Question

Why is voltage applied to star vwinding 1/root 3 x line voltage

Answer 1

In a balanced 3-phase system, VL= [(3)^(1/2)]Vph

where, VL=Line voltage magnitude, and Vph=phase voltage magnitude

To prove this refer to any standard text book on Basic Electrical Engineering. In the chapter on 3-phase circuits you will find the phasor diagram showing the phase and line voltages and phase and line currents and their relationships.