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

In summary, there is a mistake in the textbook solutions for determining the three node voltages, va, vb, and vc, when all conductances are equal to 1S. The equations provided by the student are correct, but the textbook solution includes an error where G3 is incorrectly included in node A and there is a negative sign error for node C. The student's question is whether the textbook is correct and why.
  • #1
TheRedDevil18
408
1

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


[/B]
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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  • #2
Your equations look fine. It looks like you've caught an error in the text.
 
  • #3
gneill said:
Your equations look fine. It looks like you've caught an error in the text.

That's what I thought, thanks :)
 

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

What is Node Voltage Analysis?

Node Voltage Analysis is a method used in circuit analysis to solve for the unknown voltages at different nodes in a circuit. It is based on Kirchhoff's Current Law and Ohm's Law.

How is Node Voltage Analysis performed?

To perform Node Voltage Analysis, we first label all the nodes in the circuit. Then, we choose one node as the reference node and assign it a voltage of 0. Next, we use Kirchhoff's Current Law to write equations for each node, using the unknown node voltages and known currents. Finally, we solve the resulting system of equations to find the node voltages.

What is the role of G=1S in Node Voltage Analysis?

G=1S refers to conductance, which is the inverse of resistance. In Node Voltage Analysis, we use conductance instead of resistance to simplify the calculations. By setting G=1S, we can easily calculate the voltage drop across a resistor by multiplying the conductance with the voltage at that node.

How do we handle 3A current sources in Node Voltage Analysis?

In Node Voltage Analysis, we treat 3A current sources as known currents in our equations. We can use Kirchhoff's Current Law to write equations involving the currents at different nodes, and then solve for the unknown node voltages.

What are the advantages of using Node Voltage Analysis?

Node Voltage Analysis is a systematic and efficient method for solving complex circuits. It reduces the number of equations needed to be solved compared to other methods, making it less prone to errors. It also allows us to easily determine the voltage at different nodes in the circuit, which is crucial for circuit design and troubleshooting.

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