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.

The frequencies at which the current amplitude in an LCR series circuit becomes $$\frac{1}{\sqrt{2}}$$ times its maximum value, are $$212\,\mathrm{rad} \,\mathrm{s}^{-1}$$ and $$232 \,\mathrm{rad} \,\mathrm{s}^{-1}$$. The value of resistance in the circuit is $$R=5 \,\Omega$$. The self inductance in the circuit is __________ $$\mathrm{mH}$$.

To light, a $$50 \mathrm{~W}, 100 \mathrm{~V}$$ lamp is connected, in series with a capacitor of capacitance $$\frac{50}{\pi \sqrt{x}} \mu F$$, with $$200 \mathrm{~V}, 50 \mathrm{~Hz} \,\mathrm{AC}$$ source. The value of $$x$$ will be ___________.

The effective current I in the given circuit at very high frequencies will be ___________ A.