In the given circuit,the $rms$ value of current $(I_{rms})$ through the resistor $R$ is: $..........\,A$

$A$ $400 \Omega$ resistor, a $250 \text{ mH}$ inductor, and a $2.5 \mu \text{F}$ capacitor are connected in series with an $AC$ source of peak voltage $5 \text{ V}$ and angular frequency $\omega = 2000 \text{ rad/s}$. What is the peak value of the electrostatic energy of the capacitor (in $\mu \text{J}$)?

An inductance of $0.2 \ H$ and resistance of $100 \ \Omega$ are connected in series to an $AC$ of $180 \ V$,$50 \ Hz$ supply. The $RMS$ current flowing in the circuit will be . . . . . . (Take $\pi^2$ as $10$). (in $A$)

An inductor and a resistor are connected in series to an $AC$ source of voltage $V = 144 \sin \left(100 \pi t + \frac{\pi}{2}\right) \text{ V}$. If the current in the circuit is $I = 6 \sin \left(100 \pi t + \frac{\pi}{6}\right) \text{ A}$,then the resistance of the resistor is: (in $\Omega$)

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:

In an $RL$ circuit,the resistance is $\pi \sqrt{3} \,\Omega$. The phase difference between the current and the voltage is $30^\circ$. The $ac$ frequency is $50 \,Hz$. The inductance is . . . . . . $Henry$.