For an $L-C-R$ $AC$ circuit,the resonance frequency is $5000 \ Hz$ and the frequencies at half-power points are $4950 \ Hz$ and $5050 \ Hz$. What will be the $Q$-factor?

The $Q$-factor of a resonant circuit is equal to

Two circuits are shown in the figures $(a)$ and $(b)$. At a frequency of $....\,rad/s$,the average power dissipated in one cycle will be the same in both circuits.

$A$ 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

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

An $AC$ circuit consists of an inductor of inductance $0.5 \, H$ and a capacitor of capacitance $8 \, \mu F$ in series. The current in the circuit is maximum when the angular frequency of the $AC$ source is