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 $, H$)?

In an $LCR$ series circuit, an alternating voltage source of frequency $F$ is connected. The current leads the voltage by $45^{\circ}$. The value of $L$ is

In a simple $L-R$ circuit with an $A.C.$ source,the potential difference at any instant across the inductor and the resistor are $V_L$ and $V_R$ respectively,and the $A.C.$ source has a potential difference $V_{AC}$ at the same instant. Then:

An $ac$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\omega/3$ (while maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

An arc lamp requires a direct current of $10\ A$ at $80\ V$ to function. If it is connected to a $220\ V$ (rms),$50\ Hz$ $AC$ supply,the series inductor needed for it to work is close to: (in $H$)

In an $RL$ circuit,the current is $i = 100 \sin(314t) \ A$ and the voltage is $e = 200 \sin(314t + \pi/3) \ V$. If the resistance is $1 \ \Omega$,what is the reactance?