A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, star connected load through a star-delta transformer as shown in the figure. The line-to-line voltage rating is 230 V on the star side, and 115 V on the delta side. If the magnetizing current is neglected and $${\overline{\mathrm I}}_\mathrm s=100\angle0^\circ$$, then what is the value of $${\overline{\mathrm I}}_\mathrm p$$ in Ampere?

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?

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 ________.

A 220 V, 3-phase, 4-pole, 50 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 225 % of full load torque and it occurs at 15% slip. The actual rotor resistance is 0.03 Ω/phase. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is ______.