Nodal analysis problem

asgerbj

I need to solve this circuit using nodal analysis (find the voltage in all nodes), but i need the actual equations used to solve it.

All supplied information is there.

What I've done is to create 2 supernodes, like this


And write the following equations for the three nodes that i have left.
[itex]\frac{V1}{2k}+\frac{V1-V2+6}{2k}= 9mA[/itex]
[itex]\frac{V2}{1k}+ 9mA +\frac{V2+6-V1}{2k}+\frac{V2+6-V3}{1k}= 2mA [/itex]
[itex]\frac{V3-V2+6}{1k}+\frac{V3}{1k}+\frac{V3+89}{1k}+2mA = 0[/itex]

When i try to solve these equations i get V1 = -5.8V, V2=-23V, V3=-40V
I tried to draw the circuit in LTSpice, and the result should be V1=2V, V2=-20V, V3=-35V

What did i do wrong? I've been trying to redo the circuit several times for more than 1½ hour now, but don't get the right answer.

gneill

It's a good idea to get into the habit of putting parentheses around the terms corresponding to supernode sub-nodes. That way mathematical operation ordering is maintained when you write your expressions. In your first node equation, for example, note that V1 - V2 + 6 is not the same as V1 - (V2 + 6)

asgerbj

oh god... i can't believe i spend so much time on this.... .. thanks, that solved it :)