When a capacitor is connected in a series $LR$ circuit,what happens to the alternating current flowing in the circuit?

$A$ series $LCR$ circuit consists of an inductor $L$,a capacitor $C$,and a resistor $R$ connected across a source of emf $\varepsilon = \varepsilon_0 \sin \omega t$. When $\omega L = \frac{1}{\omega C}$,the current in the circuit is $I_0$. If the angular frequency of the source is changed to $\omega^{\prime}$,the current in the circuit becomes $\frac{I_0}{2}$. Then,the value of $\left|\omega^{\prime} L - \frac{1}{\omega^{\prime} C}\right|$ is

In the adjoining figure,the impedance of the circuit will be $... \Omega$.

In the circuit shown in the figure,the $AC$ source provides a voltage $V = 20 \cos(2000t)$. Neglecting source resistance,the voltmeter and ammeter readings will be:

Find the impedance of the circuit in $\Omega$.

For the given figure,choose the correct option.