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 _______.

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?

For a single phase, two winding transformer, the supply frequency and voltage are both increased by 10%. The percentage changes in the hysteresis loss and eddy current loss, respectively are

The load shown in the figure absorbs 4 kW at a power factor of 0.89 lagging. Assuming the transformer to be ideal, the value of the reactance X to improve the input power factor to unity is ___________.