(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the node voltages for the circuit shown.

2. Relevant equations

See attachment.

3. 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 e_{n}.

Here is what I have so far. Where G = 1/R

For the node labeled e_{1}:

(e_{1}-v_{0})G_{1}+ e_{1}(G_{3}) + (e_{1}-e_{2})I_{1}+ (e_{1}-e_{2})G_{2}=0

For the node labeled e_{2}:

(e_{2}-e_{1})(-I_{2}) + e_{2}(G_{4}) + (e_{2}-e_{1})G_{2}=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 e_{1})(-I_{1}) would just become -I_{1}since I am not using ohms law for current. I think I only need current? Does that sound better?

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# Finding Node Voltages Using the Node Method

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