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An alternating $e.m.f.$ of frequency $v = \frac{1}{2\pi \sqrt{LC}}$ is applied to a series $LCR$ circuit. For this frequency of the applied $e.m.f.$:

In an $LCR$ circuit having $L = 8.0 \, H$,$C = 0.5 \, \mu F$,and $R = 100 \, \Omega$ in series,the resonance frequency in radians per second is:

In the given $LCR$ circuit,the voltage across the terminals of the resistance and the current in the circuit will be:

In the circuit shown in the figure,an a.c. source gives voltage $V = 20 \cos (2000 t)$. The impedance and r.m.s. current respectively will be:

$A$ series $LCR$ circuit with $L=0.12\, H$,$C=480\, nF$,$R=23\, \Omega$ is connected to a $230\, V$ variable frequency supply.
$(a)$ What is the source frequency for which current amplitude is maximum? Obtain this maximum value.
$(b)$ What is the source frequency for which average power absorbed by the circuit is maximum? Obtain the value of this maximum power.
$(c)$ For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
$(d)$ What is the $Q$-factor of the given circuit?

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