Dear All,

I've been stuck on this for a couple hours. I'm hoping somebody out there can give me a hand.


Objective: Solve for v using Mesh Analysis method.

Meth analysis goes like this:
1. Draw circuit in planar form (if possible.)
2. Identify meshes and name mesh currents. Mesh currents should be in the clockwise direction. The current in a branch shared by two meshes is the difference of the two mesh currents.
3. Write a KVL equation in terms of mesh currents for each mesh.
4. Solve the resulting system of equations.

I can't write KVL equations since there are no voltage sources, only current sources. So what I tried to do was this...

For the 4k resistor, the current through it is
i = 6mA - 4i
i = 6/5 mA

So the current in mesh 3 would be 4i = 24/5 mA = 4.8 mA. Using ohm's law, the voltage across the 8k resistor would be: v = 4.8 * 8 = 38.4 V. But that's wrong . The answer is -32 V. Help!

 

I am going to bed, so if no one else has answered you by tomorrow evening I will post a response.

But, you do not need a voltage source to write KVL equations.

 

Here's how you solve it:

Write your constraint equations for the current sources:

I1 = 6mA (I1 goes in the same direction of the current source)
4i = I2 - I3 (I2 goes in the direction of the current source, while I3 opposes it)

now the current "i" is I1-I2.
i = I1-I2

So here are your equations:
I1 = 6mA
4000*(I2-I1)+10000*I2+8000*I3 = 0
4i = I2 - I3, plugging in i = I1-I2, this equation becomes:
4*(I1-I2)-I2+I3=0

Now plug this into a matrix:

>> a = [1,0,0;-4e3,4e3+10e3,8e3;4,-4-1,1]

a =

1 0 0
-4000 14000 8000
4 -5 1
>> b = [6e-3;0;0]

b =

0.0060
0
0

>> a^-1*b

ans =

0.0060
0.0040
-0.0040

>> -.0040*8e3

ans =

-32

 

Thank you very much farmosh for the clear and detailed explanation.

What program were you using to do the matrix math?

Thanks again.

 

No problem. I used the math program Matlab for the matrix math.

 

Greetings jut,

You can also avail yourself of the MDETERM() function in Microsoft EXCEL to handle matrix algebra if you happen to have access to EXCEL.

hgmjr