I am stuck on a example on my notes. Below is the Example.

Supply: 400V, 50Hz, 3-phase, 3-wire
Load: non-reactive, star connected
phase A - 10kW
phase B - 6kW
phase C - 4kW
Find: current in all 4 conductors

Here is a part of the solution:
Va = 231 /_ 0 degree, Vb=231 /_120 degree, Vc=231 /_120 degree
Ra=(Va)^2/Wa = 231^2/10x1000 = 5.336Ω
Rb=(Vb)^2/Wb = 231^2/6x1000 = 8.893Ω
Rc=(Vc)^2/Wc = 231^2/4x1000 = 13.340Ω

However, In the alternative solution, it gives another way to find out the answer. It first calculates the voltage at the star point(Vn) which is equal to 22.91 /_19.06 degree.

I am confused. Take Ra as an example, if the voltage at star point is not equal to zero, then the voltage across Ra = Va-Vn, which means
Ra=(Va - Vn)^2/Wa.

Can anyone explain this to me?

Any help would be appreciated

 

Sorry, I made a mistake, it should be Find: current in all 3 conductors

 

Your point is valid.

The method of calculating the resistance values is incorrect. Is that your method or something given in class or in a textbook. With an unbalanced load the line to floating star point voltage obviously can't be assumed to be the line to neutral voltage.

I suspect the only way to solve the problem is to indeed find the offset star point voltage and go from there.