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A three-winding transformer is connected to an $AC$ voltage source as shown in the figure. The number of turns are as follows: $N_{1} = 100, N_{2} = 50, N_{3} = 50$. If the magnetizing current is neglected, and the currents in two windings are $\overline{I}_{2}=2\angle 30^{\circ}$A and $\overline{I}_{3}=2\angle 150^{\circ}$A, then what is the value of the current $\overline{I}_{1}$ in Ampere?

  1. $1\angle 90^{\circ}$
  2. $1\angle 270^{\circ}$
  3. $4\angle 90^{\circ}$
  4. $4\angle 270^{\circ}$
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