A series circuit consists of a… | JEE Advanced 2025 P1

A series circuit consists of a resistor R=30 Ω, an inductor L=0.12 H and a capacitor C=100 muF, connected across an ac source of rms voltage 100 V…

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A series circuit consists of a resistor

R=30\ \Omega

, an inductor

L=0.12\ \mathrm{H}

and a capacitor

C=100\ \mu\mathrm{F}

, connected across an ac source of rms voltage

100\ \mathrm{V}

and angular frequency

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

. Match the quantities in List-I with List-II.

List-I
(P) rms current in the circuit
(Q) average power dissipated in the circuit
(R) power factor of the circuit
(S) rms voltage across the capacitor

List-II
(1)

0.6

(2)

2\ \mathrm{A}

(3)

120\ \mathrm{W}

(4)

0.8

(5)

40\ \mathrm{V}

A. P→2, Q→3, R→4, S→5
B. P→2, Q→5, R→1, S→3
C. P→4, Q→3, R→1, S→5
D. P→2, Q→3, R→1, S→5

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Answer: (D) P→2, Q→3, R→1, S→5

The reactances are

X_L=\omega L=500\times0.12=60\ \Omega

and

X_C=\dfrac{1}{\omega C}=\dfrac{1}{500\times10^{-4}}=20\ \Omega

. The net reactance is

40\ \Omega

and the impedance

Z=\sqrt{30^2+40^2}=50\ \Omega

. (P)

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

, so P→2. (Q) The average power is

I^2R=4\times30=120\ \mathrm{W}

, so Q→3. (R) The power factor is

\cos\phi=R/Z=30/50=0.6

, so R→1 (the value

0.8

\sin\phi

, the distractor). (S)

V_C=IX_C=2\times20=40\ \mathrm{V}

, so S→5. The correct code is P→2, Q→3, R→1, S→5; the other codes use

\sin\phi

for the power factor or mismatch the power and the voltage.

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