Are These Node Method Equations Correct?

[esmeco]

I'm trying to solve an exercise on the node method but I'm not quite sure if the equations for the node tensions are right,so I was hoping if someone could give me a hand...Here are the node equations:

Node 1: v1/50 + (v1-50)/80 + (v1-v0)/40=0
Node 2: v0/200 + (v0-v1)/40 + (v0-50)/800 - 0,75=0

The link for the exercise is:
http://i75.photobucket.com/albums/i281/esmeco/nodemethod.jpg


Thanks in advance for the help!

 

[berkeman]

Not quite right. Call the voltage to ground at node 2 "V2" and try again. Vo as labelled is not V2. Vo is the voltage across the top resistor, not to ground.

 

[esmeco]

Hummm...I guess I'm not understanding quite well what you are saying...Could you or someone help me correct my equations?

 

[esmeco]

So...V0 would be something like: v0=(v2-v1)/800 ?

 

[berkeman]

So...V0 would be something like: v0=(v2-v1)/800 ?

No, don't confuse currents and voltages. The node equations that you wrote originally were to use the fact that the sum of all currents out of each node must be zero. That's why each term is a voltage difference divided by the resistance between the voltages. Vo is just V2-50V.

Just go ahead and re-write the equations one more time using V2 as a term. Don't worry about Vo for now. In the end you will have V2, and that's enough to solve for Vo.

 

[esmeco]

Thanks!I wasn't attending to the fact that it was the voltage what we wanted to know,I thoughtthe current instead...I think I'm getting it now...
So,the equations should be something like:

Eq. 1:(v1-50)/80 + v1/50 + (v1-v2)/40=0
Eq. 2: (v2-v1)/40 + v2/200 + v2/800 -0,75=0

Is this right?

 

[berkeman]

Almost, but in Equation 2, you need to also account for the current flowing through the 800 Ohm resistor up on top. Add that current out of node 2 into Equation 2, and then you can solve for V1 and V2, which gives you Vo.

 

[esmeco]

But,Isn't that current flowing through the 800 ohm resistor given by v2/800?

 

[berkeman]

No. What is the voltage on the left side of the 800 Ohm resistor? It's not zero. So the current isn't (V2-0)/800.

 

[esmeco]

I got it...The current is (V2-50)/800.Thanks for the help!