What is the Mesh Current Analysis for Finding i0 in a Circuit?

[Asphyxiated]

Homework Statement

Find i0 in http://images3a.snapfish.com/232323232%7Ffp73395%3Enu%3D52%3A%3A%3E379%3E256%3EWSNRCG%3D3359%3B24399347nu0mrj" using mesh current analysis.

Note that the ^i1, ^i2 and ^i3 are to label my currents and show they are flowing clockwise. i0--> is the direction of the i0 current. The current source is 3A.

Homework Equations

KVL
KCL
Ohm's law

The Attempt at a Solution

So i know that the current sources makes a supermesh and that you basically remove it from the circuit and do mesh analysis 'around the path of the supermesh' and you will get a constraint equation from the supermesh for your 3rd equation.

So for i1 I got:

$$2i_{1} + 6 + 4(i_{1}-i_{3})+ (i_{1}-i_{2}) = 0$$

$$2i_{1} + 4i_{1} - 4i_{3} + i_{1} - i_{2} = -6$$

$$8i_{1} - i_{2}-4i_{3}=-6$$

So the supermesh i got:

$$5i_{2} + (i_{2}-i_{1}) + 4(i_{3}-i_{1})+12=0$$

$$5i_{2} + i_{2} - i_{1} + 4i_{3}-4i_{1}=-12$$

$$-5i_{1} + 6i_{2} + 4i_{3} = -12$$

and the constraint equation:

$$i_{3}=i_{2}+3$$

$$0i_{1}-i_{2}+i_{3} = 3$$

which makes a 3x4 matrix now i got:

$$i_{1}=-1.09a$$

$$i_{2}=-2.945a$$

$$i_{3}=.054a$$

and i believe that i0 in the circuit should be i2-i1 but they are looking for -1.73a for i0 which is close to but not what you get with my numbers so where did I go wrong?

thanks!

 

[vk6kro]

[PLAIN]https://www.physicsforums.com/latex_images/31/3122511-1.png

In eq1, I think it should be 7 I₁ shouldn't it? You have 8 I₁

 

[Asphyxiated]

bah I hate when that happens, now it works out! Those small algebra mistakes really bite you in circuit analysis huh? lol

Thanks though vk6kro