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

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Discussion Overview

The discussion revolves around the application of voltage division in solving transformer line/load ratios, particularly in the context of a homework problem. Participants explore the validity of using voltage division to determine load voltage and discuss related concepts such as power losses in the distribution system.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant proposes using voltage division to find the load voltage, suggesting the formula Vload/VG based on given impedances.
  • Another participant confirms that voltage division might be appropriate for this early problem in the chapter, questioning the need for complex conjugates in power calculations.
  • A participant calculates the load voltage and expresses surprise at the favorable ratio obtained, questioning whether the result is too good to be true.
  • Another participant agrees with the calculated answer and explains that low losses are expected due to the low resistance of the power lines, noting that power lost on the line is not metered or sold.

Areas of Agreement / Disagreement

Participants generally agree on the validity of using voltage division for this problem, though there is some uncertainty regarding the implications of the results and the treatment of complex numbers in power calculations.

Contextual Notes

There are unresolved assumptions regarding the necessity of complex conjugates in power calculations and the implications of the calculated load voltage ratio.

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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 Vload/VG?

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

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

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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.
 
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 . . .
 
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.
 

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