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

The a.c. source is connected to series LCR circuit. If voltage across $$R$$ is $$40 \mathrm{~V}$$, that across $$\mathrm{L}$$ is $$80 \mathrm{~V}$$ and that across $$\mathrm{C}$$ is $$40 \mathrm{~V}$$, then the e.m.f. '$$e$$' of a.c. source is

In a series LCR circuit, $$\mathrm{C}=2 \mu \mathrm{F}, \mathrm{L}=1 \mathrm{mH}$$ and $$\mathrm{R}=10 \Omega$$. The ratio of the energies stored in the inductor and the capacitor, when the maximum current flows in the circuit, is

The a.c. source of e.m.f. with instantaneous value '$$e$$' is given by $$e=200 \sin (50 t)$$ volt. The r.m.s. value of current in a circuit of resistance $$50 \Omega$$ is