An inductor of $0.5 \ mH$,a capacitor of $20 \ \mu F$ and a resistance of $20 \ \Omega$ are connected in series with a $220 \ V$ a.c. source. If the current is in phase with the e.m.f.,the maximum current in the circuit is $\sqrt{x} \ A$. The value of '$x$' is

In the given circuit,the readings of voltmeters $V_1$ and $V_2$ are $300 \, V$ each. The readings of voltmeter $V_3$ and ammeter $A$ are respectively:

$A$ resonant frequency of a circuit is $f$. If the capacitance is made four times the initial value,then the resonant frequency will become

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:

The resonance frequency of an $L-C-R$ $AC$ circuit is $\nu_{0}$. If the capacitance is made $4$ times its initial value,then the new resonance frequency will become . . . . . . .

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?