Solve Mesh Analysis Problem: Find Current Through 4 Ohm Resistor

[Kobayashi]

Homework Statement

Use mesh analysis to find the current through the 4 Ohm resistor.

Homework Equations

The Attempt at a Solution

From this circuit I managed to work out the three mesh equations using mesh analysis.

Mesh 1 = 7I1 + 4I2 = 67
Mesh 2 = -4I1 + 15I2 - 6I3 = 152
Mesh 3 = -6I2 + 13I3 = 74

Are these mesh equations correct.
From this point in the question how do I calculate the current through the 4 ohm resistor. I know you use simultaneous equations but I can't get the correct answer. Please help.

 

[The Electrician]

I am unable to view the .jpg. Does one of the moderators know why that is? I'm using the Firefox browser.

 

[Kobayashi]

I also use firefox and it works for me. Have you tried internet explorer?

 

[The Electrician]

IE doesn't work either. I see the little symbol for a broken link. Maybe the link points to something which is on your own computer, but not accessible through the internet. Can you post the URL to the picture as simple text?

 

[Kobayashi]

I tried uploading it again.

 

[The Electrician]

still not working for me. If you right click on it and then click properties, what is the URL?

 

[Kobayashi]

Here it is: https://www.physicsforums.com/attachment.php?attachmentid=11872&d=1196884527

 

[The Electrician]

Well, now the link is working! I wonder what changed?

Your equations are a little bit off. I get:

7 I1 - 4 I2 + 0 I3 = 67

-4 I1 + 15 I2 - 6 I3 = -152

0 I1 - 6 I2 + 13 I3 = 74

Don't forget that the current in R4 is not just one of these currents; it's I1 - I2.

Do these equations give you the correct result? Do you see where you went wrong?

 

[sakkaf_90]

the correct equation is :
7 I1 - 4 I2 = 67

-4 I1 + 15 I2 - 6 I3 = -152

- 6 I2 + 13 I3 = 74

 

[sakkaf_90]

the correct equation

the correct equation is :
7 I1 - 4 I2 = 67

-4 I1 + 15 I2 - 6 I3 = -152

- 6 I2 + 13 I3 = 74
Use matrix to find the value of I1,I2 and I3 then u find he value of current in 4 ohm is
4I1-4I2=IR4

 

[Kobayashi]

Thanks.
I now have a question about analysis of a circuit containing three meshes.
When you get an equation e.g:

-11.3I1 + 9.1I2 +0I3 = 18
9.1I1 -23.4I2 + 6.8I3 = -18
0I1 + 6.8I2 -10.1I3 = -3

How do you find the individual currents in this case. I read you can use Gaussian Elimination. How does that work in this case. Thanks.

 

[sakkaf_90]

Thanks.
I now have a question about analysis of a circuit containing three meshes.
When you get an equation e.g:

-11.3I1 + 9.1I2 +0I3 = 18
9.1I1 -23.4I2 + 6.8I3 = -18
0I1 + 6.8I2 -10.1I3 = -3

How do you find the individual currents in this case. I read you can use Gaussian Elimination. How does that work in this case. Thanks.

The easier u use crimer rule :



I1= (detB/detA)

I2=(detC/detA)

I3=(detD/detA)

where

A=

-11.3000 9.1000 0
9.1000 -23.4000 6.8000
0 6.8000 -10.1000


B=

-11.3000 9.1000 18.0000
9.1000 -23.4000 -18.0000
0 6.8000 -10.1000


C=


-11.3000 18.0000 0
9.1000 -18.0000 6.8000
0 -3.0000 -10.1000



D=


18.0000 9.1000 0
-18.0000 -23.4000 6.8000
-3.0000 6.8000 -10.1000




To find the det ...for example let take matrix X=


a b c
d e f
g h i


be careful about the sign which it equivelent to

+ - +
- + -
+ - +

det(X)=a (ei-hf)-b(di-gf)+c(dh-ge)


and so on...

 

[Kobayashi]

Thanks, that helps me a lot. I've learned matrices before but I've completely forgotten. Thanks for reminding me.

 

[The Electrician]

This forum isn't really the place to explain Gaussian elimination.

Go read: http://en.wikipedia.org/wiki/Gaussian_elimination.

Another alternative is to get a calculator that can do matrix arithmetic, or a program for your PC, such as Scilab.