The resonance frequency of $LC$ circuit is

In the above circuit, $C=\frac{\sqrt{3}}{2}\mu F,R_2=20\mathrm{ \Omega },L=\frac{\sqrt{3}}{10}H$ and $R_1=10\mathrm{ \Omega }.$ Current in $L\text{-}{R}_1$ path is $I_1$ and in $C-R_2$ path it is $I_2.$ The voltage of $$AC source is given by, $V=200\sqrt{2}\sin \left(100t\right)$ volts. The phase difference between $I_1$ and $I_2$ 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

In the circuit shown below, the key is pressed at time $t=0$. Which of the following statement(s) is(are) true?

An inductor $(L=0.03\mathrm{\hspace{0.17em}}\mathrm{H})$ and a resistor $(R=0.15 \mathrm{\hspace{0.17em}}\mathrm{k\Omega })$ are connected in series to a battery of $15\mathrm{\hspace{0.17em}}\mathrm{V}$ E.M.F. in a circuit shown below. The key $K_1$ has been kept closed for a long time. Then at $t=0$, $K_1$ is opened and key $K_2$ is closed simultaneously. At $t=1\mathrm{\hspace{0.17em}}\mathrm{ms}$ , the current in the circuit will be : $\left(\text{Take}, e^5\approx 150\right)$

In the figure shown, a circuit contains two identical resistors with resistance $R=5\Omega$ and an inductance with $L=2mH.$ An ideal battery of $15V$ is connected in the circuit. What will be the current through the battery long after the switch is closed?