When the frequency of the $AC$ voltage applied to a series $LCR$ circuit is gradually increased from a low value, the impedance of the circuit

The resonant frequency of an $L-C$ circuit is

$A$ parallel combination of a pure inductor and a capacitor is connected across a source of alternating e.m.f. '$e$'. The currents flowing through the inductor and the capacitor are $i_{L}$ and $i_{C}$ respectively. In this parallel resonant circuit,the condition for the currents $i$,$i_{L}$,and $i_{C}$ is ($i =$ net r.m.s. current in the circuit).

Two circuits are shown in the figures $(a)$ and $(b)$. At a frequency of $....\,rad/s$,the average power dissipated in one cycle will be the same in both circuits.

In which of the following $AC$ circuit, we get the value of power factor $1$ at resonance condition?

Resonance frequency of $L-C-R$ series $AC$ circuit is $f_0$. Now,if the inductance is reduced to $\frac{1}{4}$ times and the capacitance is increased to $16$ times,then the new resonance frequency becomes: