In an $LCR$ oscillatory circuit,find the energy stored in the inductor at resonance. If the voltage of the source is $10 \, V$,the resistance is $10 \, \Omega$,and the inductance is $1 \, H$. (in $J$)

For the $LCR$ circuit shown here,the current is observed to lead the applied voltage. An additional capacitor $C'$,when joined with the capacitor $C$ present in the circuit,makes the power factor of the circuit unity. The capacitor $C'$ must have been connected in

Given below are two statements:
Statement $I$: When the frequency of an $a.c.$ source in a series $LCR$ circuit increases,the current in the circuit first increases,attains a maximum value,and then decreases.
Statement $II$: In a series $LCR$ circuit,the value of the power factor at resonance is one.
In the light of the given statements,choose the most appropriate answer from the options given below:

For an $R-L-C$ circuit,driven with voltage of amplitude $V_m$ and frequency $\omega_0 = \frac{1}{\sqrt{LC}}$,the current exhibits resonance. The quality factor $Q$ is

$A$ series $LCR$ circuit with resistance $R=500 \ \Omega$ is connected to an a.c. source of $250 \ V$. When only the capacitance is removed,the current lags behind the voltage by $60^{\circ}$. When only the inductance is removed,the current leads the voltage by $60^{\circ}$. The impedance of the circuit is

When the frequency of the $AC$ voltage applied to a series $LCR$ circuit is gradually increased from a low value, the impedance of the circuit