In an LC oscillator circuit L = 10 mH, C = 40µF. If initially at t = 0 the capacitor is fully charged with 4µC then find the current in the circuit when the capacitor and inductor share equal energies. 

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 $\text{'}\mathrm{i}\text{'}$