# Finding Node Voltages Using the Node Method

## Homework Statement

Find the node voltages for the circuit shown.

See attachment.

## 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?

#### Attachments

• circuit.png
3.6 KB · Views: 358

## Answers and Replies

gneill
Mentor
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?

Yup. Much better. Voltage x current yields power, not a current, so is quite unsuitable for a KCL expression!

Perfect! Thanks for the help.

It seems half the time I post problems, I get them mostly figured out just typing the post up. :)

gneill
Mentor
It seems half the time I post problems, I get them mostly figured out just typing the post up. :)

Yup. Typing it out so that it make sense to someone else can often help one re-evaluate one's logic and assumptions. 