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:

Which of the following plots may represent the reactance of a series $LC$ combination?

An e.m.f. $E = E_{0} \sin \omega t$ is applied to a circuit containing $L$ and $R$ in series. If $X_{L} = R$,then the power dissipated in the circuit is

$A$ 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-

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?

$A$ resistor of $200 \; \Omega$ and a capacitor of $15.0 \; \mu F$ are connected in series to a $220 \; V, 50 \; Hz$ $ac$ source.
$(a)$ Calculate the current in the circuit.
$(b)$ Calculate the voltage $(rms)$ across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes,resolve the paradox.