In the circuit shown in figure $S_1$ is open and, $S_2$ and $S_3$ are closed. The circuit is in steady state. At time $t=0$, switch $S_1$, is closed and $S_2$ and $S_3$ are opened simultaneously. $V=100 \mathrm{V}$, $R=10 \mathrm{\Omega }, C=100 \mathrm{\mu F}, L=0.03 \mathrm{H}$

Find the maximum charge that will appear on the capacitor at any time

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 :

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 $\text{'}\mathrm{i}\text{'}$

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.