Nodal Analysis - KVL Loop question.

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Discussion Overview

The discussion revolves around the application of nodal analysis and Kirchhoff's Voltage Law (KVL) in solving a circuit problem. Participants are examining the correctness of node equations and KVL loops, particularly focusing on a supernode situation and the implications of voltage sources in the circuit.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents their node equations and expresses uncertainty about the correctness of their KVL analysis, particularly regarding the influence of a 2V source.
  • Another participant identifies a supernode situation and prompts the original poster to clarify the boundaries of the supernode and the independent nodes.
  • The original poster confirms the supernode encompasses nodes v1 to v3 and mentions performing KCL for that supernode and node 4.
  • A suggestion is made that the KVL could be simplified by expressing v2 in terms of v1 and v3 directly, rather than using the initial KVL formulation.
  • The original poster acknowledges the suggestion and reflects on the value of practice in recognizing such simplifications.

Areas of Agreement / Disagreement

There is no explicit consensus on the correctness of the KVL analysis, as the original poster expresses uncertainty. However, participants engage in constructive dialogue about the analysis and potential simplifications.

Contextual Notes

The discussion includes assumptions about the circuit configuration and the relationships between the voltages and currents, which may not be fully detailed in the posts. The presence of a voltage source complicates the KVL analysis, and the implications of the supernode are not exhaustively explored.

Who May Find This Useful

Students and practitioners interested in circuit analysis, particularly those learning about nodal analysis and KVL in the context of electrical engineering problems.

NewtonianAlch
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Homework Statement


I've obtained the node equations that's in the matrix for rows 1, 2, and 4. I got 3 as well but I'm not sure if my analysis was correct.

http://img252.imageshack.us/img252/3151/nodeq.jpg

The Attempt at a Solution



http://img684.imageshack.us/img684/9803/dsc0010van.jpg

So basically this is from the bottom-left of the circuit.

v1 = -2 + Vx, therefore

Vx = v1 + 2 (I wrote -2 in the drawing by mistake)

So doing KVL: -Vx + 2 + 5io + v2 = 0

=> (-v1 -2) + 2 + v3 + v2 = 0

So, -v1 + v2 + v3 = 0 [which is row 3 of the matrix]

Note that io = v3/5, so 5io is just v3.

Is this correct reasoning?
 
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Hmm. Looks to me like you've got a supernode situation since some nodes are directly tied together with voltage sources. Can you identify the boundaries of the supernode? Which nodes are left as independent nodes?
 
I've done all of that, the supernode encompasses everything from v1 to v3. So I did KCL for that supernode and then KCL at node 4.

I just need to know if I've done the KVL for the loop in the bottom-left hand correctly. My answers all work out to the solutions given, but I just had a funny feeling about the KVL as I was struggling to get it initially because of that 2V source and the direction of it.
 
NewtonianAlch said:
I've done all of that, the supernode encompasses everything from v1 to v3. So I did KCL for that supernode and then KCL at node 4.

I just need to know if I've done the KVL for the loop in the bottom-left hand correctly. My answers all work out to the solutions given, but I just had a funny feeling about the KVL as I was struggling to get it initially because of that 2V source and the direction of it.

Okay. Well the KVL you wrote looks fine.

Since you know that 5i0 = v3, would it not have been simpler to just write KVL from node v1 to v2 as:

v2 = v1 - v3

and rearrange?
 
Hmm, you're right! I guess only practice helps recognise things like that easily. Thanks once again.
 

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