An alternating current is flowing through a series $L-C-R$ circuit. It is found that the current reaches a value of $1 \ mA$ at both $200 \ Hz$ and $800 \ Hz$ frequency. What is the resonance frequency of the circuit (in $Hz$)?

An inductor of $0.5 \ mH$,a capacitor of $20 \ \mu F$ and a resistance of $20 \ \Omega$ are connected in series with a $220 \ V$ a.c. source. If the current is in phase with the e.m.f.,the maximum current in the circuit is $\sqrt{x} \ A$. The value of '$x$' is

What is the $Q$-factor (Quality factor) and on what factors does it depend?

$A$ series resonant $LCR$ circuit has a quality factor ($Q$-factor) $= 0.4$. If $R = 2 \, k\Omega$ and $C = 0.1 \, \mu F$,then the value of inductance is: (in $, H$)

In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad/s$. At resonance,the voltage across $L$ is......$V$.

For an $R-L-C$ circuit,driven with voltage of amplitude $V_m$ and frequency $\omega_0 = \frac{1}{\sqrt{LC}}$,the current exhibits resonance. The quality factor $Q$ is