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 $J$)

The resonant frequency of a series $LCR$ circuit is $f$. The circuit is now connected to a sinusoidally alternating e.m.f. of frequency $2f$. The new reactance $X_{L}^{\prime}$ and $X_{C}^{\prime}$ are related as:

The power in an $AC$ circuit is given by $P = E_{rms}I_{rms} \cos \phi$. The value of $\cos \phi$ in a series $LCR$ circuit at resonance 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

In a series $LCR$ resonant circuit,the quality factor is measured as $100$. If the inductance is increased by two fold and resistance is decreased by two fold,then the quality factor after this change will be .........

$A$ $L-C-R$ series $AC$ circuit is tuned to resonance. The impedance of the circuit is now . . . . . . .