In an $L-C-R$ series $AC$ circuit,$L = 9 \ H$,$R = 10 \ \Omega$,and $C = 100 \ \mu F$. The $Q$-factor of the circuit is . . . . . . .

The output voltage (taken across the resistance) of an $L-C-R$ series resonant circuit falls to half its peak value at a frequency of $200 \,Hz$ and again reaches the same value at $800 \,Hz$. The bandwidth of this circuit is ............. $\,Hz$.

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?

$A$ resonance circuit having inductance and resistance $2 \times 10^{-4} \ H$ and $6.28 \ \Omega$ respectively oscillates at $10 \ MHz$ frequency. The value of the quality factor of this resonator is .........
$[\pi = 3.14]$

In an a.c. $LCR$ circuit,a capacitor and an inductor in series are connected with an a.c. voltage source of $90\,V$. An ammeter and a voltmeter are connected in the circuit to measure the current in the circuit and the voltage across the capacitor plus the inductor combination. If $X_L = X_C = 4\,\Omega$ and $R = 45\,\Omega$,the readings of the ammeter $(I)$ and the voltmeter $(V)$ are:

$A$ series combination of a resistor of resistance $100\,\Omega$,an inductor of inductance $1\,H$,and a capacitor of capacitance $6.25\,\mu F$ is connected to an $AC$ source. The quality factor of the circuit will be $.............$.