How Do You Solve This Complex Mutual Inductance Problem?

[p75213]

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?

 

[gneill]

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.

 

[The Electrician]

[

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

 

[p75213]

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.

 

[DeeNos]

After reviewing the equations and attempting to solve them, I believe the error may be in the calculation of the magnitude and angle of the currents. It is possible that the software may not be taking into account the complex numbers and their interactions. I would recommend double checking the equations and using a calculator or software specifically designed for complex numbers to solve them. Additionally, it may be helpful to consult with a colleague or professor for assistance in solving this mutual inductance problem.