What are the steps for solving a circuit using node voltage analysis?

[rugerts]

Homework Statement

Using node voltage analysis, find the node voltages.

Homework Equations

n-1 Kirchhoff's Current Law equations for n nodes (since ground is a node).

The Attempt at a Solution

I've tried doing KCL at each node and then getting a fourth equation from a potential difference between nodes 2 and 3. I'm not sure if taking the fourth equation is entirely valid but I do believe I have seen this been done before solving using substitution. I am trying, however, to use Cramer's Rule through a calculator.

Since uploading pictures here always seems to turn out blurry, here's an imgur link: https://imgur.com/Xd8gqRx

 

[scottdave]

2 of your equations use the current i, but only second row of the matrix has a coefficient which will multiply by i.

 

[scottdave]

I think you didn't transcribe correctly or forgot some terms when this one got put into the matrx:

And yes you should have 4 independent equations if you want to solve for the 4 unknown variables. It appears that your equations are independent.

 

[rugerts]

2 of your equations use the current i, but only second row of the matrix has a coefficient which will multiply by i.

Well, it looks like that was the solution because my answers now agree with what the book has. Thank you for the keen eye! I appreciate the help.

 

[gneill]

Note that nodes V2 and V3 have a fixed potential difference thanks to the voltage source V. Hence, V2 and V3 comprise a supernode, and you have only two essential nodes. The circuit can be solved using just two node equations, (say for V1 and the supernode V2/3).