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

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SUMMARY

The discussion centers on solving a node equation in a circuits problem, specifically the equation 6 - Vo/2 - Io/4 - Vo/8 = 0. The user initially struggles with the equation but receives guidance on applying Ohm's Law, leading to the realization that Io = Vo/(2 Ω) provides a second equation. The user ultimately corrects their approach to the equation, confirming that the term Io/4 should indeed be represented as Vo/8, which clarifies their calculations.

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  • Understanding of Kirchhoff's Current Law (KCL)
  • Familiarity with Ohm's Law
  • Basic knowledge of circuit analysis techniques
  • Ability to manipulate algebraic equations
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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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