For the circuit shown in figure the rms value of voltage across $R$ and coil are $E_1$ and $E_2$ respectively. The thermal power dissipated in coil is

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