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Which of the following statement is correct regarding the AC circuit shown in the adjacent figure?

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Average power dissipated in the circuit is 500 W

The rms value of current through the circuit is $i_{r m s} = 5 \sqrt{2} A$

The phase difference between source emf and current is $ϕ = \cos^{- 1} (\frac{1}{3})$

None of the above

answer is D.

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Detailed Solution

$X_{C} = X_{L} ∴ Z = R = 2 Ω I_{r m s} = \frac{V_{r m s}}{Z} = \frac{(\frac{100}{\sqrt{2}})}{2} = 25 \sqrt{2} A$

Phase difference will be zero as the circuit is effectively purely resistive at this frequency.

Average power $P_{a v} = V_{r m s} I_{r m s} \cos ϕ = \frac{100}{\sqrt{2}} \times 25 \sqrt{2} \times \cos 0^{\circ} = 2500 W$

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