JEE Main 2018 · Physics · Electromagnetic Induction and Alternating Current · medium

A series circuit has a resistor of 30 Ω, an inductor of 80 mH and a capacitor of 25 muF, driven by a 200 V (rms) source of angular frequency 1000 rad…

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A series circuit has a resistor of

30\ \Omega

, an inductor of

80\ \mathrm{mH}

and a capacitor of

25\ \mu\mathrm{F}

, driven by a

200\ \mathrm{V}

(rms) source of angular frequency

1000\ \mathrm{rad\,s^{-1}}

. The average power dissipated in the circuit is

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Answer: (A) $480\ \mathrm{W}$

Reactances:

X_L=\omega L=1000\times0.08=80\ \Omega

and

X_C=\dfrac1{\omega C}=\dfrac{1}{1000\times25\times10^{-6}}=40\ \Omega

. Impedance

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

. The rms current is

I=\dfrac{200}{50}=4\ \mathrm{A}

. Only the resistor dissipates power:

P=I^2R=16\times30=480\ \mathrm{W}

(equivalently

VI\cos\phi=200\times4\times0.6

). The value

V^2/R=1333\ \mathrm{W}

ignores the reactance, and

VI=800\ \mathrm{W}

is the apparent power.

Original question written in the JEE Main 2018 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake