With an increase in the frequency of an $A.C.$ supply,the impedance of an $L-C-R$ series circuit

An inductance of $\left(\frac{200}{\pi}\right) \text{mH}$,a capacitance of $\left(\frac{10^{-3}}{\pi}\right) \text{F}$,and a resistance of $10 \, \Omega$ are connected in series with an $AC$ source of $220 \, \text{V}, 50 \, \text{Hz}$. The phase angle of the circuit is:

The power factor of the given $LCR$ circuit is $1/\sqrt{2}$. Find the capacitance $C$ of the circuit in $\mu F$.

Power dissipated in an $LCR$ series circuit connected to an $a.c.$ source of electromotive force (emf) $\varepsilon$ is:

When $L$, $C$, and $R$ are connected in series with an $AC$ source of frequency $f$, the current leads the voltage by a phase angle of $45^{\circ}$. What is the value of $C$?

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 $= 10 \sqrt{2} \ V$