Mesh Analysis of a Larger Circuit

In summary: So with KVL (1), I get:i1=65*i1-40*i3i2=-4*i2i3=10*i3+70*i1And with KVL (3), I get:i1=0*i1+10*i2+70*i3i2=-40*i2+10*i1i3=50*i3-20*i4Now that you have these three equations, you can use Thevinin's Theorem to find the voltage at node A, and node B. With KVL (1): iA=-65*i1+40*i
  • #1
prettyinpink5
4
0

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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  • #2
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?
 
  • #3
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
 
  • #4
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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  • #5
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!
 
  • #6
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.
 
  • #7
Thanks!
 

1. What is mesh analysis and when is it used in circuit analysis?

Mesh analysis is a method used to analyze larger circuits with multiple loops and branches. It involves creating mesh equations for each loop in the circuit and solving them simultaneously to determine the currents flowing through each branch. It is typically used when there are more than two loops in a circuit.

2. How do I create mesh equations for a larger circuit?

To create mesh equations, identify all the independent loops in the circuit and assign a current variable to each loop. Then, use Kirchhoff's Voltage Law to write an equation for each loop, taking into account the voltage drops across each component in the loop. Make sure to also include any current sources in the equation. Repeat this process for all the loops in the circuit.

3. Can mesh analysis be used to analyze circuits with dependent sources?

Yes, mesh analysis can be used to analyze circuits with dependent sources. The dependent source equations can be incorporated into the mesh equations by treating them as additional voltage or current sources. This may require additional variables and equations in the mesh analysis.

4. Are there any limitations to using mesh analysis?

Mesh analysis has some limitations, such as being applicable only to circuits with independent voltage sources and dependent sources with linear characteristics. It is also not very efficient for circuits with a large number of loops or branches, as it can become complex and time-consuming to solve the simultaneous equations.

5. What is the benefit of using mesh analysis over other circuit analysis methods?

Mesh analysis is useful for larger circuits because it reduces the number of equations and variables needed to solve the circuit compared to other methods such as nodal analysis. It also provides a systematic approach to solving complex circuits and can be easily applied to circuits with multiple loops and branches.

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