Nodal Analysis Question - Find the Node Voltages

[NewtonianAlch]

Homework Statement

http://img12.imageshack.us/img12/6886/nodalanalysisproblem.jpg

The Attempt at a Solution

I put in the currents for KCL in the diagram, though I'm not sure if I've done it right.

So essentially I get the equation as i1 + 3 = i2 + i3

Current in = current out.

i1 = v1/10
i2 = v1/5
i3 = v2/4


So we get v1/10 + 3 = v1/5 + v2/4

Simplifying, this becomes: 2v1 + 60 = 4v1 + 5v2 => 2v1 + 5v2 = 60

I wasn't quite sure what to make of the current source, I first thought maybe I should convert the 6A current source and the 2 ohm resistor in parallel to a voltage and resistor in series which makes it a 12 V source and then apply KVL to the loop to get -v1 + 12 +v2 = 0; however going down this path and solving for the voltages does not get me the correct answer.

The correct answer is v1 = 0 and v2 = 12V - where have I gone wrong?

 

[gneill]

It would be easier to write two separate node equations for V1 and V2. That'll handle the 6A source and its parallel resistor. Two equations for two unknowns.

 

[NewtonianAlch]

So essentially don't treat it as a supernode?

OK, I will give that a go now.

 

[NewtonianAlch]

http://img3.imageshack.us/img3/6886/nodalanalysisproblem.jpg

I treated them as two separate nodes now.

The two equations I got were

1) i1 = i2 + i4 + 6

2) 9 + i4 = i3

i1 = v1/10
i2 = v1/5
i3 = v2/4
i4 = (v1 - v2)/2

Therefore:

1) v1/10 = v1/5 + (v1 - v2)/2 + 6
=> 6v1 - 5v2 = -60

2) 2v1 - 3v2 = -36

Solving the two I get v2 = 12V, and v1 = 0 -- which are the correct answers! So thanks for that!

Though...I don't understand what I was doing wrong when I treated it as a supernode, can you explain?

 

[NewtonianAlch]

Never mind, I read the definition of supernode and it says encircling a voltage source. I only wish I had read the definition twice, so I didn't have to waste an hour, lol.

 

[zonedestruct]

bro its better if you do currents coming out of a node equals zero. So these are the two equations you will end up with: first let's do the equation for node v2: (v2-0)/4 + (-3) + (-6) + (v2 - v1)/2 = 0 and then the equation for node v1: (v1-0)/5 + 6 + (v1-0)/10 + (v1-v2)/2 = 0 now you have 2 equations and 2 unknowns so you can solve them and find the voltages v2 and v1. notice that because i done currents coming out of the node i turned the 3 amp current source into -3 cause i reversed its direction since I am taking all currents to go out of the node and that 3 amp source was going into the node so i made it negative (i also done the same for the 6amp one since his going into the node v2). it gets more confusing when you get supernodes and when the reference node is not so clear as in this question but you should just practice heaps cause when you do circuit analysis your going to need to know these basic stuff heaps well.