Question

2. In a balanced Y-Y four-wire connection system, the source is an abc sequence of voltage and ??? = 100∠0 0 . The load impedance per phase is 4 + ?7 Ω , and the line impedance per phase is 2+?1 Ω. Solve for the Line Current and Neutral Current.

Answer 1

okay so here lets understand few concepts Beforehand , Then we swill start the question.

In Y or ( Star ) connected system the phase voltage = 1/ times the line voltage and the line current = phase current

And further the neutral current only exists when there is a load imbalance or impedance imbalance ( as in such a case different phase have different currents thus to equalise them the extra current exits through the neutral ) but since here the line and load impedence per phase are equal ,the system is balanced thus neutral current is 0.

now once we have figured out these consider the picture below to get through the solving process. here we are provided directly with the phase voltage ( Van means voltage between a and neutral ie the phase voltage ) so no need for conversion

the dotted box here shows the phase we are considering ,also notice that since this is three phase the supply voltage can have different phases ie 0 , 120 and -120 but in all cases only the phase of the line current will change but its magnitude will remain constant as 10A . further I've shown the phasor conversion of the impedance on the top right corner .

Hope This Helps !

Edit : in the first and third line the voltage is 100 not 10 .( sorry for the misprint )