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

An electric bulb rated $100 \,W - 300 \,V$ is connected to an $AC$ supply of $500 \,V$ and $\frac{150}{\pi} \,Hz$. The required inductance to save the electric bulb is .......... $H$.

Two resistors are connected in series across a $5\,V\,rms$ source of alternating potential. The potential difference across the $6\,\Omega$ resistor is $3\,V$. If $R$ is replaced by a pure inductor $L$ of such magnitude that the current remains the same,then the potential difference across $L$ is.......$V$.

For the $L-R$ circuit shown in the figure,calculate the phase angle in degrees if the frequency is $f = 100/\pi \ Hz$. The inductance is $L = 0.025 \ H$ and the resistance is $R = 5 \ \Omega$.

Which of the following dimensions will be the same as that of time?

$A$ circuit contains an inductance of $\frac{1}{6 \pi} \text{ H}$ and a resistance of $15 \text{ } \Omega$ in series. If an $AC$ voltage of $100 \text{ V}$ and $60 \text{ Hz}$ is applied to the circuit,then the current in the circuit and the phase difference between voltage and current are,respectively: