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Mesh Analysis - (4 meshes)

  • #1
180
0
Mesh Analysis -- (4 meshes)

Homework Statement



http://img185.imageshack.us/img185/1541/screenshot01ly9.jpg [Broken]

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... thats 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?
 
Last edited by a moderator:

Answers and Replies

  • #2
14
0
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.
 

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