Nodal Voltage Analysis with dependent sources

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sparkie
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Homework Statement


All the data is on the sheet. I named the nodes V1 to V4, however I'm primarily evaluating in terms of V3 and V4. The x=V3 and y=V4 are for the systems solving I'm using. I've looked and looked at this problem, and seem to be hung up, but I suspect it is going to be on my equation for Io or having to do with the branch V3-V4.
Handwritten circuit schematic with nodal analysis equations on graph paper, showing nodes V1 to V4, resistors of 10, 20, 40 and 60 ohms, an 80 V source, dependent sources 4Vo and 2io, and node equations including V3-80 over 10 plus V3-V4 over 20 plus V3-(V4-96) over 40 equals 0.

Homework Equations


All the relevant info is on my work, I tried to be clear, neat and verbose with it.

The Attempt at a Solution


Handwritten nodal analysis work: V1 = 80, V2 = 4 Vo, Vo = V4, Io = (V3 - 80)/10, then KCL equations (V3-80)/10 + (V3-4V4)/20 + (V3-(V4-96))/40 = 0 and (V4-(V3+96))/40 + (-2Io) + V4/60 = 0.
https://pasteboard.co/H8OUDW8.jpg
H8OUDW8.jpg
 
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  • Handwritten circuit schematic with nodal analysis equations on graph paper, showing nodes V1 to V4, resistors of 10, 20, 40 and 60 ohms, an 80 V source, dependent sources 4Vo and 2io, and node equations including V3-80 over 10 plus V3-V4 over 20 plus V3-(V4-96) over 40 equals 0.
    upload_2018-2-22_9-46-35.png
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  • Handwritten nodal analysis work: V1 = 80, V2 = 4 Vo, Vo = V4, Io = (V3 - 80)/10, then KCL equations (V3-80)/10 + (V3-4V4)/20 + (V3-(V4-96))/40 = 0 and (V4-(V3+96))/40 + (-2Io) + V4/60 = 0.
    upload_2018-2-22_9-47-16.png
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Last edited by a moderator:
What, specifically, are you asked to solve for? It's not mentioned in your problem statement.

sparkie said:
I've looked and looked at this problem, and seem to be hung up, but I suspect it is going to be on my equation for Io or having to do with the branch V3-V4.
Your equations look okay except, as you say, your equation for ##i_o## (Assuming that it's properly labelled on your schematic).

Generally it's only necessary to name essential nodes for analysis. Your V1 and V2, being in the middle of branches, are not essential nodes.
 
So, re-think your equation for ##i_o## and show us how you get on...
 
So I ended up using the branch V3-V4 to get the current for Io and it worked. I tried a couple other things and failed before I realized it this morning. Of course, the homework has already been submitted, but I wanted to find out what I was missing, so thank you for the help.
 
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