How Do I Solve This Node Equation in a Circuits Problem?

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Discussion Overview

The discussion revolves around solving a node equation in a circuits problem, specifically focusing on the application of Kirchhoff's Current Law (KCL) and Ohm's Law. Participants are attempting to derive the correct equation for a node involving voltage and current relationships in a circuit.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents the initial node equation: 6 - Vo/2 - Io/4 - Vo/8 = 0, expressing confusion about how to proceed.
  • Another participant suggests using Ohm's Law to express Io in terms of Vo, proposing the equation i0 = v0/(2 Ω) as a second equation to solve for the unknowns.
  • A participant revisits their calculations, stating they derived 6 - Vo/2 - Vo/4 - Vo/8 = 0 and multiplied through by 8, leading to an incorrect result of Vo = 6.85V. They question whether the direction of current across the 8 ohm resistor affects the equation.
  • A later reply points out an error in the participant's equation, clarifying that the term should be v0/8 instead of the incorrectly stated term, and explains the derivation of that term from the earlier equation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to the problem, as there are differing interpretations of the node equation and the direction of current flow across the resistors. The discussion remains unresolved regarding the correct assumptions and calculations.

Contextual Notes

Some limitations include potential misunderstandings of the current direction across the 8 ohm resistor and the implications of those assumptions on the node equation. There are also unresolved mathematical steps in the participants' calculations.

Would
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Homework Statement


practiceprob.jpg



Homework Equations


I am trying to do some self study here before I take my circuits course. I am stuck on this problem for some reason.. The equation I am coming up with for the node is : 6 - Vo/2 - Io/4 - Vo/8 = 0.. After getting at equation I can't seem to come to the answer. Do I need to do another equation here? Thanks


The Attempt at a Solution

 
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Welcome to PF Would!

Would said:

Homework Statement


practiceprob.jpg



Homework Equations


I am trying to do some self study here before I take my circuits course. I am stuck on this problem for some reason.. The equation I am coming up with for the node is : 6 - Vo/2 - Io/4 - Vo/8 = 0.. After getting at equation I can't seem to come to the answer. Do I need to do another equation here? Thanks


The Attempt at a Solution


Ohm's law for the 2 ohm resistor tells you that i0 = v0/(2 Ω). That's your second equation. Now you have everything in terms of only one unknown, and you can therefore solve the system.
 
Thanks a lot for the help! I must be doing some simple math wrong here.. but I am getting : 6 - Vo/2 - Vo/4 - Vo/8 = 0 then multiplying all of that by 8 to get 48- 4Vo - 2Vo - Vo = 0 then ultimately getting Vo = 6.85V but that is wrong... What am I doing wrong there? Should I be assuming that the current in across the 8 ohm resistor is moving upward and therefore making the equation 48 - 4Vo - 2Vo + Vo = 0? It works out that way but if it is like that could you tell me why? Since it is not marked i assumed it was a voltage drop across the 8 ohm resistor..
 
Would said:
Thanks a lot for the help! I must be doing some simple math wrong here.. but I am getting : 6 - Vo/2 - Vo/4 - Vo/8 = 0 then multiplying all of that by 8 to get 48- 4Vo - 2Vo - Vo = 0 then ultimately getting Vo = 6.85V but that is wrong... What am I doing wrong there? Should I be assuming that the current in across the 8 ohm resistor is moving upward and therefore making the equation 48 - 4Vo - 2Vo + Vo = 0? It works out that way but if it is like that could you tell me why? Since it is not marked i assumed it was a voltage drop across the 8 ohm resistor..

The third term in your equation is simply wrong. In your original KCL equation, this term was i0/4, which was correct. Then we determined that i0 = v0/2. Hence, i0/4 = (v0/2)/4 = v0/8. The third term (in red) should therefore be v0/8.
 
Wow I feel stupid after looking back at that. Thank you for the help.
 

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