Troubleshooting Nodal Analysis for a 2 PSU Resistor Circuit

[pat666]

Homework Statement

see attached

Homework Equations

The Attempt at a Solution

Hey, I'm having trouble with a 2 PSU resistor NA circuit. here is what I've done:
N1=V1
N2=v2
N3=v3 = 0V
N4=v4

0=(10-v1)/4K7-V2/10k-(V1-V2)/1K

0=(V1-V2)/1K-(V2-V4)/470-(V2-V4)/1K

0=(V4-5)/10K-V4/10K

there's at least something wrong with eq 3 because it can't be solved?

Thanks for any help

 

[Saladsamurai]

Perhaps you can simplify the circuit first? I think that R4 and R5 are in parallel and the resulting R45 in series with R2.

 

[pat666]

Shouldn't it be easy enough without simplifying + I lose node 4 if I do that.

 

[WesleyPipes]

Do a KCL at Nodes 1-4.

Hah...just read it and saw you did already I think.

But as an example at Node 1...

(Vx1-10)/R1 + (Vx1-Vx3)/10K + (Vx1-Vx2)/1K = 0

I think in your KCLs you worked backwards compared to me so not sure if this will help or confuse you.

 

[pat666]

thats the same as mine I think, V3=0V

node 4 is what I have wrong I think.

Thanks

 

[WesleyPipes]

Node 4:
(Vx4-5)/10K + (Vx4-Vx3)/10K + (Vx4-Vx2)/470R + (Vx4-Vx2)/1K = 0

Should be right for that node.

 

[pat666]

arhh I forgot to include the R's up the top, can you tell me if my EQ's for N1 AND 2 are correct.

thanks