How Do You Solve a Circuit with Four Meshes Using Mesh Analysis?

[DefaultName]

Mesh Analysis -- (4 meshes)

Homework Statement

http://img185.imageshack.us/img185/1541/screenshot01ly9.jpg

Homework Equations

V=IR
KVL

The Attempt at a Solution

Loop 1 is the top left loop.
Loop 2 is the top right loop.
Loop 3 is the bottom right loop.
Loop 4 is the bottom left loop.
(Think of the quadrants in the cartesian coordinate system... that's my loop and loop currents).

Loop currents are going in the CW direction.

For Loop 1:

-14 + I_1 + (I_1 - I_2) + (I_1 - I_4) = 0

For Loop 2:

I_2 = 2mA

For Loop 3 & 4:

Since they are super meshes because of the shared current source... this is what I have:

4mA = I_3 - I_4
-- and --
using the supermesh idea, and short-circuiting the shared 4mA current source...

I4 + 2*I3 + I3 + I4 = 0... which is 3I_3 + 2I_4 = 0

Is my setup correct?

If so, this is what I did...

solved for I_4 in the equation 3I_3 + 2I_4 = 0... I_4 = (-3I_3) / 2

I plugged that I_4 into the eq. 4mA = I_3 - I_4... and I got I_3 = 2mA.

I assumed I_0, what we're trying to find, is equal to I_3. Is this a valid assumption since the current is going around that mesh?

 

[quaker]

Your supermesh equation is incorrect. Starting from the lower left it should be 1k*i_4 + 1k*(i_4 - i_1) + 2k*(i_3 - i_2) + 1k*i_3 = 0

Because of that, your assumption about I_0 is also wrong. The current in that branch is flowing between meshes 2 and 3, so the current is a combination of the two: I_0 = I_3 - I_2.

 

[piercas]

Yes, your setup and solution seem correct. Assuming that I_0 is equal to I_3 is a valid assumption because the current is indeed going around that mesh. Great job using the supermesh concept to simplify the problem! Keep up the good work.