An inductance of $1\, mH$,a capacitor of $10\, \mu F$,and a resistance of $50\, \Omega$ are connected in series. The reactances of the inductor and the capacitor are the same. The reactance of either of them will be........$\Omega$.

$A$ $20 \Omega$ resistance,$10 \text{ mH}$ inductance coil,and $15 \mu \text{F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination,the circuit resonates. If the resistance is made $1/3$ rd of its original value,the resonant frequency:

$A$ series $LCR$ circuit containing a resistance $R$ has angular frequency $\omega$. At resonance,the voltage across the resistance and the inductor are $V_R$ and $V_L$ respectively. Then,the value of inductance $L$ will be:

$A$ series $LCR$ circuit is connected across a source of alternating emf of changing frequency and resonates at frequency $f_0$. Keeping capacitance constant,if the inductance $(L)$ is increased by $\sqrt{3}$ times and resistance is increased $(R)$ by $1.4$ times,the resonant frequency now is

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 $.........\,mH$.

The plot given below shows the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is