Mesh Current Analysis w/ Controlled Current Source

[zarrin77]

Solve i_x when a=2. (See attached picture)

This is my attempt (mesh current analysis):

I made i1 be the lower left loop current.
I made i2 be the lower right loop current.
I made i3 be the upper loop current.

Mesh1: i1 = 2ix

Mesh2: -10 + 3(i2-i3) + 20i2 = 0

Mesh3: -5 + 3(i3 - i2) + 10(i3-i1) = 0

Also: ix = i3 - i2 => -i1 - 2i2 + 2i3 = 0


Using those last three equations: i1=0, i2=.5, i3=.5

I don't think that i1 can be 0... and I can't figure out any place I went wrong; it seems pretty straightforward?

Thank you very much for your help!

 

[gneill]

Solve i_x when a=2. (See attached picture)

This is my attempt (mesh current analysis):

I made i1 be the lower left loop current.
I made i2 be the lower right loop current.
I made i3 be the upper loop current.

Mesh1: i1 = 2ix

Mesh2: -10 + 3(i2-i3) + 20i2 = 0

Mesh3: -5 + 3(i3 - i2) + 10(i3-i1) = 0

Also: ix = i3 - i2 => -i1 - 2i2 + 2i3 = 0


Using those last three equations: i1=0, i2=.5, i3=.5

I don't think that i1 can be 0... and I can't figure out any place I went wrong; it seems pretty straightforward?

Thank you very much for your help!

There's no reason why i1 (and hence Ix) cannot be zero. Your solution looks okay to me.