When a coil is connected across a $20 \ V$ $DC$ supply,it draws a current of $5 \ A$. When it is connected across a $20 \ V, 50 \ Hz$ $AC$ supply,it draws a current of $4 \ A$. The self-inductance of the coil is .............. $mH$. (Take $\pi=3$)

An emf $E = 6 \cos(6000t) \ V$ is applied to an $L-R$ circuit of inductance $L = 4 \ mH$ and resistance $R = 7 \ \Omega$. The amplitude of the current in the circuit is . . . . . . (in $A$)

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 $\omega$.

In a circuit made up of a resistance $4\,\Omega$ and an inductance $0.01\,H$,an alternating $emf$ of $200\,V$ at $50\,Hz$ is connected. The phase difference between the current and the $emf$ in the circuit is:

In a series $L-C-R$ circuit,the frequency of a $10 \, V$ $a.c.$ voltage source is adjusted in such a fashion that the reactance of the inductor measures $15 \, \Omega$ and that of the capacitor $11 \, \Omega$. If $R = 3 \, \Omega$,the potential difference across the series combination of $L$ and $C$ will be.....$V$.

An e.m.f. $E = E_0 \cos \omega t$ is applied to an $L-R$ circuit. The inductive reactance is equal to the resistance $R$ of the circuit. The power consumed in the circuit is: