In an $LCR$ circuit having $L = 8.0 \, H$,$C = 0.5 \, \mu F$,and $R = 100 \, \Omega$ in series,the resonance frequency in radians per second is:

In a series $LCR$ circuit with $C = 2 \mu F$,$L = 1 \ mH$,and $R = 10 \ \Omega$,when the current in the circuit is maximum,what is the ratio of the energy stored in the capacitor to the energy stored in the inductor?

$A$ $100 \, \Omega$ resistance,a $0.1 \, \mu \text{F}$ capacitor,and an inductor are connected in series across a $250 \, \text{V}$ supply at variable frequency. Calculate the value of inductance of the inductor at which resonance will occur. Given that the resonant frequency is $60 \, \text{Hz}$. (In $\text{H}$)

In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

$A$ 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 $L-C-R$ series circuit with $100 \, \Omega$ resistance is connected to an $ac$ source of $100 \, V$ and angular frequency $300 \, rad/s$. When the capacitance is removed, the current lags behind the voltage by $45^{\circ}$. When the inductance is removed, the current leads the voltage by $45^{\circ}$. The current flowing in the circuit will be ... $A$.