An $AC$ circuit consists of an inductor of inductance $0.5 \, H$ and a capacitor of capacitance $8 \, \mu F$ in series. The current in the circuit is maximum when the angular frequency of the $AC$ source is

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:

To increase the resonant frequency in a series $LCR$ circuit,

$A$ series resonant circuit consists of an inductor $L$ and capacitor $C$ which produces resonant frequency $f$. If $L$ is increased by $2L$ (making the new inductance $L' = L + 2L = 3L$) and $C$ is changed to $9C$, the new resonant frequency will be:

The power factor of an $LCR$ circuit at resonance is:

An $LC$ circuit consists of a capacitor and a coil with a large number of turns. Suppose all the linear dimensions of all elements of the circuit are increased by a factor of $2$ while keeping the number of turns on the coil constant. How much does the resonant frequency of the circuit change?