A square shaped coil of area $$70 \mathrm{~cm}^{2}$$ having 600 turns rotates in a magnetic field of $$0.4 ~\mathrm{wbm}^{-2}$$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes 500 revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $$60^{\circ}$$ with the field, will be ____________ V. (Take $$\pi=\frac{22}{7}$$)

A series LCR circuit is connected to an ac source of $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$. The circuit contain a resistance $$\mathrm{R}=100 ~\Omega$$ and an inductor of inductive reactance $$\mathrm{X}_{\mathrm{L}}=79.6 ~\Omega$$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $$\mu \mathrm{F}$$.

An inductor of $$0.5 ~\mathrm{mH}$$, a capacitor of $$20 ~\mu \mathrm{F}$$ and resistance of $$20 ~\Omega$$ are connected in series with a $$220 \mathrm{~V}$$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $$\sqrt{x}$$ A. The value of $$x$$ is ___________