In an $LCR$ circuit,at resonance

An inductor of $0.5 \text{ mH}$, a capacitor of $20 \text{ } \mu\text{F}$ and resistance $20 \text{ } \Omega$ are connected in series with a $220 \text{ V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2} \text{ A}$. The value of $x$ is

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

$A$ telegraph line of length $100 \, km$ has a capacity of $0.01 \, \mu F/km$ and it carries an alternating current at $0.5 \, kHz$. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is . . . . . . $mH$. (Take $\pi = \sqrt{10}$)

An a.c. e.m.f. of peak value $V_0 = 230 \ V$ and frequency $f = 50 \ Hz$ is connected to a circuit with $R = 11.5 \ \Omega$,$L = 2.5 \ H$ and a capacitor $C$ all in series. For the current in the circuit to be maximum,the circuit must be in resonance. Find the value of $C$ and the maximum current $I_{max}$ (take $\pi^2 = 10$).

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