The mesh current method - Am I doing it right?

[foxofdesert]

Homework Statement

Apply the mesh current method to find I₀

Homework Equations

Mesh current method

The Attempt at a Solution

On the left bottom square circuit, I set a mesh current, I₁, and on the right bottom square circuit, I set a mesh current, I₂.

Then, I₀=I₁-I₂.

Since there is a current source on the mesh I₁, I₁=-5 (negative sign because of the direction.)
and
(1+2+4)I₂+22.5=0, so I₂=(-22.5)/7.
Therefore, I₀=-5-(-22.5)/7=(-12.5)/7.

Am I doing it right?

 

[foxofdesert]

Please check the attachment to see the problem.

 

[gneill]

On the left bottom square circuit, I set a mesh current, I₁, and on the right bottom square circuit, I set a mesh current, I₂.

Then, I₀=I₁-I₂.

Okay.

Since there is a current source on the mesh I₁, I₁=-5 (negative sign because of the direction.)
and
(1+2+4)I₂+22.5=0, so I₂=(-22.5)/7.
Therefore, I₀=-5-(-22.5)/7=(-12.5)/7.

Check your mesh current direction; the potential changes across the resistors in the second mesh should drop in the direction of mesh current flow.

Also, you need to take into account the effect of the other currents in the circuit. In particular, the mesh current in the top right mesh also passes through the 2Ω resistor shared with the bottom right mesh. Similarly, the top left mesh affects conditions in the top right mesh (in general, all the meshes interact due to shared components).

You'll have to write equations relating all the meshes in order to capture the interactions. For the bottom left mesh you can take its current as given (-5A) since it's constrained by a current source there. For the top pair, you might want to employ the supermesh method to write the two equations that describe it.

 

[foxofdesert]

Thanks for your help.

I set up the super mesh on the top since they share a current source, so I set up total of 3 mesh ( 1 supermesh, 2 mesh for each bottom circuit) and solved the problem.

Thank you so much