Obtain the resonant frequency $\omega_{r}$ of a series $LCR$ circuit with $L=2.0 \;H, C=32\; \mu F$ and $R=10\; \Omega$. What is the $Q$-value of this circuit?

Assertion: In a series $LCR$ circuit,resonance can take place.
Reason: Resonance takes place if inductive and capacitive reactances are equal and opposite.

Obtain the equation of bandwidth for an $L-C-R$ series $AC$ circuit and deduce the equation of $Q$ factor.

$A$ 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:

$A$ series $LCR$ circuit with inductance $L = 10\,H$,capacitance $C = 10\,\mu F$,and resistance $R = 50\,\Omega$ is connected to an $AC$ source of voltage $V = 200 \sin(100t)\,V$. If the resonant frequency of the $LCR$ circuit is $\nu_{0}$ and the frequency of the $AC$ source is $\nu$,then:

$A$ circuit containing resistance $R_1$,inductance $L_1$,and capacitance $C_1$ connected in series resonates at the same frequency $f_r$ as another circuit containing $R_2$,$L_2$,and $C_2$ in series. If the two circuits are connected in series,then the new frequency at resonance is