In an $AC$ circuit,a resistance of $R$ $\Omega$ is connected in series with an inductor of self-inductance $L$. If the phase angle between voltage and current is $45^{\circ}$,the value of inductive reactance $(X_{L})$ will be equal to . . . . . . .

The time constant of the given $LR$ circuit is $\tau$. If the battery is replaced by an $AC$ source having voltage $V = V_0 \cos \omega t$,the power factor of the circuit will be

$A$ series $LCR$ circuit containing an $a.c.$ source of $100 \text{ V}$ has an inductor and a capacitor of reactance $24 \text{ } \Omega$ and $16 \text{ } \Omega$ respectively. If a resistance of $6 \text{ } \Omega$ is connected in series, then the potential difference across the series combination of inductor and capacitor only is: (in $\text{ V}$)

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:

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

In a circuit made up of a resistance $4\,\Omega$ and an inductance $0.01\,H$,an alternating $emf$ of $200\,V$ at $50\,Hz$ is connected. The phase difference between the current and the $emf$ in the circuit is: