Circuits: Mesh Analysis with Phasors

[Saladsamurai]

Homework Statement

I am supposed to use mesh current analysis using the following circuit diagram which is in the phasor domain:

Homework Equations

KVL

The Attempt at a Solution

Let's number these meshes from left to right 1,2,3. Here is what confuses me:
If take a look at the 3rd mesh, wouldn't we just have the equation:

-(8 - 4j)*I₂ + (8 - 4j)*I₃ = 0

So I would naturally conclude that I₂ and I₃ are equal and opposite.

But I₃= - 2e^-30j is known. But if I use this logic, I get the wrong answer. I really suck at mesh, but when we had regular DC circuits, if there was a current source in a mesh, then we would just equate the mesh current to the source current. Is this different for AC? Or is my mistake somewhere else?

 

[gneill]

In the third mesh there will be an unknown voltage across the current supply, so no, you can't conclude that I₂ and I₃ are equal.

All the "usual" techniques work for complex impedances.

For this circuit I would be tempted to convert the current supply and its parallel impedance into its Thevenin equivalent (a simple enough operation), thus reducing the number of meshes by one and leaving only KVL equations to deal with.

 

[Saladsamurai]

I see. Would it be just as correct to write out the mesh equations for the first two meshes, the second of which would have an I₃ in it that is given by I₃=2e^-30º*j? I did it this way and got the correct answer, but I want to make sure it was not by luck.

Thanks gneill

 

[gneill]

Sure, I don't see why not. If there happened to be other components in the third mesh that were not in common with the other i2 mesh (such as another resistor in series with the current supply), then it would be problematical.

 

[skye2388]

Hello all!

Sorry to bring up this thread again (I can see it was from mid March). I am quite lucky that I found this on Google (gotta love Google ) but I am actually studying this exact problem since it was assigned on one of our homeworks and I do not know how to solve the KVL equations derived from the Mesh Analysis...can someone please help walk me through this?? I am actually quite desperate right now as I have a midterm on this material on Wednesday...any help would be much appreciated...I attached a picture of where I am having trouble (refer to the red boxed in part of the KVL equations).

http://www.freeimagehosting.net/uploads/th.f98e70477c.jpg

 

[gneill]

Your equations look okay. Your results are only a bit iffy with respect to accuracy, most likely due to some rounding that's taken place during the process of solving. Carry more significant figures up to the last step.

I get |I2| = 0.968A, angle 78.32 degrees.

 

[skye2388]

Hey Gneill,

Thanks. The picture I attached is actually a solutions guide written by the professor. I actually ended up figuring out the solution and I agree his answer is slightly off from what I got.

I ended up getting I2 = .9677 < 78.2766 degrees. I agree, the differences are probably due to rounding.

 

[Saladsamurai]

Hey Gneill,

Thanks. The picture I attached is actually a solutions guide written by the professor. I actually ended up figuring out the solution and I agree his answer is slightly off from what I got.

I ended up getting I2 = .9677 < 78.2766 degrees. I agree, the differences are probably due to rounding.

Funny, I have a midterm in this class on Wednesday too Not by any chance NU?

 

[skye2388]

Saladsamurai,

Yes, actually, I thought you might have been a NU student when I found this thread on google. Pretty ironic.

Maybe we could get together to go over some last minute stuff? I'll be on campus all day today (until like 10 p.m.). Let me know if you want to meet up...

email: KL22388@gmail.com or Liu.yet@husky.neu.edu