Engineering What are the Nodal equations for the circuit?

[t_jorgic]

Homework Statement

The problem is explained in the picture. It asks to find the value of Is given that Vo = 6v.

http://img24.imageshack.us/img24/9935/circuitst.jpg

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Homework Equations

The Attempt at a Solution

I am attempting the Nodal Method to get a system of equations which i will solve. The problem is getting those equations. I think I am missing a few equations. Heres my attempt:

There are two nodes that I have written equations for.

Va/7 + (Va - Vb)/3 = Is

(Vb-Va)/3 + Vb/2 + Vb/3 = Is

Im not sure if these equations are right or not.

 

[Basher]

you have two independent nodes so you only need two equations which you have. and by the looks of it you have almost perfect equations. there is one mistake though.

What is the fundamental law that you are applying when you do node analysis?

 

[CDTOE]

The first equation is correct, but the second one isn't. You can't equate the second equation to 'Is' for two reasons. First, there's a current flowing through the 7Kohm which is equal to (Va/7k), and second, there's no current source flowing toward or out of node 'Vb'. You need to equate the second equation to zero and find the value of Va, then, substitute in the first equation to get the value of 'Is'.

Note that Vb equals 6V.