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

[billyray]

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]

 

[billyray]

here is the pic of the spread sheet

 

[gneill]

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!

 

[billyray]

hi gneil

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

 

[gneill]

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

 

[billyray]

thanks gneill will do tommorow. Thanks again so much

 

[scottdave]

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?

 

[Numbskull]

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.

 

[scottdave]

Matlab is commercial software package. If you don't have access to that, Scilab and Octave are pretty good alternatives, which are free.

 

[billyray]

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