Deduce the relationship between the phase and the line voltages of a three-phase star-connected system.

3.C] Deduce the relationship between the phase and the line voltages of a three-phase star-connected system.

Consider a balanced star-connected load as shown in fig.

The three phase voltages are displaced by 120° from each other. The phasor diagram to get
V_RY is shown in the above. The V_Y is reversed to get −V_Y and then it is added to V_R to get V_RY.
The perpendicular is drawn from point A on vector OB representing V_L. In triangle OAB, the
sides OA and AB are same as phase voltages. Hence OB bisects angle between V_R and −V_Y.