A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as follows: N₁=100, N₂=50, N₃=50. If the magnetizing current is neglected, and the currents in two windings are $${\overline I}_2=2\angle30^\circ$$ A and $${\overline I}_3=2\angle30^\circ$$ A, then what is the value of the current $${\overline I}_1$$ in Ampere?

A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is 200 radian/second. At its rated torque of 500 Nm, its speed is 180 radian/second. The motor is used to directly drive a load whose load torque T_L depends on its rotational speed $$\omega_r$$ (in radian/second), such that $$T_L=2.78\times\omega_r$$. Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is _______.

Two three-phase transformers are realized using single-phase transformers as shown in the figure. The phase difference (in degree) between voltages V₁ and V₂ is _______.

The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 50 Hz. The 'air-gap' voltage, V_g across the magnetizing inductance, is 210V_rms, and the slip, s, is 0.05. The torque (in Nm) produced by the motor is ________.