A series LCR circuit is designed to resonate at an angular frequency $\omega_{0}=10^{5} \mathrm{rad} / \mathrm{s}$. The circuit draws 16 W power from 120 V source at resonance. The value of resistance ' R ' in the circuit is \_\_\_\_ $\Omega$.

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Alternating Current

A series LCR circuit is designed to resonate at an angular frequency

ω_{0} = 1 0^{5} rad / s

. The circuit draws 16 W power from 120 V source at resonance. The value of resistance ' R ' in the circuit is
____

Ω

Answer: 900

Solution

At resonance the inductive and capacitive reactances cancel, so the impedance of the series circuit is the resistance alone and the whole source voltage appears across it. The power drawn is then

P = \frac{V ^{2}}{R}

R = \frac{V ^{2}}{P} = \frac{( 120 ) ^{2}}{16} = \frac{14400}{16}

. The resistance in the circuit is

900 Ω

JEE Main · 2021 · 24 Feb 2021 · Shift 2 · Integer answer

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