A series LCR circuit with $R=20 \Omega, L=1.6 \mathrm{H}$ and $C=40 \mu \mathrm{~F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\_\_\_\_$ $\Omega$.

An inductor of 10 mH , capacitor of $0.1 \mu \mathrm{~F}$ and a resistor of $100 \Omega$ are connected in series across an $a . c$ power supply $220 \mathrm{~V}, 70 \mathrm{~Hz}$. The power factor of the given circuit is 0.5 . The difference in the inductive reactance and capacitance reactance is $\sqrt{3} \alpha \Omega$. The value of $\alpha$ is $\_\_\_\_$ .

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ______. ($\pi = 3.14$)

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for $V=5 \sin (100 t)$ The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor ( C ) used is $\_\_\_\_$ $\mu \mathrm{F}$.