In an $LCR$ circuit,$L = 8.0 \, H$,$C = 0.5 \, \mu F$,and $R = 100 \, \Omega$ are connected in series. The resonance angular frequency is ........ $rad/s$.

In a series $R-L-C$ $AC$ circuit,for a particular value of $R, L$ and $C$,the power supplied by the source is $P$ at resonance. If the value of inductance is halved,then the power from the source again at resonance is $P'$. Then:

$A$ resonant frequency of a circuit is $f$. If the capacitance is made four times the initial value,then the resonant frequency will become

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 $Hz$)?

Which graph shows the correct variation of r.m.s. current '$i$' with frequency '$f$' of a.c. in case of a series resonant circuit?

For better tuning of a series $LCR$ circuit in a communication system,the preferred combination is