Mesh Analysis Problem

1. Dec 5, 2007

Kobayashi

1. The problem statement, all variables and given/known data
Use mesh analysis to find the current through the 4 Ohm resistor.

2. Relevant equations

3. 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.

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2. Dec 5, 2007

The Electrician

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

3. Dec 5, 2007

Kobayashi

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

4. Dec 5, 2007

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?

5. Dec 5, 2007

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6. Dec 5, 2007

The Electrician

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

7. Dec 5, 2007

8. Dec 5, 2007

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?

9. Dec 6, 2007

sakkaf_90

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

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

- 6 I2 + 13 I3 = 74

10. Dec 6, 2007

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

Last edited: Dec 6, 2007
11. Dec 6, 2007

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.

12. Dec 6, 2007

sakkaf_90

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......

13. Dec 6, 2007

Kobayashi

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

14. Dec 6, 2007

The Electrician

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