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1. The problem statement, all variables and given/known data

This comes from "practice problem" 12.10 from Alexander's and Sadiku's Fundamentals of Electric circuits 3rd edition, chapter 12.

The problem statement is:

"Find the line currents in the unbalanced three-phase circuit of Fig. 12.26 and the real power absorbed by the load."

http://img413.imageshack.us/img413/8428/circuits.png [Broken]

2. Relevant equations

- LCK

3. The attempt at a solution

The problem is I can't get to the shown answer. I have followed two methods:

Getting I_AB and I_CA from the known phase voltages:

I_AB = (220|0º) / (5|-90º)

I_CA = (220|-120º)/(10|0º)

And then doing I_a = I_AB - I_CA.

The second method is to construct a 3x3 matrix with complex coefficients based on the three meshes shown in the circuit. For those of you familiar with mathematica notation my matrix is:

LinearSolve[{{-5 I, 5 I, 0}, {5 I, 10 + 5 I, -10 I}, {0, -10 I, 10 I}}, {220, 0, -110 + Sqrt[3]*0.5*I}]

where I is the imaginary number and the first solution would be I_a.

Both methods yield 11 + 44.866i, far different from the listed result.

Any idea of how the authors got to (64, 80.1º)?

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# Homework Help: Unbalanced Three-phase circuit.

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