Finding Node Voltages Using the Node Method

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Discussion Overview

The discussion revolves around finding node voltages in a circuit using the node method, focusing on the participant's approach to applying Kirchhoff's Current Law (KCL) and handling currents and voltages in the equations. The context is primarily homework-related, with participants exploring their reasoning and problem-solving strategies.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • The participant has labeled their ground node and unknown voltages, presenting equations based on their understanding of the node method.
  • There is uncertainty about the treatment of currents in relation to resistors, with the participant questioning whether to use voltage differences or just the current itself in their equations.
  • One participant suggests that using voltage multiplied by current is inappropriate for KCL expressions, indicating a need for clarity in the application of Ohm's Law in this context.
  • Another participant expresses that articulating their thought process in writing helps them clarify their logic and assumptions.

Areas of Agreement / Disagreement

Participants appear to agree on the importance of correctly applying KCL and the role of currents in the node method, but there is no consensus on the specific approach to handling the equations or the treatment of currents and voltages.

Contextual Notes

The discussion reflects limitations in the participant's understanding of the relationship between voltage and current in the context of KCL, as well as potential dependencies on specific circuit configurations not fully explored in the examples referenced.

erok81
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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 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

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erok81 said:
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. :)
 
erok81 said:
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. :smile:
 

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