Can Voltage Division Be Used to Solve Transformer Line/Load Ratio?

[Bluestribute]

Homework Statement

(in picture)

Homework Equations

V=IZ

The Attempt at a Solution

So last time I had to do KCL to find voltages, so I want to make sure I'm doing this one right. Can I do voltage division and do V_load/V_G?

My division would be V_G(500<36.87)/(500<36.87 + 60<53.13)

But that approach seems incredibly simply when normally, these problems have some more work involved . . .

 

[CalcNerd]

It's an early problem in the chapter, so it is probably just that simple to provide voltage division across the load. Confirm you don't need to use complex conjugate for power across load.

 

[Bluestribute]

Really? So I got VL as 11.83<-1.726. The ratio is a complex number, but the real part is 0.89 . . . That seems incredibly good? Is it too good?

And for the second part of the question (distribution losses), I'm assuming V^2/R over the Zline component, ignoring the "imaginary" portion of the impedance because it's power losses . . .

 

[CalcNerd]

Your answer looks correct to me. And it looks good. It is supposed to look good. The low losses are due to the low resistance of the power lines (delivery system) of the grid. Power lost on the line doesn't get metered and sold.