Solve Node Voltage Analysis: All G=1S, 3A Current Source

AI Thread Summary
The discussion revolves around solving for node voltages va, vb, and vc in a circuit where all conductances are equal to 1S, and a 3A current source is present. The user presents their equations for the nodes but questions the textbook's solutions, particularly regarding the inclusion of G3 in Node A and the treatment of Vc in Node C. Responses confirm that the user's equations are correct and suggest that the textbook contains errors. The consensus is that the user's understanding is accurate, highlighting discrepancies in the textbook's approach.
TheRedDevil18
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Homework Statement



Determine the three node voltages, va, vb, and vc, when all the conductance's are equal to 1S
Circuit Diagram:
Circuit_Diagram.jpg


The labels are a bit cut off, hope you guys can see it. The current source parallel with G2 is 3A

Homework Equations

The Attempt at a Solution


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I think their is a mistake in their solutions to the equations
These are my equations:

Node A:
Va(G1+G2+G6) - G2*Vb - G6*Vc = 9-3
Node B: -G2*Va + Vb(G2 + G3+ G4) - G4*Vc = 3
Node C: -G6*Va - G4*Vb + Vc(G4 + G5+ G6) = 7

These are the textbook solutions:

Node A:
Va(G1+G2+G3) - G2*Vb - G6*Vc = 9-3......How is G3 included when it is part of node B ?
Node B: -G2*Va + Vb(G2 + G3+ G4) - G4*Vc = 3
Node C: -G6*Va - G4*Vb - Vc(G4 + G5+ G6) = 7.....How did they get -Vc ?

My main question is, Is the textbook correct, If yes, then why ?

Thanks
 
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Your equations look fine. It looks like you've caught an error in the text.
 
gneill said:
Your equations look fine. It looks like you've caught an error in the text.

That's what I thought, thanks :)
 

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