$A$ current of $\frac{25}{\pi} \text{ Hz}$ frequency is passing through an $AC$ circuit having a series combination of $R=100 \ \Omega$ and $L=2 \text{ H}$. The phase difference between voltage and current is . . . . . . . (in $^{\circ}$)

When a d.c. voltage of $200 \, V$ is applied to a coil of self-inductance $\left(\frac{2 \sqrt{3}}{\pi}\right) \, H$, a current of $1 \, A$ flows through it. But by replacing the d.c. source with an a.c. source of $200 \, V$, the current in the coil is reduced to $0.5 \, A$. Then the frequency of the a.c. supply is: (in $ \, Hz$)

$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be-

$A$ coil of negligible resistance is connected in series with a $90 \Omega$ resistor across a $120 \text{ V}, 60 \text{ Hz}$ supply. $A$ voltmeter reads $36 \text{ V}$ across the resistor. The inductance of the coil is: (in $\text{ H}$)

What will be the self-inductance of a coil,to be connected in series with a resistance of $\pi \sqrt{3} \, \Omega$,such that the phase difference between the $EMF$ and the current at $50 \, Hz$ frequency is $30^o$ (in $, H$)?

$A$ pure inductor of $25.48 \ mH$ and a pure resistor of $8 \ \Omega$ are connected in series with an $AC$ source of frequency $50 \ Hz$. The phase difference between current $(I)$ and voltage $(V)$ in this circuit is . . . . . . . (in $^{\circ}$)