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 __________.

A coil has an inductance of $$2 \mathrm{H}$$ and resistance of $$4 ~\Omega$$. A $$10 \mathrm{~V}$$ is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ___________ $$\times 10^{-2} \mathrm{~J}$$.

A series combination of resistor of resistance $$100 ~\Omega$$, inductor of inductance $$1 ~\mathrm{H}$$ and capacitor of capacitance $$6.25 ~\mu \mathrm{F}$$ is connected to an ac source. The quality factor of the circuit will be __________