Explain resonance for an $L-C-R$ series circuit and write its uses. In what kind of circuit will it be possible?

(N/A) For an $L-C-R$ series circuit driven by a voltage source with amplitude $V_{m}$ and angular frequency $\omega$,the current amplitude $I_{m}$ is given by:
$I_{m} = \frac{V_{m}}{Z} = \frac{V_{m}}{\sqrt{R^{2} + (X_{C} - X_{L})^{2}}}$
where $X_{C} = \frac{1}{\omega C}$ is the capacitive reactance and $X_{L} = \omega L$ is the inductive reactance.
Resonance occurs when the current amplitude $I_{m}$ is maximum. This happens when the impedance $Z$ is minimum. Since $Z = \sqrt{R^{2} + (X_{C} - X_{L})^{2}}$,$Z$ is minimum when $X_{C} - X_{L} = 0$,or $X_{C} = X_{L}$.
At this condition:
$X_{C} = X_{L} \implies \frac{1}{\omega_{0} C} = \omega_{0} L \implies \omega_{0}^{2} = \frac{1}{LC} \implies \omega_{0} = \frac{1}{\sqrt{LC}}$
where $\omega_{0}$ is the resonant angular frequency.
At resonance,the impedance $Z = R$,and the current amplitude is $I_{m} = \frac{V_{m}}{R}$.
Uses: Resonance in $L-C-R$ circuits is primarily used in tuning circuits for radio and television receivers to select a specific frequency from a range of signals.
It is possible only in a series $L-C-R$ circuit containing both an inductor $(L)$ and a capacitor $(C)$.