Engineering Mesh Analysis of a Larger Circuit

[prettyinpink5]

Homework Statement

We have been doing mesh analysis of circuits, and I am just trying to work out how to do it in a larger circuit.

Homework Equations

2. Using mesh analysis work out the currents flow through each of the three meshes. From these current values calculate the voltage of node A, and node B with respect to the ground node.
3. Find equivalents of sub-circuits A-G, B-G, A-B by applying Thevinin’s theory. Then place these equivalents together and determine the voltage at Node A, and Node B. Also deduce the mesh currents from your results for the voltages at Node A an Node B and other information in the circuit.

The Attempt at a Solution

I have only gotten as far as working out the KVL's in the individual Mesh's. Not sure how to put them together in matrices

 

[gneill]

Hi prettyinpink5. Welcome to Physics Forums.

You'll have to show some more of your solution attempt so that we can see how to help you. How about writing out your mesh KVL equations?

 

[prettyinpink5]

Okay, Well I did the KVL for Mesh's 1,3 and 4. Wasn't sure what to do for the 2nd mesh. (Top one)

KVL Mesh 1
55=40i3-65i1

KVL Mesh 3
0=-40i1-10i2+70i3-20i4

KVL Mesh 4
30=20i3-50i4

 

[Zryn]

When you do your analysis, its good to define (graphically) the direction you assume current to flow, i.e. for the first mesh (the way I defined my currents in the diagram):

KVL (1): 55 - 25*i1 - 40*i1 + 40*i3 = 0 --> 55 = 65*i1 - 40*i3

Also, when you have a current source in only one mesh you are being given the current value in that mesh, i.e. i2 = -4A (the way I defined my currents in the diagram).

 

[prettyinpink5]

Yeah, sorry, I have defined the directions for all meshes as Counter-Clockwise. I need to just work out the equations for Mesh 2 (The top one) and then find out where to go from there. Our textbook is really badly written, so I am struggling to pick it up for anything bigger than two meshes side by side. Haha.

Thanks Guys!

 

[Zryn]

With the current going counter clockwise, I get the following:

KVL (4): -30*i4 -20*i4 + 20*i3 + 30 = 0 --> 30 = 50*i4 - 20*i3

Given the equations you have developed, you should be able to solve the three simultaneous equations to find the three unknowns.

 

[prettyinpink5]

Thanks!