An inductor of inductance $L$,a capacitor of capacitance $C$,and a resistor of resistance $R$ are connected in series to an $ac$ source. The quality factor of the circuit is

$A$ series $LCR$ circuit with $L=0.5 \text{ H}$ and $R=10 \Omega$ is connected to an $AC$ supply with $rms$ voltage and frequency equal to $200 \text{ V}$ and $\frac{150}{\pi} \text{ Hz}$, respectively. The magnitude of the capacitance is varied so that the current amplitude in the circuit becomes maximum. The $rms$ voltage difference across the inductor is (in $\text{ V}$)

The plot given below shows the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is

$A$ $100 \, \Omega$ 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 $\text{H}$)

The quality factor of an $LCR$ circuit having resistance $(R)$ and inductance $(L)$ at resonance frequency $(\omega)$ is given by:

$A$ resistor of $50 \Omega$,an inductor of self-inductance $\left(\frac{3}{\pi^2}\right) H$,and a capacitor of unknown capacity are connected in series to an a.c. source of $100 \ V$ and $50 \ Hz$. When the voltage and current are in phase,the value of capacitance is (nearly):