Circuits: Mesh Analysis with Phasors

In summary, the student is struggling to solve a KVL circuit involving meshes. They have attached a picture of where they are having trouble and the professor's answer is slightly off.
  • #1
Saladsamurai
3,020
7

Homework Statement



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

Doc-3_13_114_26PM-page-1.jpg



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?
 
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  • #2
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.
 
  • #3
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 :smile:
 
  • #4
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.
 
  • #5
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 :tongue:) 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
 
  • #6
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.
 
Last edited:
  • #7
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.
 
  • #8
skye2388 said:
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 :smile: Not by any chance NU?
 
  • #9
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
 

1. What is mesh analysis in circuits?

Mesh analysis is a method used to analyze electric circuits, specifically those containing multiple current sources and resistors. It involves creating a system of equations using Kirchhoff's voltage law (KVL) and solving for the unknown currents in each loop, or "mesh," of the circuit.

2. What are phasors in the context of mesh analysis?

Phasors are mathematical representations of the complex amplitudes of AC voltages and currents in a circuit. They are used in mesh analysis to simplify the calculations and make it easier to solve for the unknown currents in each mesh.

3. How is mesh analysis with phasors different from traditional mesh analysis?

In traditional mesh analysis, the unknown currents in each mesh are represented by variables and the equations are solved algebraically. In mesh analysis with phasors, the unknown currents are represented by complex numbers and the equations are solved using complex algebra.

4. Can mesh analysis with phasors be used for circuits with multiple frequency sources?

Yes, mesh analysis with phasors can be used for circuits with multiple frequency sources. The phasors for each frequency source are added together to find the total phasor for the mesh, and the equations are then solved using complex algebra.

5. Are there any limitations to using mesh analysis with phasors?

Mesh analysis with phasors is most effective for linear circuits that have a single frequency source. It may not be as accurate for non-linear circuits or circuits with multiple frequency sources. Additionally, it may be more complex and time-consuming for circuits with many meshes.

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