Supermeshes and Dependent Current Sources: Determining the Constraint EQ

[Saladsamurai]

Homework Statement

I am doing some review and I though that I had this down pat, but I am getting confused a little. I am looking at the Wikipedia on Mesh Analysis.

I do not understand the last equation of each section. How are they getting the signs of the currents?

In the top image it looks like i₁ flows down the middle branch, i_s flows up the middle branch, and i₂ flows up the middle branch, so I would have said that i₂ + i_s = i₁ but that is wrong.

In a similar manner, I get the equation in the second diagram wrong too!

Where is my thinking flawed? How can systematically determine the contraint equation no matter what way the currents are directed?

http://en.wikipedia.org/wiki/Mesh_analysis#Supermesh"

 

[Saladsamurai]

Well, I guess my logic does work for the dependent source in the bottom example, but not for the current source...

any thoughts?

 

[gneill]

In the first example, i₁ and i₂ are the loop currents. i_s is the actual current flowing in a branch. That means that the sum of i₁ and i₂ in that branch must be i_s.

Since i₂ flows in the same direction as i_s, you write: i_s = i₂ - i₁