Can Mesh Analysis with Three Loops Solve a Four-Loop Circuit?

In summary, Homework statement states that I need to use an excel matrix sheet to solve three unknowns. The user attempted to solve the problem but was lost. They found help from another user and included their results. The user has found the correct answer by entering a very small number into the spreadsheet.
  • #1
billyray
58
1

Homework Statement


I have a circuit that I am to analyse and find I. I am told to use an excel matrix sheet given to me to solve 3 unknowns. I have 4 loops so this is a problem. I have made an attempt using three loops and referred to a previous thread on here for some help. It says I can do it with three loops.
https://www.physicsforums.com/threads/ac-circuit-analysis-mesh-and-nodal.791744/
[/B]

Homework Equations

I have attempted the question many times and am including my results. They do not seem to agree with the results for the agreed answer on here.
Loop 1 --- 120-(2)I1-(I1-I2)(-j5)=0
Loop2 --- (-j5)(I2-I1)+(j4)(I2-I3)-14.14+j14.14=0
Loop3 --- (j4)(I3-I2)+(4)I3-j120=0

Answers;
I1=19.1624+j12.5642
I2= 14.1367-j3.77088
I3= 23.9538+j20.1829 [/B]
I can't seem to upload spread sheet

The Attempt at a Solution


I am incuding this and a spead sheet I am using. any pointers would be amazing as I am completely lost wheln I use the spreadsheet.[/B]
 

Attachments

  • attemp.pdf
    365.8 KB · Views: 235
  • Using the Spreadsheet Complex Matrix by Decomposition.pdf
    48.2 KB · Views: 204
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  • #2
here is the pic of the spread sheet
 

Attachments

  • excell screen shot.PNG
    excell screen shot.PNG
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  • #3
billyray said:
Loop 1 --- 120-(2)I1-(I1-I2)(-j5)=0
Loop2 --- (-j5)(I2-I1)+(j4)(I2-I3)-14.14+j14.14=0
Loop3 --- (j4)(I3-I2)+(4)I3-j120=0
Are you confident about the sign of the voltage terms in loops 2 and 3? Read through the related conversation with the OP in the thread you referenced: he had the same issue!
 
Last edited:
  • #4
hi gneil

thanks again for help. I have changed my answers but they still won't work in spread sheet
 

Attachments

  • attemp2.pdf
    146.5 KB · Views: 198
  • steven.xlsx
    60 KB · Views: 178
  • #5
billyray said:
hi gneil

thanks again for help. I have changed my answers but they still won't work in spread sheet
As far as I can tell with a quick glance, your recent attemp2.pdf shows correct loop equations. Good!

Regarding the spreadsheet's inability to solve the equations, take a look at the conversation that occurred in the thread that you referenced previously, starting around post #98 :wink:
 
  • #6
thanks gneill will do tommorow. Thanks again so much
 
  • #7
I'm trying to follow along. I put a 0.001 in the center cell of the Real matrix, as the warning suggested. This allows the spreadsheet to calculate values.
I put the same matrix into Matlab and solved the system and arrive at the same answers as the spreadsheet.
As far as I can tell, your loops and matrices look correct. Are the answers in the original post the "correct" answers that you are supposed to arrive at?
 
  • #8
I have done this question and can tell you that I couldn't get the thing to work at all with some zero values. As scottdave above says, you need to put in a very small number just to allow it to compute.

Having just looked at my tutor feedback document, I did get the phases incorrect in my answer (+ instead of -), but the magnitudes were all correct, and mine don't match any of those in your original post.
 
  • #9
Matlab is commercial software package. If you don't have access to that, Scilab and Octave are pretty good alternatives, which are free.
 
  • #10
Thanks scottdave and Numbskull.

I have obtained the correct answers by entering 0.0001 in the spreadsheet. Thanks for help though. I always thought it would be me wrong and not the spreadsheet
 

FAQ: Can Mesh Analysis with Three Loops Solve a Four-Loop Circuit?

1. What is mesh analysis and how does it work?

Mesh analysis is a method used to analyze electrical circuits. It involves dividing the circuit into smaller loops, or meshes, and applying Kirchhoff's voltage law to each loop. This allows us to calculate the currents flowing through each loop and ultimately determine the voltage and current at each component in the circuit.

2. How do I know when to use mesh analysis?

Mesh analysis is most commonly used when the circuit contains multiple current sources and voltage sources. It is also useful when there are more than two unknown currents in the circuit.

3. What are the steps involved in solving a circuit using mesh analysis?

The steps for solving a circuit using mesh analysis are as follows:

  1. Identify the meshes in the circuit.
  2. Apply Kirchhoff's voltage law to each mesh to create equations.
  3. Solve the resulting system of equations for the mesh currents.
  4. Use Ohm's law and Kirchhoff's current law to determine the voltage and current at each component in the circuit.

4. Can I use mesh analysis for circuits with dependent sources?

Yes, mesh analysis can be used for circuits with dependent sources. In this case, the dependent source is treated as a variable, and its value is determined using the resulting system of equations.

5. What are some common mistakes to avoid when using mesh analysis?

Some common mistakes to avoid when using mesh analysis include:

  • Not properly identifying the meshes in the circuit.
  • Forgetting to include all sources in the equations.
  • Incorrectly assigning the direction of current in the equations.
  • Not using proper units or incorrectly converting units in calculations.

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