E_{0}}{2 R} \sin ω t I = I_{1} + I_{2} = 2 (\frac{E_{0}}{2 R} \cos 30^{0}) \sin (ω t + \frac{π}{6})$

$\frac{\sqrt{3} E_{0}}{2 R} \sin (ω t + \frac{π}{6}) = \frac{E_{0}}{Z} \sin (ω t + \frac{π}{6})$

$Z = \frac{2 R}{\sqrt{3}}, P h a s e d i f f e r e n c e ϕ = \frac{π}{6}, p o w e r f a c t o r = \cos ϕ = \frac{\sqrt{3}}{2}, \tan ϕ = \frac{Reactance}{Resistance} = \frac{x}{R'} = \frac{1}{\sqrt{3}} \sqrt{R'^{2} + x^{2}} = Z \Rightarrow R' = R_{1} x = \frac{R}{\sqrt{3}}$