When a $DC$ voltage of $100 \, V$ is applied to an inductor, a $DC$ current of $5 \, A$ flows through it. When an $AC$ voltage of $200 \, V$ peak value is connected to the inductor, its inductive reactance is found to be $20\sqrt{3} \, \Omega$. The power dissipated in the circuit is . . . . . . $W$.

$A$ capacitor and a resistor of resistance $100 \sqrt{3} \Omega$ are connected in series to an $AC$ source of voltage $V = 100 \sin(200t) \text{ V}$,where $t$ is time in seconds. If the phase difference between the voltage and the current in the circuit is $30^{\circ}$,then the capacitance of the capacitor is: (in $\mu \text{F}$)

In an $RL$ circuit,the reactance of the coil is $\sqrt{3}$ times the resistance. The phase difference between the voltage and the current is:

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 $\Omega$)

Which one of the following curves represents the variation of impedance $(Z)$ with frequency $(f)$ in a series $L-C-R$ circuit,when connected to an $AC$ source?

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: