How Do Circuit Currents Distribute in Complex Networks?

[Learnphysics]

Homework Statement

[PLAIN]http://img195.imageshack.us/img195/7725/1038d.png

Homework Equations

KVL.

The Attempt at a Solution

I'v set up the equation for node v1 node, but v2 node confuses me.

would it be correct to assume that the 1A current flows into node 2? Or does only part of it flow into node 2, (with the other part going down the 10 ohm resistor into ground)

How do i find out how much current that 1A source is contributing into node 2.

Also when setting up the KVL for node 1, i have (v1/5ohms) + (v1 - v2)/5ohms... but i can't figure out the current coming through the 10v Voltage source to V1. I coudl do V1-V2, and then divide it by the resistance of the voltage source. but i don't know the resistance of the voltage source.

please help

 

[ehild]

You know the voltage across the resistor between the nodes v2 and v1: it is 10 V. What is the magnitude and direction of the current flowing through it?

The nodes at v2 are connected with a single wire so they can be replaced by a single node. Write the sum of currents for it. Do not forget to include i_s.

You know the relation between the voltages: v1=v2+10. Express the current flowing between v1 and the ground through the left 5 ohm resistor.

Write an equation for the currents at the node at v1, including i_s .

These equation must be enough to get the unknown voltages and currents.

ehild

 

[Learnphysics]

After working through it, the answer i got for Is was -4A.

The book however says -3.33A. But this book has been wrong before. Have i made a mistake, or is the book wrong. I looked through my working and didn't spot anything mathamatically incorrect, but it's multiple pages in length.

 

[ehild]

The book is correct. And the solution is just a few lines. Try to follow my post.

ehild

 

[Learnphysics]

Hmm.. I seem to be doing something wrong.

here are my two equations:

at V1 I have

(V1/5) + Is -2 = 0

and at V2 i have

Is + 2 + (v2/10) +1 = 0

Does this look right?

 

[quanticism]

You're close but both expressions have an error due to incorrect sign/s.

I like to think of using KCL as: sum of current coming in = sum of current going out

Edit: Oh, and you're forgetting Is at V2

 

[ehild]

Hmm.. I seem to be doing something wrong.

here are my two equations:

at V1 I have

(V1/5) + Is -2 = 0

and at V2 i have

Is + 2 + (v2/10) +1 = 0

Does this look right?

No. Remember the current flows in the direction of the electric field which is proportional to the negative potential difference, from a place at a more positive potential to the negative one. You know that the potential at the left terminal of the top 5 ohm (v1) resistor is 10 V higher than that of the right terminal. So the current flows from left to right. At the 10 ohm resistor: The upper end is at v2 potential, the lower one is at 0 potential. The current flows from the node v2 to the ground.

ehild