Solve Circuit Analysis Homework: Find v1, v2, v3 with Nodal Analysis

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Discussion Overview

The discussion focuses on solving a circuit analysis homework problem using nodal analysis to find the voltages v1, v2, and v3. Participants explore the formulation of nodal equations and the implications of treating certain nodes as a supernode.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant starts with initial equations based on current relationships and voltage differences but expresses uncertainty about the next steps.
  • Another participant suggests that the nodes can be treated as a supernode and provides a hint to write the nodal equation referencing v1.
  • A participant questions the validity of their nodal equation and discusses the treatment of a branch with a 6-ohm resistor as negligible.
  • Clarifications are made regarding the formulation of node equations and the importance of expressing currents in terms of node voltages.
  • One participant reports successfully finding the correct answer after receiving guidance.

Areas of Agreement / Disagreement

Participants generally agree on the need to use nodal analysis and the concept of a supernode, but there is some uncertainty about the correct formulation of the nodal equations and the treatment of certain branches in the circuit.

Contextual Notes

Some participants note missing complete nodal equations and the need for clarity on how to handle specific components in the circuit analysis.

Dunder
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Homework Statement


Find v1, v2, v3
Must be done with nodal analysis

Homework Equations


I=V/R


The Attempt at a Solution


So i started by saying i1 = v2/4, i = v1/2, i3 = v3/3
i + i1 + i2 = 0
v3-v2=51
v1-v2=0

I am not really sure to what to do from here, i can't seem to come across the right solution, the answer given in the book is v1=3.043, v2=-6.956, v3=0.6522

Any help would be much appreciated
 

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Dunder said:

Homework Statement


Find v1, v2, v3
Must be done with nodal analysis

Homework Equations


I=V/R


The Attempt at a Solution


So i started by saying i1 = v2/4, i = v1/2, i3 = v3/3
i + i1 + i2 = 0
v3-v2=51
v1-v2=0

I am not really sure to what to do from here, i can't seem to come across the right solution, the answer given in the book is v1=3.043, v2=-6.956, v3=0.6522

Any help would be much appreciated

The problem says to use nodal analysis. You haven't written any complete nodal equations.

Hint: The nodes designated by V1, V2, and V3 are all separated by voltage sources. This implies that you can treat all three nodes as one supernode. Write the nodal equation for the supernode by referencing v1, and note that i = v1/2Ω. (v2 = v1 - 10V; v3 = v1 - 10V + 5i).
 
So is my nodal equation with the super node i + i1 + i2 = 0 ?
The branch including the 6 ohm resister is negligible since it theoretically exits the node and enters it as well?
Using this, I ended up solving for v1, but ended up finding v1 = 0, so I must be going in the wrong direction
 
Dunder said:
So is my nodal equation with the super node i + i1 + i2 = 0 ?
The branch including the 6 ohm resister is negligible since it theoretically exits the node and enters it as well?
That is true.
Using this, I ended up solving for v1, but ended up finding v1 = 0, so I must be going in the wrong direction

Node equations involve the node voltages and the resistances connected between nodes (including the reference, or "ground" node). You shouldn't need to designate any particular current as "i1", or "i2", etc. The exception here is that the current given the label "i" is important for the dependent voltage source. You should be able to replace it with a node branch current expression (v1/2).
 
Okay thank you, I worked to the right answer. Thank you again
 

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