An inductance of $2 \text{ mH}$,a capacitor of $20 \mu\text{F}$,and a resistance of $50 \Omega$ are connected in series to an $A.C.$ source. The reactance of the inductor and the capacitor are the same. The reactance of either of them will be: (in $Omega$)

An $LCR$ circuit as shown in the figure is connected to a voltage source $V_{ac}$ whose frequency can be varied. The frequency,at which the voltage across the resistor is maximum,is......$Hz$.

The frequencies at which the current amplitude in an $LCR$ series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value are $212\,rad\,s^{-1}$ and $232\,rad\,s^{-1}$. The value of resistance in the circuit is $R = 5\,\Omega$. The self-inductance in the circuit is $.........\,mH$.

$A$ resistor of resistance $R$, an inductor of inductive reactance $2R$, and a capacitor of capacitive reactance $X_C$ are connected in series to an $A.C.$ source. If the series $LCR$ circuit is in resonance, then the power factor of the circuit and the value $X_C$ are respectively:

$A$ parallel plate capacitor in series with a resistance of $100 \Omega$,an inductor of $20 \text{ mH}$,and an $AC$ voltage source of variable frequency shows resonance at a frequency of $\frac{1250}{\pi} \text{ Hz}$. If this capacitor is charged by a $DC$ voltage source to a voltage of $25 \text{ V}$,what amount of charge will be stored in each plate of the capacitor?

What is the sharpness of resonance and obtain an equation for the $Q$ factor?