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.

A capacitor of capacitance 500 $$\mu$$F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _______ A.