When $100\, V$ $DC$ is applied across a solenoid,a current of $1\, A$ flows in it. When $100\, V$ $AC$ is applied across the same coil,the current drops to $0.5\, A$. If the frequency of the $AC$ source is $50\, Hz$,the impedance and inductance of the solenoid are:

The diagram shows a capacitor $C$ and a resistor $R$ connected in series to an $ac$ source. $V_1$ and $V_2$ are voltmeters and $A$ is an ammeter. Consider the following statements:
$I$. Readings in $A$ and $V_2$ are always in phase.
$II$. Reading in $V_1$ lags behind the reading in $V_2$ by $\frac{\pi}{2}$.
$III$. Readings in $A$ and $V_1$ are always in phase.
Which of these statements is/are correct?

The following series $L-C-R$ circuit,when driven by an emf source of angular frequency $70 \text{ krad/s}$,behaves effectively as:

An a.c. source of $15 \, V, 50 \, Hz$ is connected across an inductor $(L)$ and resistance $(R)$ in series. The $R.M.S.$ current of $0.5 \, A$ flows in the circuit. The phase difference between the applied voltage and current is $\left(\frac{\pi}{3}\right)$ radian. The value of resistance $(R)$ is $\left(\tan 60^{\circ}=\sqrt{3}\right)$. (in $\Omega$)

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

$A$ $220\, V$,$50\, Hz$ $ac$ source is connected to an inductance of $0.2\, H$ and a resistance of $20\, \Omega$ in series. What is the current in the circuit (in $, A$)?