The impedance of the given circuit is......$\Omega $

The $L-C-R$ circuit shown below is driven by an ideal $AC$ voltage source. At frequency $f=\frac{1}{2 \pi \sqrt{L C}}$,choose the correct statement.

$A$ coil is connected to an $AC$ source with peak emf, $8 \, V$ and frequency $\frac{30}{\pi} \, Hz$. The coil has a resistance of $8 \, \Omega$. If the average power dissipated by the coil is $0.4 \, W$, then the inductance of the coil is (in $, H$)

$A$ capacitor and an inductance coil are connected in separate $AC$ circuits with a bulb glowing in both the circuits. The bulb glows more brightly when

$A$ resistor of resistance $30 \Omega$, an inductor of reactance $10 \Omega$, and a capacitor of reactance $10 \Omega$ are connected in series to an $AC$ voltage source $V = 300 \sqrt{2} \sin(\omega t)$. The current in the circuit is . . . . . . (in $\text{ A}$)

The power factor of the given $LCR$ circuit is $1/\sqrt{2}$. Find the capacitance $C$ of the circuit in $\mu F$.