Two identical coils each having inductance L are placed together on the same core. If an overall inductance of $$\alpha$$L is obtained by interconnecting these two coils, the minimum value of $$\alpha$$ is ________.

In the given network $$V_1=100\angle0^\circ V$$, $$V_2=100\angle-120^\circ V$$, $$V_3=100\angle+120^\circ V$$. The phasor current i (in Ampere) is

A series RLC circuit is observed at two frequencies. At $$\omega_1$$ = 1k rad / s, we note that source voltage $$V_1=100\angle0^\circ V$$ results in a current $$I_1=0.03\angle31^\circ\;A$$. At $$\omega_2$$ = 2 k rad/s, the source voltage $$V_2=100\angle0^\circ\;V$$ results in a current $$I_2=2\angle0^\circ\;A$$. The closest values for R,L,C out of the following options are

The total power dissipated in the circuit, show in the figure, is 1kW. The ideal voltmeter, across the load, reads 200 V. The value of X_L is _________.