In a series $RLC$ circuit,the resonance frequency is $12 \text{ kHz}$. If $R = 5 \text{ } \Omega$ and $X_L$ at resonance is $300 \text{ } \Omega$,the half-power frequencies will be:

An $AC$ circuit has $R = 100 \, \Omega$,$C = 2 \, \mu F$,and $L = 80 \, mH$ connected in series. The quality factor of the circuit is $.......$

In an $LCR$ series circuit at resonance:

What is the value of inductance $L$ in $mH$ for which the current is maximum in a series $LCR$ circuit with $C = 10 \, \mu F$ and $\omega = 1000 \, rad/sec$?

$A$ 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?

In a series $LCR$ resonant circuit,the capacitance is changed from $C$ to $3C$. To obtain the same resonant frequency,the inductance should be changed from $L$ to