In a series $RLC$ circuit $(AC)$:
$L = 10 \, mH$
$C = 0.01 \, \mu F$
$R = 50 \, \Omega$
If the supply voltage is $V = 10 \sin \omega t$,find the power dissipated at resonance in $W$.

$A$ series $LCR$ circuit containing a resistance $R$ has angular frequency $\omega$. At resonance,the voltage across the resistance and the inductor are $V_R$ and $V_L$ respectively. Then,the value of inductance $L$ will be:

In an $LCR$ circuit, at a particular angular frequency $\omega_0$, the capacitive reactance and inductive reactance are the same. If the angular frequency is doubled to $2\omega_0$, what will be the ratio of the reactance of the capacitor to that of the inductor?

For a series $LCR$ circuit with $L=2 \ H, C=18 \ \mu F$ and $R=10 \ \Omega$. What is the value of the $Q$ factor of this circuit?

The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated,the resonance frequency of the circuit is $10\, kHz$. When the container is filled with a gas,the resonance frequency changes by $50\, Hz$. The dielectric constant of the gas is

In a series $L-C-R$ circuit,$C = 2 \mu F$,$L = 1 \ mH$,and $R = 10 \ \Omega$. What is the ratio of energies stored in the inductor and the capacitor when the maximum current flows in the circuit?