In an $LCR$ circuit, the resonant frequency is $600 \ Hz$ and the half-power points are at $650 \ Hz$ and $550 \ Hz$. The quality factor is:

In a series $LCR$ circuit, $C = 2 \mu F$, $L = 5 \text{ mH}$, and $R = 5 \Omega$. What is the ratio of the energy stored in the inductor to that in the capacitor when the maximum current flows through the circuit (in $:$)?

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?

$A$ series $LCR$ circuit is connected to a $45 \sin (\omega t) \text{ V}$ source. The resonant angular frequency of the circuit is $10^5 \text{ rad s}^{-1}$ and current amplitude at resonance is $I_0$. When the angular frequency of the source is $\omega = 8 \times 10^4 \text{ rad s}^{-1}$, the current amplitude in the circuit is $0.05 I_0$. If $L = 50 \text{ mH}$, match each entry in List-$I$ with an appropriate value from List-$II$ and choose the correct option.

List-$I$	List-$II$
$(P)$ $I_0$ in $\text{mA}$	$(1)$ $44.4$
$(Q)$ The quality factor of the circuit	$(2)$ $18$
$(R)$ The bandwidth of the circuit in $\text{rad s}^{-1}$	$(3)$ $400$
$(S)$ The peak power dissipated at resonance in $\text{Watt}$	$(4)$ $2250$
	$(5)$ $500$

$A$ circuit containing resistance $R_1$,inductance $L_1$,and capacitance $C_1$ connected in series resonates at the same frequency $f_r$ as another circuit containing $R_2$,$L_2$,and $C_2$ in series. If the two circuits are connected in series,then the new frequency at resonance is

An $LC$ series resonant circuit produces a resonant frequency $f$. If $L$ is tripled and $C$ is increased by $3C$ (making the new capacitance $4C$),the new resonant frequency will be: