# Issue with mesh analysis of 4 loop circuit

1. Nov 17, 2009

### GeoMike

1. The problem statement, all variables and given/known data
The problem, as given in the textbook is:
http://www.mcschell.com/circuit.jpg [Broken]

2. Relevant equations
KCL, KVL

3. The attempt at a solution
The issue I'm having with this problem is that I get two different values for Ix depending on how I set up the equations for this circuit.

If I do 2 KVL loops and KCL using:
Supermesh: Ix(1) + I1(1) + I1(j1) - I2(j1) + 12 = 0
Loop I2: I2(j1 - j1 + 1) - I0(1) - I1(j1) = 0
KCL at left node: Ix = I1 + 2
Given I0: I0 = 4+j0 = 4

For this system I get Ix = -9/5 + j(13/5)

However, if I replace the supermesh with a KVL loop around the outer edges of the circuit (leaving the other loops unchanged):
Outer (edges) loop: Ix(1) + I1(1) + I2(-j1) + I0(1) = 0

For this system I get Ix = j(4/3)

Worse still, the solutions manual has:
KCL at left node: Ix - I1 = 2 + j0 = 2
I0 loop: 12 = I0(2) - I2
Outer (edges) loop: Ix(1) + I1(1) + I2(-j1) + I0(1) = 0
Given I0: I0 = 4+j0 = 4

With Ix = -1 - j2

I double checked my mesh equations and solved using Mathematica. I don't understand what is "wrong" with my approaches. Why am I getting different values for Ix? Shouldn't they be the same regardless of the analysis method used?

Thanks,
GeoMike

Last edited by a moderator: May 4, 2017