An ideal inductance coil is connected to a parallel plate capacitor. Electrical oscillation with energy $\mathrm{W}$ are set up in this circuit. The capacitor plates are slowly drawn apart till the frequency of oscillations is doubled. The work done in this process will be - 

An$\mathrm{LC}$ oscillatory circuit is shown in the figure. Its natural frequency is given by

The sinusoidal output current by a rectifier is shown in figure. The current amplitude is $2\mathrm{\pi } \mathrm{A}$. The average value of output current is:

A series $\mathrm{LCR}$ circuit is shown in the figure. If inductor is removed from the circuit then current leads the voltage by $45°$ while if the capacitor is removed then the current lags the voltage by $45°$. The rms current in the original$\mathrm{LCR}$ circuit is

The current in a certain circuit varies with time as shown. The peak value of current is $I_0$. If $i_v$ and $i_m$ represent the virtual (rms) and mean value of current for a complete cycle respectively, then

For a series$\mathrm{LCR}$ circuit given below, ${\mathrm{\omega }}_0$ is the resonance frequency. Then $\left(R=12\Omega , {\mathrm{\omega }}_{0}L=6\right.$$\mathrm{\Omega }$and operating angular frequency, $\mathrm{\omega }$ is half of the resonance frequency i.e. $\mathrm{\omega }=\frac{{\mathrm{\omega }}_0}{2}$)