Power factor is maximum in an $LCR$ circuit when

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

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

On which factor does the sharpness of resonance depend?

An inductor of inductance $2 \mu H$ is connected in series with a resistance,a variable capacitor and an a.c. source of frequency $5 \text{ kHz}$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x} \text{ F}$,where the value of '$x$' is (Take $\pi^2 = 10$).

In a series resonant $LCR$ circuit,for the power dissipated to become half of the maximum power dissipated,the current amplitude is