An inductance coil has a resistance of $80 \Omega$. When an $AC$ signal of frequency $480 \text{ Hz}$ is applied to the coil,the voltage leads the current by $45^{\circ}$. The inductance of the coil in henry is $\left[\sin 45^{\circ}=\cos 45^{\circ}=1 / \sqrt{2}\right]$

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

The figure given below shows an $LCR$ series circuit with two switches $S_1$ and $S_2$. When switch $S_1$ is closed keeping $S_2$ open, the phase difference $(\phi)$ between the current and source voltage is $30^\circ$ and the phase difference is $60^\circ$ when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1 - L_2)$ is . . . . . . $H$.

$A$ long solenoid connected to a $12\,V\, DC$ source passes a steady current of $2\,A.$ When the solenoid is connected to a source of $12\,V\, RMS$ at $50\,Hz,$ the current flowing is $1\,A\, RMS.$ Then the inductance of the solenoid is ....$mH$.

An inductor and a resistor are connected in series to an ac supply. If the potential differences across the inductor and the resistor are $180 \ V$ and $240 \ V$ respectively,then the voltage of the ac supply is (in $V$)

$A$ circuit element $X$ when connected to an a.c. supply of peak voltage $100\,V$ gives a peak current of $5\,A$ which is in phase with the voltage. $A$ second element $Y$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi}{2}$. If $X$ and $Y$ are connected in series to the same supply,what will be the rms value of the current in ampere?