In a series $LCR$ circuit,$C = 2\,\mu F$,$L = 1\,mH$,and $R = 10\,\Omega$. When the current in the circuit is maximum,what is the ratio of the energy stored in the capacitor to the energy stored in the inductor?

Given below are two statements:
Statement $I$: When the frequency of an $a.c.$ source in a series $LCR$ circuit increases,the current in the circuit first increases,attains a maximum value,and then decreases.
Statement $II$: In a series $LCR$ circuit,the value of the power factor at resonance is one.
In the light of the given statements,choose the most appropriate answer from the options given below:

$A$ series $L-C-R$ circuit containing a resistance $R$ has angular frequency $\omega$. At resonance,the voltages across the resistance and the inductor are $V_R$ and $V_L$ respectively. The value of the capacitance is:

In a series $LCR$ circuit, $C = 2 \text{ } \mu\text{F}$, $L = 1 \text{ mH}$, and $R = 10 \text{ } \Omega$. What is the ratio of energies stored in the capacitor and inductor when maximum current flows through the circuit (in $: 1$)?

In a series $LCR$ resonant circuit,the quality factor is measured as $100$. If the inductance is increased by two fold and resistance is decreased by two fold,then the quality factor after this change will be .........

$A$ $50 \text{ Hz}$ $AC$ circuit has a $10 \text{ mH}$ inductor and a $2 \text{ } \Omega$ resistor in series. The value of capacitance to be placed in series in the circuit to make the circuit power factor as unity is