$A$ series $LCR$ circuit is connected to an ac voltage source. When $L$ is removed from the circuit,the phase difference between current and voltage is $\frac{\pi}{3}$. If instead $C$ is removed from the circuit,the phase difference is again $\frac{\pi}{3}$ between current and voltage. The power factor of the circuit is:

$A$ parallel plate capacitor in series with a resistance of $100 \Omega$, an inductor of $20 \text{ mH}$, and an $AC$ voltage source of variable frequency shows resonance at a frequency of $\frac{1250}{\pi} \text{ Hz}$. If this capacitor is charged by a $DC$ voltage source to a voltage of $25 \text{ V}$, what amount of charge will be stored in each plate of the capacitor?

The total impedance of a series $L-C-R$ circuit varies with the angular frequency of the $AC$ source connected to it,as shown in the graph. The quality factor $Q$ of the series $L-C-R$ circuit is:

$A$ sinusoidal voltage having a maximum value of $283 \ V$ and a frequency of $50 \ Hz$ is applied to an $LCR$ series circuit where $R = 3 \ \Omega$,$L = 25.48 \ mH$,and $C = 796 \ \mu F$. What is the impedance at resonance condition (in $\Omega$)?

$A$ resistor of $100 \Omega$,an inductor of self-inductance $(\frac{4}{\pi^2}) \text{ H}$,and a capacitor of unknown capacitance are connected in series to an $A$.$C$. source of $200 \text{ V}, 50 \text{ Hz}$. When the current and voltage are in phase,the capacitance and the power dissipated are respectively:

$A$ capacitor of $250\,\mu F$ is connected in parallel to a coil of inductance $0.16\,mH$, while its effective resistance is $20\,\Omega$. Determine the resonant frequency.