The current in a series $LCR$ circuit will be maximum when $\omega$ is

An $AC$ voltage $V = 220 \sin(2 \times 10^3 t) \text{ V}$ is applied to a series $LCR$ circuit. The current amplitude in this circuit is: (Given: $L = 10 \text{ mH}$, $C = 25 \mu\text{F}$, $R = 100 \Omega$) (in $\text{ A}$)

$A$ 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

The resonance point in the $X_L - f$ and $X_C - f$ curves is

In the circuit shown,the ratio of the quality factor to the bandwidth is: (in $\text{ s}$)

$A$ 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 $\mu \text{F}$)