Node Voltage (is my answer correct )

[pokie_panda]

http://www.flickr.com/photos/84781786@N03/7822251544/
Find the node VOLTAGE for V1,V2,V3,V4

Homework Equations

KVL

The Attempt at a Solution

V1 = 6V
V4= 16V
V2= V2/1.5k - 6/1.5k + V2/ 1k + V2/3.3k - V3/3.3k
6/1500 = V2/5.8k - V3/3.3k
V3 = V3/2.2k + V3 / 4.7k + V3/3.3k - V2/3.3k - 16/2200
16/2200 = - V2/3.3k + V3/ 10.2k

But I'm getting 2 negative answers
V2= -34.6 V V3= -32.9

 

[gneill]

http://www.flickr.com/photos/84781786@N03/7822251544/
Find the node VOLTAGE for V1,V2,V3,V4

Homework Equations

KVL

The Attempt at a Solution

V1 = 6V
V4= 16V
V2= V2/1.5k - 6/1.5k + V2/ 1k + V2/3.3k - V3/3.3k

Why is that V2 = ? Surely you're forming a sum of currents at the node, which should yield a (zero) current?

6/1500 = V2/5.8k - V3/3.3k

How did you arrive at the V2/5.8k term?

V3 = V3/2.2k + V3 / 4.7k + V3/3.3k - V2/3.3k - 16/2200
16/2200 = - V2/3.3k + V3/ 10.2k

Again, the "V3 =" doesn't make sense. Perhaps you're just being a tad sloppy with terminology? The "=" sign is reserved for use in equations. Did you mean to indicate that "This is the expression for node V3?"

Also again, can you explain how you arrived at the term V3/10.2k?

 

[tindel]

I agree with Gneill - Your equations are a bit off - I think you mean:

V1: V1 = 6V
V2: V2 = 16V
V3: 0 = V2 / 1.5k - V1 / 1.5k + V2 / 1.0k + V2 / 3.3k - V3 / 3.3k
V4: 0 = V3 / 3.3k - V2 / 3.3k + V3 / 4.7k + V3 / 2.2k - V4 / 2.2k

Note that using the node voltage method used Kirchov's Current Law which states that all the currents going into a node must equal zero. Using the node voltage method you are simply summing the currents into each node and setting them equal to zero - not V3 or V4.

If you solve these equations you will come up with the correct answer... it took me a couple tries - my arithmetic is rusty, I guess... but I think I just fat fingered a value into my calculator. I did finally arrive at the correct answer, which I verified with software.

Hope this helps.

Also note that:
V2 / 1.5k + V2 / 1.0k + V2 / 3.3k does NOT equal V2 / 5.8k
http://www.mathsisfun.com/fractions_addition.html
I think there was some confusion there as well which could have been the root of your negative number solution.

On the plus side - good for you for realizing there was no way the answer could be negative without a negative voltage source.