With which of the following is the relationship between the phase of current and voltage in an $AC$ circuit represented?

The self-inductance of a choke coil is $10\, mH$. When it is connected to a $10\, V$ $dc$ source,the power loss is $20\, W$. When it is connected to a $10\, V$ $ac$ source,the power loss is $10\, W$. The frequency of the $ac$ source is......$Hz$.

Statement-$I$: $A$ capacitor can be used in an $a.c.$ circuit in place of a choke coil.
Statement-$II$: $A$ capacitor blocks $d.c.$ and allows $a.c.$ to pass.

Match List-$I$ with List-$II$ and choose the correct answer from the options given below:

List-$I$	List-$II$
$A$. Purely capacitive circuit	$I$. $I$ leads $V$ by $90^{\circ}$
$B$. Purely inductive circuit	$II$. $I$ and $V$ are in phase
$C$. $LCR$ series at resonance	$III$. $V$ leads $I$ by angle $\theta$
$D$. $LCR$ series circuit	$IV$. $V$ leads $I$ by $90^{\circ}$

You are given many resistances,capacitors and inductors. These are connected to a variable $DC$ voltage source (the first two circuits) or an $AC$ voltage source of $50 \ Hz$ frequency (the next three circuits) in different ways as shown in Column $II$. When a current $I$ (steady state for $DC$ or rms for $AC$) flows through the circuit,the corresponding voltage $V_1$ and $V_2$ (indicated in circuits) are related as shown in Column $I$. Match the two.

In domestic electric mains supply,the voltage and the current are