To increase the resonant frequency in a series $LCR$ circuit,

The plot given below is of the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is

$A$ $50 \text{ Hz}$ $AC$ circuit has a $10 \text{ mH}$ inductor and a $2 \text{ } \Omega$ resistor in series. The value of capacitance to be placed in series in the circuit to make the circuit power factor as unity is

Figure $(a)$ shows the plot of voltage across the capacitor as a function of the driving frequency for a sinusoidally driven electromagnetic $LCR$ oscillator 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 $(b)$. Choose the correct statement:

In the circuit shown in the figure, the ratio of the quality factor $(Q)$ to the bandwidth $(\Delta \omega)$ is $.............$ s.

For a series $LCR$ circuit at resonance,the statement which is not true is: