In a series $RLC$ circuit $(AC)$:
$L = 10 \, mH$
$C = 0.01 \, \mu F$
$R = 50 \, \Omega$
If the supply voltage is $V = 10 \sin \omega t$,find the power dissipated at resonance in $W$.

$A$ series $LCR$ circuit is shown in the figure. Where the inductance of $10 \ H$,capacitance $40 \ \mu F$,and resistance $60 \ \Omega$ are connected to a variable frequency $240 \ V$ source. The current at resonating frequency is (in $A$)

In a series $LCR$ circuit,the inductance $L$ is $10\,mH$,capacitance $C$ is $1\,\mu F$ and resistance $R$ is $100\,\Omega$. The frequency at which resonance occurs is:

An inductor of inductance $2 \text{ } \mu\text{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of $10 \text{ kHz}$. The value of capacitance for which maximum current is drawn in the circuit is $\frac{1}{x} \text{ F}$, where the value of $x$ is (Take $\pi^2 = 10$).

Match List-$I$ with List-$II$ :

List-$I$	List-$II$
$(a)$ $\omega L > \frac{1}{\omega C}$	$(i)$ Current is in phase with $emf$
$(b)$ $\omega L = \frac{1}{\omega C}$	$(ii)$ Current lags behind the applied $emf$
$(c)$ $\omega L < \frac{1}{\omega C}$	$(iii)$ Maximum current occurs
$(d)$ Resonant frequency	$(iv)$ Current leads the $emf$

Choose the correct answer from the options given below :

Obtain an equation for the sharpness of resonance in an $L-C-R$ series $AC$ circuit. What is the quality factor $Q$? Explain bandwidth.