JEE Main 2023 · Physics · Electromagnetic Induction and Alternating Current · medium

A 100 V (rms) source of angular frequency 400 rad s^-1 drives a series circuit of a 30 Ω resistor, an ideal inductor of 0.2 H and a capacitor of 62.5…

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100\ \mathrm{V}

(rms) source of angular frequency

400\ \mathrm{rad\,s^{-1}}

drives a series circuit of a

30\ \Omega

resistor, an ideal inductor of

0.2\ \mathrm{H}

and a capacitor of

62.5\ \mu\mathrm{F}

. The average power dissipated in the circuit is

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Answer: (A) $120\ \mathrm{W}$

X_L=\omega L=80\ \Omega

and

X_C=\dfrac1{\omega C}=\dfrac{1}{400\times62.5\times10^{-6}}=40\ \Omega

. Impedance

Z=\sqrt{30^2+(80-40)^2}=50\ \Omega

I_{rms}=100/50=2\ \mathrm{A}

and the power is dissipated only in the resistor:

P=I_{rms}^2R=4\times30=120\ \mathrm{W}

(equivalently

VI\cos\phi=100\times2\times0.6

V^2/R=333\ \mathrm{W}

would be the value only at resonance.

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