$A$ resistor $R$,an inductor $L$,and a capacitor $C$ are connected in series to an oscillator of frequency $N$. If the resonance frequency is $N_R$,then the current lags behind the voltage when:

For the $LCR$ circuit shown here,the current is observed to lead the applied voltage. An additional capacitor $C'$,when joined with the capacitor $C$ present in the circuit,makes the power factor of the circuit unity. The capacitor $C'$ must have been connected in

$A$ telegraph line of length $100 \, km$ has a capacity of $0.01 \, \mu F/km$ and it carries an alternating current at $0.5 \, kHz$. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is . . . . . . $mH$. (Take $\pi = \sqrt{10}$)

An inductor coil is connected to a capacitor and an $AC$ source of rms voltage $8 \, V$ in series. The rms current in the circuit is $16 \, A$ and is in phase with the emf. If this inductor coil is connected to a $6 \, V$ $DC$ battery, the magnitude of the steady current is (in $A$)

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:

Obtain the resonant frequency $\omega_{r}$ of a series $LCR$ circuit with $L=2.0 \;H, C=32\; \mu F$ and $R=10\; \Omega$. What is the $Q$-value of this circuit?