MHT CET · Physics · Alternating Current

In series LCR circuit $R = 18 Ω$ and impedance is $33 Ω$ . An RMS voltage of $220 V$ is applied across the circuit. The true power consumed in the AC circuit is

A $220 W$
B $400 W$
C $600 W$
D $800 W$

Verified Solution

Answer & Solution

Correct Answer

(D) $800 W$

Step-by-step Solution

Detailed explanation

P = e_{r m s} . i_{r m s} . \cos ϕ

= e_{r m s} . \frac{e_{r m s}}{Z} . \frac{R}{Z}

= \frac{220 \times 220 \times 18}{33 \times 33}

= \frac{20 \times 20 \times 18}{3 \times 3}

= 20 \times 20 \times 2

= 800 W

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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In series LCR circuit R=18 Ω and impedance is 33 Ω. An RMS voltage of 220 V is applied across the circuit. The true power consumed in the AC circuit is

Step-by-step Solution

In series LCR circuit $R = 18 Ω$ and impedance is $33 Ω$ . An RMS voltage of $220 V$ is applied across the circuit. The true power consumed in the AC circuit is