At a particular angular frequency,the reactance of a capacitor and that of an inductor are the same. If the angular frequency is doubled,the ratio of the reactance of the capacitor to that of the inductor will be:

$A$ bulb is connected first with $DC$ and then $AC$ of the same voltage. In which case will it shine more brightly?

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. $AC$ generator	$I$. Detects the presence of current in the circuit
$B$. Galvanometer	$II$. Converts mechanical energy into electrical energy
$C$. Transformer	$III$. Works on the principle of resonance in $AC$ circuit
$D$. Metal detector	$IV$. Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below:

Given below are two statements:
Statement $I$: An $AC$ circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement $II$: An $AC$ circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.
In the light of the above statements,choose the correct answer from the options given below:

An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit,the capacitor is charged to $Q_0$ and then connected to the $L$ and $R$ as shown below. If a student plots graphs of the square of maximum charge $(Q_{Max}^2)$ on the capacitor with time $(t)$ for two different values $L_1$ and $L_2$ $(L_1 > L_2)$ of $L$,then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale.)

$A$ resistor $R$, an inductor $L$, and a capacitor $C$ are connected in series with an a.c. source. When $L$ is removed from the circuit, the phase difference between voltage and current in the circuit is $\pi/3$. If instead, $C$ is removed from the circuit, the phase difference is again $\pi/3$. The power factor of the circuit is