How Do You Solve This Complex Mutual Inductance Problem?

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Discussion Overview

The discussion revolves around solving a complex mutual inductance problem presented as a homework statement. Participants share their attempts at deriving equations and seek clarification on their solutions, focusing on the mathematical treatment of mutual inductance.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a set of equations derived from the problem statement, yielding specific values for currents I1 and I2, but notes these do not match provided answers.
  • Another participant requests clarification on the derivation of the equations and expresses concern about the treatment of mutual inductance, suggesting the use of variable names for clarity.
  • A later reply identifies a sign error in the original equations and provides corrected versions, indicating that the equations should include different signs for certain terms.
  • Another participant acknowledges the correction and mentions reviewing previous examples to identify their own mistakes.

Areas of Agreement / Disagreement

There is no consensus on the correct approach or final answers, as participants are still working through the equations and identifying errors. Multiple viewpoints regarding the treatment of mutual inductance and the correctness of the equations remain present.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in the problem, and there are indications of missing assumptions regarding the treatment of mutual inductance in the equations.

p75213
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Homework Statement


See attached.


Homework Equations





The Attempt at a Solution


(5+j8)I1-j6I2-j3I2-j3I1*2=magnitude(12) degrees (60)
(5+j2)I1-j9I2=magnitude(12) degrees (60)

j2I2-j6I1-j3I1=0
-j9I1+j2I2=0

I put these equations into mathematics software and get the answers:
I1=magnitude (0.3091) angle (142.60) degrees
I2=magnitude (1.3909) angle (142.60) degrees.

These are not the answers provided. Can somebody show me where the error is?
 

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p75213 said:

Homework Statement


See attached.


Homework Equations





The Attempt at a Solution


(5+j8)I1-j6I2-j3I2-j3I1*2=magnitude(12) degrees (60)
(5+j2)I1-j9I2=magnitude(12) degrees (60)

j2I2-j6I1-j3I1=0
-j9I1+j2I2=0

I put these equations into mathematics software and get the answers:
I1=magnitude (0.3091) angle (142.60) degrees
I2=magnitude (1.3909) angle (142.60) degrees.

These are not the answers provided. Can somebody show me where the error is?

Can you show how you derived your equation? I'm concerned about how you treated the mutual inductance. Perhaps assign variable names to the component values for easy tracking in the equations.
 
p75213 said:
[

The Attempt at a Solution


(5+j8)I1-j6I2-j3I2-j3I1*2=magnitude(12) degrees (60)
(5+j2)I1-j9I2=magnitude(12) degrees (60)

j2I2-j6I1-j3I1=0
-j9I1+j2I2=0

You have a sign error. The equations should be:

(5+j8)I1-j6I2+j3I2-j3I1*2=magnitude(12) degrees (60)
(5+j2)I1-j3I2=magnitude(12) degrees (60)

j2I2-j6I1+j3I1=0
-j3I1+j2I2=0
 
The Electrician said:
You have a sign error. The equations should be:

(5+j8)I1-j6I2+j3I2-j3I1*2=magnitude(12) degrees (60)
(5+j2)I1-j3I2=magnitude(12) degrees (60)

j2I2-j6I1+j3I1=0
-j3I1+j2I2=0

Thanks for that. I had to go over some of the previous examples in the book. However I figured out what I was doing incorrectly.
 

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