Find the node voltages for the circuit shown.
The Attempt at a Solution
I have chosen my ground node as the set of nodes in the bottom of the image and labeled all of my unknown voltages as en.
Here is what I have so far. Where G = 1/R
For the node labeled e1:
(e1-v0)G1 + e1(G3) + (e1-e2)I1 + (e1-e2)G2=0
For the node labeled e2:
(e2-e1)(-I2) + e2(G4) + (e2-e1)G2=0
I am pretty sure my problem lies in the way I am handling the currents in the node. I started plugging in numbers after I simplified it all and one of my unknown voltages went away. After that I looked at it again and knew I was doing it wrong. Most of the examples in the book don't deal with a current parallel to a resistor.
I think the way I should have done it is rather than subtracting voltages and multiplying like I am doing with the resistor nodes, is just take the current by itself.
So in my above equation e1)(-I1) would just become -I1 since I am not using ohms law for current. I think I only need current? Does that sound better?