Applying nodal analysis on this simple circuit

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Discussion Overview

The discussion revolves around the application of nodal analysis to a circuit problem, with participants seeking assistance in resolving discrepancies in their calculations. The focus includes the formulation of equations, potential alternative methods like mesh analysis, and the verification of current values.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant notes a discrepancy in their calculated value for V1, which they believe should be 80V according to the book's answer, despite checking their equations multiple times.
  • Another participant points out a mistake in the equations related to the current at V2, suggesting a correction in the expression for Ix.
  • A participant questions whether nodal analysis is necessary, proposing that mesh analysis might provide a quicker solution due to the presence of a current source.
  • There is a request for clarification on how to derive certain equations using mesh analysis, indicating a need for further explanation of the process.
  • One participant confirms that they were required to use nodal analysis as per the book, expressing uncertainty about the applicability of mesh analysis.
  • Another participant provides a detailed approach to mesh analysis, outlining equations derived from the circuit, but later acknowledges that this method also leads to multiple equations.
  • A participant raises a question about the current through a resistor and its relationship to the KCL at different nodes, prompting a confirmation from another participant.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and effectiveness of nodal versus mesh analysis. There is no consensus on the best approach to solve the circuit problem, and several calculations and assumptions remain under discussion.

Contextual Notes

Some participants highlight potential mistakes in their equations and the need for clarification on specific steps in their reasoning. The discussion includes unresolved mathematical steps and varying interpretations of circuit behavior.

Who May Find This Useful

Readers interested in circuit analysis techniques, particularly those studying electrical engineering or related fields, may find this discussion relevant.

PainterGuy
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Hi, :)

Almost all the details you will find in the given link below:
http://img171.imageshack.us/img171/9797/nodalysis1.jpg

You will find the expected (or, target answers) in the top right corner.

As you can see my value for V1 is wrong. It should have been 80V according to the answer given in the book. I have checked my equations several times but I found nothing wrong with them. Please help me with it. Many thanks for your help.

Cheers
 
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3rd line: At V2: Ix = 4Ix + I2 --> 0 = 5Ix + I2 ... silly mistake, 4Ix - Ix = 3Ix!

7th line: At V3: ... --> (V1)/2 - (V3)/2 = (V3)/6 + (V2) --> 1/2(V2) = -2/3(V3) ... how do you turn - V(3)/2 - (V3)/6 = (V2) - (V1)/2 into 1/2(V2) = -2/3(V3), specifically the combining of V2 and V1?
 
PainterGuy said:
Hi, :)

Almost all the details you will find in the given link below:
http://img171.imageshack.us/img171/9797/nodalysis1.jpg

You will find the expected (or, target answers) in the top right corner.

As you can see my value for V1 is wrong. It should have been 80V according to the answer given in the book. I have checked my equations several times but I found nothing wrong with them. Please help me with it. Many thanks for your help.

Cheers

Are you required to use nodal analysis for the solution?

That current source in the LHS means that you could quickly solve this with 2 equations using mesh analysis.

Just a thought, I usually take the easiest route possible.
 
That current source in the LHS means that you could quickly solve this with 2 equations using mesh analysis.

Just a thought, I usually take the easiest route possible.

Out of curiosity, could you demonstrate which two equations you would use?

Considering the other two mesh current variables, the third variable from the dependent current source and the super mesh it doesn't look that much easier either way, unless you're familiar with one method over the other I guess.
 
Many thanks, Zryn, for helping wit this problem, and also with the one from yesterday. Thanks a lot.

jegues, I was required by the book to use nodal analysis. To be honest I don't know if mesh analysis is applicable.

Once again many thanks. Hope you guys will keep on helping me.

Cheers
 
Zryn said:
Out of curiosity, could you demonstrate which two equations you would use?

Considering the other two mesh current variables, the third variable from the dependent current source and the super mesh it doesn't look that much easier either way, unless you're familiar with one method over the other I guess.

If we label the leftmost mesh with a mesh current i1, the rightmost i2 and the mesh above it i3 we can apply mesh analysis to this problem.

By inspection,

i_{1} = 10A

Followed by a simple KCL gives,

i_{x} = \frac{-10}{3}A

Now we write the equation for the supermesh,

5i_{3} + 10i_{2} - 7i_{1} = 0 \quad \text{Equation 1}

Looking at the dependent source,

4i_{x} = i_{3} - i_{2} \quad \text{Equation 2}

Now I realize that this gives 3 equations as well, but when I had quickly glanced at the circuit I didn't notice that the other current source was a dependent source because it wasn't drawn with the correct diamond symbol.
 
Followed by a simple KCL gives,

<br /> i_{x} = \frac{-10}{3}A<br />

Wouldn't the current through the 3R resistor be equal to 10A - i_{3} by KCL at node 1, thus making the KCL at node 2 result in i_{x} =4i_{x} + 10 - i_{3} --> i_{x} = \frac{(i_{3} - 10)}{3}?
 
Zryn said:
Wouldn't the current through the 3R resistor be equal to 10A - i_{3} by KCL at node 1, thus making the KCL at node 2 result in i_{x} =4i_{x} + 10 - i_{3} --> i_{x} = \frac{(i_{3} - 10)}{3}?

Yes you are absolutely correct.
 

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