In an $ac$ circuit,the reactance of a coil is $\sqrt{3}$ times its resistance. The phase difference between the voltage across the coil and the current through the coil will be:

$A$ coil has a resistance of $30 \Omega$ and an inductive reactance of $20 \Omega$ at $50 \text{ Hz}$ frequency. If an $AC$ source of $200 \text{ V}$,$100 \text{ Hz}$ is connected across the coil,the current in the coil is

In an $LCR$ series $a.c.$ circuit,the voltage across each of the components $L, C$ and $R$ is $60 \,V$. The voltage across the $LC$ combination is

$A$ resistor and a pure inductor are connected to an $AC$ supply of $120\,V$ and $50\,Hz$. The current in the circuit is $3\,A$. If the power consumed in the circuit is $108\,W$,then the resistance in the circuit is.....$\Omega $

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$,(keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is

With an alternating voltage source of frequency $f$,an inductor $L$,a capacitor $C$,and a resistor $R$ are connected in series. The voltage leads the current by $45^{\circ}$. The value of $L$ is $(\tan 45^{\circ} = 1)$.