A alternating current at any instant is given by $$i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]$$ A. The $$r m s$$ value of the current is ______ A.

A power transmission line feeds input power at $$2.3 \mathrm{~kV}$$ to a step down transformer with its primary winding having 3000 turns. The output power is delivered at $$230 \mathrm{~V}$$ by the transformer. The current in the primary of the transformer is $$5 \mathrm{~A}$$ and its efficiency is $$90 \%$$. The winding of transformer is made of copper. The output current of transformer is _________ $$A$$.

A series LCR circuit with $$\mathrm{L}=\frac{100}{\pi} \mathrm{mH}, \mathrm{C}=\frac{10^{-3}}{\pi} \mathrm{F}$$ and $$\mathrm{R}=10 \Omega$$, is connected across an ac source of $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$ supply. The power factor of the circuit would be ________.

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $$\frac{E^{a}}{2 b} \mathrm{~J} / s$$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $$\frac{b}{a}$$ will be __________.