Mesh-Current Analysis, VCCS with phasors

[Tet]

http://img247.imageshack.us/img247/7035/problemso9.jpg

Ok so I have to do mesh-current analysis and I think I'm doing it correctly but my answer doesn't match the one given. This has to be done using phasors.

I labeled my meshes from left to right 1, 2, and so on.

Mesh 1:
33.8 = 1I1 + j2I1 + 3(I1 - I2) + (-j5)(I1-I2)
33.8 = 1I1 + j2I1 + 3I1 - 3I2 - j5I1 + j5I2
33.8 = (4 - j3) I1 + (-3 + j5) I2

Mesh 2:
0 = j5(I1 - I2) - 3(I1 - I2) + 2(I2 - I3)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2I3

(mesh current with the VCCS)
I3 = -0.75 Vx
where
Vx = (-j5)(I1 - I2)
I3 = -0.75 * (-j5)(I1-I2)
I3 = j3.75(I1 - I2)

substituting into Mesh 2 equation:
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2( j3.75 (I1 - I2) )
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5(I1 - I2)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5I1 + j7.5I2
0 = -3I1 + (5+j2.5)I2

I know:
I = I1

I put both mesh equations in a matrix and the answer isn't what it's displayed in that picture (I get I = I1 = 8.98021 angle -1.828). Am i missing something here? I'm thinking I'm approaching this totally wrong. I always have a hard time with Mesh analysis and always prefer Nodal over it... but I'm almost certain that it has something to do with the VCCS (voltage controlled current source) and my equations for it.

 

[Tet]

Solved this by simply adding a third equation with
I3 = -0.75 Vx
where
Vx = (-j5)(I1 - I2)
I3 = -0.75 * (-j5)(I1-I2)
I3 = j3.75(I1 - I2)

I3 - (j3.75)I1 + (j3.75)I2 = 0 (third equation)

I put the previous 2 Mesh equations and this one in a matrix and got the values of all 3 currents.

(4 - j3) I1 + (-3 + j5) I2 = 33.8 (mesh 1)
(-3 + j5) I1 + (5 - j5) I2 - (2)I3 = 0 (mesh 2)
(- j3.75)I1 + (j3.75)I2 + I3 = 0 (third equation derived from Vx)

I1 = i = 29 + j2 or 29.07 angle 3.95



In this case this should be corrected:

Mesh 2:
0 = j5(I1 - I2) - 3(I1 - I2) + 2(I2 - I3)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2I3

(mesh current with the VCCS)
I3 = -0.75 Vx
where
Vx = (-j5)(I1 - I2)
I3 = -0.75 * (-j5)(I1-I2)
I3 = j3.75(I1 - I2)

substituting into Mesh 2 equation:
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - 2( j3.75 (I1 - I2) )
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5(I1 - I2)
0 = j5I1 - j5I2 - 3I1 + 3I2 + 2I2 - j7.5I1 + j7.5I2
0 = -3I1 + (5+j2.5)I2
^ red text not used

 

[piercas]

It seems like you are on the right track with your mesh-current analysis using phasors. However, there are a few things that could be causing your answer to be different from the one given in the problem.

First, make sure you are using the correct values for the components in the circuit. Double check the values given in the problem and make sure you are using the correct units (e.g. ohms, volts, etc.).

Second, it is possible that you made a mistake in your calculations. Make sure you are carefully simplifying and solving your equations, and check for any errors in your algebra.

Third, it is possible that the answer given in the problem is incorrect. It is always a good idea to double check your solution and make sure it makes sense in the context of the problem. If you are confident in your approach and calculations, it is possible that the given answer is incorrect.

Finally, it is important to remember that there can be multiple ways to solve a circuit problem. If you are confident in your approach and calculations, it is possible that your solution is correct even if it doesn't match the given answer. You may want to check with your instructor or a classmate to see if they can verify your solution.

In conclusion, it seems like you are approaching the problem correctly, but there may be a mistake in your calculations or the given answer. Double check your work and make sure everything is correct before making any changes to your solution. Good luck!