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 .......... $H$.

$A$ 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-

In a series $CR$ circuit shown in the figure,the applied voltage is $10 \, V$ and the voltage across the capacitor is found to be $8 \, V$. Then the voltage across $R$,and the phase difference between the current and the applied voltage will respectively be:

An induction coil has an impedance of $10\,\Omega$. When an $AC$ signal of frequency $1000\,Hz$ is applied to the coil,the voltage leads the current by $45^o$. The inductance of the coil is

$A$ student connects a long air-cored coil of manganin wire to a $100 \ V$ $DC$ supply and records a current of $25 \ A$. When the same coil is connected across a $100 \ V, 50 \ Hz$ $AC$ supply,the current reduces to $20 \ A$. The reactance of the coil is $...... \Omega$.

If $L$ and $R$ are respectively the inductance and resistance,then the dimensions of $\frac{R}{L}$ will be