Mesh Analysis of a Larger Circuit

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Discussion Overview

The discussion revolves around the application of mesh analysis in a larger electrical circuit, focusing on the formulation of Kirchhoff's Voltage Law (KVL) equations for multiple meshes and the subsequent calculations for node voltages and mesh currents.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant is attempting to apply mesh analysis to a larger circuit and has formulated KVL equations for three of the meshes but is uncertain about the second mesh.
  • Another participant suggests that the original poster should share more of their solution attempt, specifically the mesh KVL equations, to facilitate assistance.
  • Specific KVL equations for Mesh 1, Mesh 3, and Mesh 4 are provided, with one participant noting the importance of defining current directions graphically.
  • A participant mentions that when a current source is present in a mesh, it directly provides the current value for that mesh.
  • There is a mention of difficulties with the textbook's clarity regarding larger circuits, indicating a struggle with understanding beyond two meshes.
  • Another participant provides a KVL equation for Mesh 4 and suggests that the established equations can be solved simultaneously to find the unknown currents.

Areas of Agreement / Disagreement

Participants generally agree on the need to define current directions and formulate KVL equations for each mesh. However, there is no consensus on the complete approach to solving the circuit, as one participant is still working on the equations for the second mesh.

Contextual Notes

Participants express uncertainty regarding the application of mesh analysis to larger circuits and the clarity of their textbook, which may limit their understanding of the problem.

Who May Find This Useful

This discussion may be useful for students learning about mesh analysis in electrical circuits, particularly those struggling with larger circuit configurations and KVL applications.

prettyinpink5
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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
 

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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?
 
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
 
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).
 

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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!
 
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.
 
Thanks!
 

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