(B) In an $LR$ circuit,the impedance $Z$ is given by $Z = \sqrt{X_{L}^{2} + R^{2}}$.Given $X_{L} = R$,we have $Z = \sqrt{R^{2} + R^{2}} = \sqrt{2}R$.T

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(B) In an $LR$ circuit,the impedance $Z$ is given by $Z = \sqrt{X_{L}^{2} + R^{2}}$.Given $X_{L} = R$,we have $Z = \sqrt{R^{2} + R^{2}} = \sqrt{2}R$.The power factor $P_{1} = \cos \phi = \frac{R}{Z} = \frac{R}{\sqrt{2}R} = \frac{1}{\sqrt{2}}$.When a capacitor is added such that $X_{L} = X_{C}$,the circuit becomes a series $LCR$ circuit at resonance.In resonance,the impedance $Z = R$.The power factor $P_{2} = \cos \phi = \frac{R}{Z} = \frac{R}{R} = 1$.Therefore,the ratio $\frac{P_{1}}{P_{2}} = \frac{1/\sqrt{2}}{1} = \frac{1}{\sqrt{2}}$.

Class 12 Physics Alternating Current Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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In a series $LR$ circuit,$X_{L} = R$ and the power factor of the circuit is $P_{1}$. When a capacitor with capacitance $C$ such that $X_{L} = X_{C}$ is put in series,the power factor becomes $P_{2}$. The ratio $\frac{P_{1}}{P_{2}}$ is

JEE MAIN 2022 All JEE MAIN

A
$\frac{1}{2}$
B
$\frac{1}{\sqrt{2}}$
C
$\frac{\sqrt{3}}{\sqrt{2}}$
D
$1$

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Alternating Current

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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In a series $LR$ circuit,$X_{L} = R$ and the power factor of the circuit is $P_{1}$. When a capacitor with capacitance $C$ such that $X_{L} = X_{C}$ is put in series,the power factor becomes $P_{2}$. The ratio $\frac{P_{1}}{P_{2}}$ is

Similar Questions

For an $RLC$ circuit driven with voltage of amplitude $v_m$ and frequency $\omega_0 = \frac{1}{\sqrt{LC}}$,the current exhibits resonance. The quality factor,$Q$,is given by:

$A$ series $LCR$ circuit of $R=5 \, \Omega, L=20 \, \text{mH}$ and $C=0.5 \, \mu \text{F}$ is connected across an $AC$ supply of $250 \, \text{V}$,having variable frequency. The power dissipated at resonance condition is $..... \times 10^{2} \, \text{W}$.

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