At a moment $\left(t=0\right),$ when the charge on capacitor $C_1$ is zero, the switch is closed. If $I_0$ be the current through the inductor at $t=0$, for $\mathrm{ }t>0$ (initially, $C_2\mathrm{ }$is uncharged.)

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 $\text{'}\mathrm{i}\text{'}$