REAL QUICK HELP nodal analysis?

[asdf12312]

REAL QUICK HELP nodal analysis??

Homework Statement

Homework Equations

n/a

The Attempt at a Solution

i am having trouble with my nodal equations for nodes 1 and 3. and that's just for the current on the top of those nodes, where the 4V is at. For node 1 my current equation is (V1-4)/0.2 for the top. and for node 3 i got current is just 0A, because there's no resistor between it and the 4V source. but i know that can't be right...so i got at least one of those currents wrong. any quick thuoghts?Node 1:
(V1-2)/0.1 + (V1-4)/0.2 + (V1-V2)/0.5 = 0

Node 2:
(V2-V1)/0.5 + V2/0.1 + (V2-V3)/0.5 = 0

Node 3:
(V3-V2)/0.5 + (V3-3)/0.1 = 0

 

[gneill]

Keep in mind that the current you're looking for is due to the potential difference between nodes. So for your node 1 equation, the term for the upper path through the 4V supply should reference V3 too. The 4V supply is added to V3, so the potential difference becomes V1 - (V3 + 4).

One way to keep this straight is to use KVL along the path of interest. For the top branch you want to start at V1 and work your way over to V3. Assume the current is I flowing from V1 to V3, then

V1 - I*0.2 - 4 = V3

Rearrange:

I = (V1 - V3 - 4)/0.2

and that's your 'I' term for your node equation for that path.

Do the same for other branches that you find confusing. Note that the order of voltage sources and resistances along a given path doesn't matter.

 

[asdf12312]

thanks! was confusing for me at 1st but now i undrstand it. and the equation for the upper path from V3 to V1 would be (V3-V1)+4/0.2 (the polarity of the voltage source is switched. also the same as the negative value of current from V1 to V3.