Finding Node Voltages Using the Node Method

[erok81]

Homework Statement

Find the node voltages for the circuit shown.

Homework Equations

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 e_n.

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?

 

[gneill]

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!

 

[erok81]

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]

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.

 

[DeeNos]

I would suggest that you carefully review your equations and make sure they accurately represent the circuit shown. It is important to consider all components and their relationships in the circuit when using the node method. Additionally, ensure that you are using the correct units for each quantity (e.g. voltage in volts, resistance in ohms). It may also be helpful to draw a diagram of the circuit and label all components and nodes to visualize the problem more clearly. Keep in mind that the node method is a systematic approach and it may be helpful to break down the circuit into smaller sections to make the calculations more manageable. Once you have double-checked your equations and have a clear understanding of the circuit, you should be able to solve for the node voltages using the node method. Good luck!