In an a.c. circuit with pure capacitance $C$ and a.c. source $E=E_0 \sin \omega t$,the equation of instantaneous current is given by

The inductive reactance of a coil is $R$. If the inductance of the coil is doubled and the frequency of the $A.C.$ supply is also doubled,then the new inductive reactance will be:

If we decrease the frequency of the applied $A.C.$ with a purely capacitive load,do $(1)$ the amplitude of $V_c$ and $(2)$ amplitude of $I_c$ increase,decrease,or remain the same?

Given below are two statements:
Statement-$I$: In an $AC$ circuit,the current through a capacitor leads the voltage across it.
Statement-$II$: In $AC$ circuits containing pure capacitance only,the phase difference between the current and the voltage is $\pi$.
In the light of the above statements,choose the most appropriate answer from the options given below:

As shown in the figure,an inductor of inductance $L = 200 \, mH$ is connected to an $AC$ source of emf $220 \, V$ and frequency $f = 50 \, Hz$. The peak value of current is given by $\frac{\sqrt{a}}{\pi} \, A$. The value of $a$ is..........

$A$ sinusoidal supply of frequency $10 \,Hz$ and $r.m.s.$ voltage $12 \,V$ is connected to a $2.1 \,\mu F$ capacitor. What is the $r.m.s.$ value of current in $mA$?