An inductor of inductance 2 $$\mathrm{\mu H}$$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit $$\frac{1}{x}\mathrm{F}$$, where the value of $$x$$ is ___________.

(Take $$\pi=\frac{22}{7}$$)

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80$$\Omega$$, an inductor of inductive reactance $$\mathrm{X_L=70\Omega}$$, and a capacitor of capacitive reactance $$\mathrm{X_C=130\Omega}$$. The power factor of circuit is $$\frac{x}{10}$$. The value of $$x$$ is :

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $$\Omega$$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH.

(Take $$\pi^2=10$$)

In the circuit shown in the figure, the ratio of the quality factor and the band width is ___________ s.