Relationship between phase voltage and line voltage in 3 phase wye connection Or Root 3 factor between line and phase voltage, current in delta, Wye connection

There is √3 function in between wye and delta voltage and current relationship in case of phase and line, this might have easy for you but forgot in time. As this a simple tricky question asked in the interview board so better to understand this basic electrical facts.

In case of Wye connection iL = ip, but vL = √3 x vp. And in case of delta connection iL = √3 x ip, but vL = vp. The core reason behind this is the vector sum of two parameters. Say for simple arithmetic sum p + p = 2p, but with vector sum p+p by angle 120 = √3p. 

Why- Root 3 factor between line and phase voltage, current
Whether it is delta connection or Wye connection the addition will follow the vector triangle rule in these case.

For delta connection line voltage = phase voltage,

But line current = phase current 1 + Phase current 2.

Vector triangle rule for adding 

                                   

Sine rule to calculate √3 function in between wye and delta voltage and current relationship