When capacitor is fully charged, find current drawn from the cell. $9\, V $ (in $mA$)

A particle, of mass $10^{-3} kg$ and charge $1.0 C$, is initially at rest. At time $t =0$, the particle comes under the influence of an electric field $\dot{E}( t )= E _0 \sin \omega t \hat{ i }$, where $E _0=1.0 N C ^{-1}$ and $\omega=10^3 rad s ^{-1}$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in $m s ^{-1}$, attained by the particle at subsequent times is. . . . . .

In the given circuit, the $AC$ source has $\omega=100 \ rad / s$. considering the inductor and capacitor to be ideal, the correct choice $(s)$ is(are)

$(A)$ The current through the circuit, $I$ is $0.3 \ A$

$(B)$ The current through the circuit, I is $0.3 \sqrt{2} \ A$.

$(C)$ The voltage across $100 \Omega$ resistor $=10 \sqrt{2} \ V$

$(D)$ The voltage across $50 \Omega$ resistor $=10 \ V$

A light bulb and an open coil inductor are connected to an ac source through a key as shown in Figure

The switch is closed and after sometime, an iron rod is inserted into the interior of the inductor. The glow of the light bulb $(a)$ increases; $(b)$ decreases; $(c)$ is unchanged, as the iron rod is inserted. Give your answer with reasons

$AC$ alternating emf $\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$ volt is applied to a capacitor of $2 \mu \mathrm{F}$, the rms value of current in the circuit is.. . . . . .$\mathrm{mA}$.