Mastering Mesh and Nodal Analysis with KVL for Complex Circuits

In summary: If you want to look at it another way, recall that components in parallel share the same potential difference, and their order doesn't matter so long as they remain parallel-conected. So you can swap the locations of Z2 and V3 without altering the circuit behavior at all. That puts V3 in the second loop and removes Z2 from it. The current through Z2 is trivially given by Ohms law since you have the impedance and the potential difference, so no need to include loop ##I4## in your set of equations. The circuit then looks like...In summary, the homework statement says that you should see a picture.
  • #36
Back on track after break with V40 = -60.1+5.31j and V30 = -45.9+19.51j in a need of your physics assistance
 
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  • #37
M P said:
Back on track after break with V40 = -60.1+5.31j and V30 = -45.9+19.51j in a need of your physics assistance
Your value for V30 doesn't look right, and it's the important value here since it determines the current through Z4.

You can check your result by comparing the current through Z4 due to V30 to the result from the previous mesh analysis.
 
  • #38
Is it ok to show calcs? I did check it and I am not sure what is causing damage.
 
  • #39
M P said:
Is it ok to show calcs? I did check it and I am not sure what is causing damage.
Yes! Showing your work is highly encouraged. Trying to determine where things are going awry from the results alone requires a good deal more effort :) Show your calculations, preferably with notations as to what the steps are trying to accomplish.
 
  • #40
I have another one to check :confused: V40 = 60.1j - 214.5 V30 = 74.3j - 200.3 ?
 
  • #41
gneill said:
Yes! Showing your work is highly encouraged. Trying to determine where things are going awry from the results alone requires a good deal more effort :) Show your calculations, preferably with notations as to what the steps are trying to accomplish.

Now what calcs you prefer from first results or second ?
 
  • #42
M P said:
I have another one to check :confused: V40 = 60.1j - 214.5 V30 = 74.3j - 200.3 ?
You should be in a position to determine the node potentials from the results of your previous mesh calculations. V30, for example, is given by the potential across Z4. The mesh currents will yield that from Ohm's Law. Since your mesh calculations were successful, you have a "standard result" against which you can compare new results.

If there's a problem with the method by which you're finding new results, then while it's easy to declare the result wrong or right, it's more difficult to tell you why it's wrong and what to do to fix it from the result alone. Can you explain what you're trying?
 
  • #43
M P said:
Now what calcs you prefer from first results or second ?
If by "first results" you mean the mesh analysis portion of the problem, then that's not required since I believe that you found the correct results there. If you are having difficulty achieving the same results with nodal analysis, then those are the calculations that need to be examined.
 
  • #44
M P said:
one more question is version of V1-V30/Z1-V30/Z4+V2-V40/Z3-V40/Z5=0 also work?
I was trying to do complex numbers on this ...
 
  • #45
M P said:
one more question is version of V1-V30/Z1-V30/Z4+V2-V40/Z3-V40/Z5=0 also work?
and on this ? that is what I understood to obtain V3 and V4 of this with complex numbers..
 
  • #46
none of them seems ok as you explained?
 
  • #47
that is what coursework shows using substitution
 
  • #48
I can't comment on what I don't see. Can you show more of your work?
 
  • #49
gneill said:
I can't comment on what I don't see. Can you show more of your work?
 

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  • #50
gneill said:
I can't comment on what I don't see. Can you show more of your work?

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  • #51
I bet you smiling now ;)
 
  • #52
x1.gif


Check the sign of the term.
 
  • #53
gneill said:
View attachment 76995

Check the sign of the term.
before I go further -55.74 - 20.06j + 0.25 V40 - 0.05 j V40 ?
 
  • #54
M P said:
before I go further -55.74 - 20.06j + 0.25 V40 - 0.05 j V40 ?
I'm not seeing where that's coming from. Sorry.

Did you make a V30 substitution? Really you should eliminate V40 instead, since you need V30 to find the current through Z4.
 
  • #55
thank you I will do as suggested and see how it goes..
 
  • #56
thank you for all your help
 
  • #57
can you please confirm if I have conducted my kvl loops correctly as per diagram on post #9

V1 - I1Z1 - Z4(I1-I2) = 0...Eq 1

-V3 - Z5(I2-I3) - Z4(I2-I1) = 0...Eq 2

I3Z3 - V2 - Z5(I3-I2) = 0...Eq 3
 
  • #58
It all looks fine except for the sign of the Z3 term in the third equation. I3 causes a potential drop in Z3.
 
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  • #59
thnx gneill
 
  • #60
I3(-Z3) - V2 - Z5(I3-I2) = 0...Eq 3 new and revised eq 3
 
  • #61
Ebies said:
I3(-Z3) - V2 - Z5(I3-I2) = 0...Eq 3 new and revised eq 3
That'll work. Or,

-I3*Z3 - V2 - Z5(I3-I2) = 0
 
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  • #62
when using mesh analysis to determine the voltage drop direction, do you use conventional current flow or do you use the clockwise current you chosen at the beginning when assigned your clockwise mesh currents...? I am asking so I know when to add or subtract when doing the "KVL" walk... I am a bit confused about what the sign needs to be when walking the "KVL" loop and you encounter components... spent a lot of time going through my books and watching online tutorials and its confused me even more now
 
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  • #63
Ebies said:
when using mesh analysis to determine the voltage drop direction, do you use conventional current flow or do you use the clockwise current you chosen at the beginning when assigned your clockwise mesh currents...? I am asking so I know when to add or subtract when doing the "KVL" walk... I am a bit confused about what the sign needs to be when walking the "KVL" loop and you encounter components... spent a lot of time going through my books and watching online tutorials and its confused me even more now
While you can use either direction to achieve valid equations, you must be consistent in your choice. Once you've made a selection of current direction for a mesh you must not change it, otherwise where loops "touch" the current sums through the shared components will be compromised.

This is why it's common practice to simply choose all the mesh current directions to be one direction (say, clockwise), so that you can get in the habit of doing things the same way every time. It helps to avoid mistakes if you don't have to think about how the current directions interact at the mesh boundaries. It also makes it possible to write the mesh equations directly by inspection in the form of a matrix equation. Then there's practically no thinking involved at all, just apply the trivial algorithm! I'm sure you'll come across this method shortly.

That said, sometimes a particular problem may make it advantageous to choose a particular direction for a given loop (say if you are to find a current that's given a defined direction through some wire or component). Then you need to apply the mental effort to keep the current directions consistent and worry about their directions at the mesh boundaries.
 
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  • #64
Thanks gneill yet gain for the response, I comprehend the mesh current concept now, what I do not understand however is: you know between the individual terms for a single equation: how do you decide if it's a "+" or "-" term? I watched a lecture last night which said it is always "+" for example: IL1Z1 "+" Z4(IL1-IL2) "+" V = 0. Yet what the gentleman said in the lecture can not be true as it will change the result of the equation no? in our books it states the following: "In writing the mesh equations, imagine you are walking around the mesh in the direction of the current loop. Then use the convention that all voltages pointing in the direction you are walking are positive and those pointing in the opposite direction are negative", now reading that it does not really explain how you decide on the sign of any single term within the equation as it does not tell me how to consider the direction of voltage drop (whether it will be gain or a drop). This is really my only sticking point with mesh analysis and any help or guidance will be greatly appreciated...
 
  • #65
The way I look at it is that the mesh current is causing potential drops across resistances as it flows through them. If you "walk the loop" in the direction of the mesh current, then each passage through a resistor is a drop (negative term) for that current. Naturally, voltage sources always produce a potential change according to their fixed potential as you "walk" through them.

You can, if you wish, write down drops as positive terms instead. Mathematically this is equivalent to multiplying the entire equation by -1. An equation remains valid if you multiply both sides by the same value. It's pretty easy to write the terms down in this fashion, the only tricky bit being to remember that a voltage rise caused by a source should be written as a negative term, and vice versa (because a "drop" is positive and a "rise" is negative in this paradigm). You also need to remember to treat the signs of the potential changes due to the boundary currents accordingly.

Personally, when I write a mesh equation manually I write drops as negative terms. Thus I don't have to do any mental gymnastics when it comes to walking through sources or dealing with boundary currents. Once I've recorded the equation I can always multiply through by -1 to pretty it up.
 
  • #66
Thank you very much for the speedy reply Sir, you are a star and your help and guidance are greatly appreciated!
 
<h2>1. What is Mesh Analysis and how is it different from Nodal Analysis?</h2><p>Mesh Analysis is a method used to analyze complex electrical circuits by dividing them into smaller loops or meshes. It involves applying Kirchhoff's Voltage Law (KVL) to each mesh to determine the currents flowing through each component. Nodal Analysis, on the other hand, involves applying Kirchhoff's Current Law (KCL) to each node or junction in the circuit to determine the voltages at each node. While Mesh Analysis is better suited for circuits with many current sources, Nodal Analysis is more efficient for circuits with many voltage sources.</p><h2>2. What is Kirchhoff's Voltage Law (KVL) and how is it used in Mesh Analysis?</h2><p>Kirchhoff's Voltage Law states that the algebraic sum of voltages around a closed loop in a circuit is equal to zero. In Mesh Analysis, KVL is used to write equations for each mesh in the circuit by considering the voltage drops across each component. These equations are then solved simultaneously to find the currents flowing through each component.</p><h2>3. How do you handle dependent sources in Mesh Analysis?</h2><p>Dependent sources, such as voltage-controlled voltage sources or current-controlled current sources, can be handled in Mesh Analysis by treating them as independent sources. This means that the dependent source is included in the equations for each mesh and its value is determined by solving the equations simultaneously.</p><h2>4. Can Mesh Analysis be used for circuits with multiple loops?</h2><p>Yes, Mesh Analysis can be used for circuits with multiple loops by dividing the circuit into smaller meshes. Each mesh is then analyzed separately using KVL, and the results are combined to find the overall solution for the circuit.</p><h2>5. What are the limitations of Mesh Analysis?</h2><p>Mesh Analysis is not suitable for circuits with many nodes or junctions, as it can become complex and time-consuming. It also cannot be used for circuits with non-linear elements, such as diodes or transistors. In addition, Mesh Analysis assumes that the current flows in one direction around each mesh, which may not always be the case in real circuits.</p>

1. What is Mesh Analysis and how is it different from Nodal Analysis?

Mesh Analysis is a method used to analyze complex electrical circuits by dividing them into smaller loops or meshes. It involves applying Kirchhoff's Voltage Law (KVL) to each mesh to determine the currents flowing through each component. Nodal Analysis, on the other hand, involves applying Kirchhoff's Current Law (KCL) to each node or junction in the circuit to determine the voltages at each node. While Mesh Analysis is better suited for circuits with many current sources, Nodal Analysis is more efficient for circuits with many voltage sources.

2. What is Kirchhoff's Voltage Law (KVL) and how is it used in Mesh Analysis?

Kirchhoff's Voltage Law states that the algebraic sum of voltages around a closed loop in a circuit is equal to zero. In Mesh Analysis, KVL is used to write equations for each mesh in the circuit by considering the voltage drops across each component. These equations are then solved simultaneously to find the currents flowing through each component.

3. How do you handle dependent sources in Mesh Analysis?

Dependent sources, such as voltage-controlled voltage sources or current-controlled current sources, can be handled in Mesh Analysis by treating them as independent sources. This means that the dependent source is included in the equations for each mesh and its value is determined by solving the equations simultaneously.

4. Can Mesh Analysis be used for circuits with multiple loops?

Yes, Mesh Analysis can be used for circuits with multiple loops by dividing the circuit into smaller meshes. Each mesh is then analyzed separately using KVL, and the results are combined to find the overall solution for the circuit.

5. What are the limitations of Mesh Analysis?

Mesh Analysis is not suitable for circuits with many nodes or junctions, as it can become complex and time-consuming. It also cannot be used for circuits with non-linear elements, such as diodes or transistors. In addition, Mesh Analysis assumes that the current flows in one direction around each mesh, which may not always be the case in real circuits.

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