$A$ tuned amplifier circuit is used to generate a carrier frequency of $ 2 \text{ MHz} $ for amplitude modulation. The value of $ \sqrt{LC} $ is

$A$ resistor of $50 \Omega$,an inductor of self-inductance $(\frac{2}{\pi^2}) \text{ H}$,and a capacitor of unknown capacity are connected in series to an $A$.$C$. source of $100 \text{ V}, 50 \text{ Hz}$. When the voltage and current are in phase,the value of the capacitance is: (in $\mu \text{F}$)

Figure $(a)$ shows a plot of voltage across the capacitor as a function of the driving frequency for a sinusoidally driven electromagnetic $LCR$ circuit. Figure $(b)$ shows the phase angle $\phi$ (phase difference between voltage and current) vs $\omega / \omega_0$ graph for the same circuit,for three different quality factors corresponding to graphs $1, 2, 3$ of figure $(a)$. Each graph in figure $(a)$ can be matched by one of the graphs $a, b, c$ in figure $(b)$. Which of the following statements is correct?

For the series $LCR$ circuit shown in the figure,what is the resonance angular frequency and the amplitude of the current at the resonating frequency? The source voltage is given as $220 \, V$ ($RMS$ value).

In an $LCR$ circuit, the resonant frequency is $600 \ Hz$ and the half-power points are at $650 \ Hz$ and $550 \ Hz$. The quality factor is:

The $Q$-value of a series $LCR$ circuit with $L=2 \ H$,$C=32 \ \mu F$,and $R=20 \ \Omega$ is: