In an $LC$ circuit shown in figure, $C=2 \mathrm{F}$ and $L=2 \mathrm{H}$. At time $t=0$, charge on the capacitor is $3$ coulomb and it is decreasing with rate of $\sqrt{4} \mathrm{C} {\mathrm{s}}^{-1}$. Then choose the correct statement.

If the instantaneous emf and the instantaneous current equations of an A.C. circuit are respectively.

$e=E0\sin (\omega t-\pi /6),i=I0\sin (\omega t+\pi /6),$ then the phase difference between voltage and current is :

At a certain moment, the switch shown in the figure is disconnected. The energy of the oscillations immediately after the switch $S$ is disconnected and at time $0.1 \sec$ from the time switch is disconnected are, respectively

Obtain an expression for the energy associated with an inductor.

Using the equation

 $\frac{\mathrm{di}}{\mathrm{dt}}+\frac{\mathrm{R}}{\mathrm{L}}\mathrm{i}+\frac{1}{\mathrm{LC}}\int \mathrm{idt}=\frac{{\mathrm{V}}_{\mathrm{m}}}{\mathrm{L}}{\mathrm{e}}^{\mathrm{i\omega t}}$.  for L-C-R circuit, obtain an equation for the complex current  $\text{'}\mathrm{i}\text{'}$ and explain its different terms in the equation. Hence obtain the equation for real current $\text{'}\mathrm{i}\text{'}$