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. $\mathrm{\omega }=\frac{{\mathrm{\omega }}_0}{2}$)

Which of the following is/are correct for alternating current circuit?

An alternating voltage $E=6\sin 20t+8\cos 20t$, is applied to a series resonant circuit as shown. The correct statements are :

In the circuit shown, a parallel combination of a coil of inductance $L$, resistance $R$ and a capacitor of capacitance $C$ are connected across a battery of emf ${\mathrm{\epsilon }}_0$ and internal resistance $r_0$. At $t=0$, switch $S$ is closed, then