Give the value of impedance in resonance condition.

The frequency of $AC$ at which a $16 \mu F$ capacitor and a $\frac{10}{\pi^2} \ mH$ inductor will have the same reactance is: (in $kHz$)

$A$ series $LCR$ circuit with $L=0.12\, H$,$C=480\, nF$,$R=23\, \Omega$ is connected to a $230\, V$ variable frequency supply.
$(a)$ What is the source frequency for which current amplitude is maximum? Obtain this maximum value.
$(b)$ What is the source frequency for which average power absorbed by the circuit is maximum? Obtain the value of this maximum power.
$(c)$ For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
$(d)$ What is the $Q$-factor of the given circuit?

In an $L-C-R$ series circuit,the value of only capacitance $C$ is varied. The resulting variation of resonance frequency $f_0$ as a function of $C$ can be represented as

The $Q$-factor of a resonant circuit is equal to

$A$ series $L-C-R$ circuit containing a resistance $R$ has angular frequency $\omega$. At resonance,the voltages across the resistance and the inductor are $V_R$ and $V_L$ respectively. The value of the capacitance is: