JEE Main 2025 · Physics · Electromagnetic Induction and Alternating Current · medium

In a series LCR circuit driven by an AC source of frequency 50√(15) Hz, three ideal voltmeters read 160 V across the resistor, 300 V across the…

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In a series LCR circuit driven by an AC source of frequency

50\sqrt{15}\ \mathrm{Hz}

, three ideal voltmeters read

160\ \mathrm{V}

across the resistor,

300\ \mathrm{V}

across the inductor and

180\ \mathrm{V}

across the capacitor. The resonant frequency of the circuit is

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Answer: (B) $150\ \mathrm{Hz}$

With the same current in all elements, the voltage ratio equals the reactance ratio:

\dfrac{X_C}{X_L} = \dfrac{180}{300} = \dfrac35

. Now

X_L=\omega L

and

X_C = 1/\omega C

, so

\dfrac{X_C}{X_L} = \dfrac{1}{\omega^2 LC} = \dfrac{\omega_0^2}{\omega^2}

. Hence

\dfrac{f_0}{f} = \sqrt{\dfrac35}

and

f_0 = 50\sqrt{15}\times\sqrt{\dfrac{3}{5}} = 50\sqrt{9} = 150\ \mathrm{Hz}

. The resistor reading

160\ \mathrm{V}

is not needed for this ratio.

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