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

In summary, the conversation revolves around a person seeking help with a problem in their self-study of circuits. After getting an equation for the node, they are having trouble solving it and ask for assistance. Another person suggests using Ohm's law for the 2 ohm resistor to get a second equation in terms of only one unknown. The original person realizes their mistake in the equation and thanks the other person for their help.
  • #1
Would
4
0

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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  • #2
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.
 
  • #3
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..
 
  • #4
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.
 
  • #5
Wow I feel stupid after looking back at that. Thank you for the help.
 

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

1. What is a "Stuck on Circuits" problem?

A "Stuck on Circuits" problem refers to a situation where a circuit is unable to function properly due to a specific component being stuck in a certain state. This can happen when a component, such as a transistor or relay, fails to switch between its ON and OFF states, causing the entire circuit to malfunction.

2. What causes a "Stuck on Circuits" problem?

A "Stuck on Circuits" problem can be caused by a variety of factors, such as a damaged or faulty component, a short circuit, or incorrect wiring. It can also occur due to environmental factors, such as high temperatures or excessive moisture.

3. How can I troubleshoot a "Stuck on Circuits" problem?

The first step in troubleshooting a "Stuck on Circuits" problem is to carefully inspect the circuit for any obvious damage or loose connections. Next, check the individual components for any signs of damage or malfunction. If the problem persists, it may be necessary to use a multimeter or other testing equipment to further diagnose the issue.

4. Can a "Stuck on Circuits" problem be fixed?

Yes, in most cases, a "Stuck on Circuits" problem can be fixed by identifying and replacing the faulty component or correcting any wiring issues. However, if the damage is extensive or the circuit is highly complex, it may be more cost-effective to replace the entire circuit.

5. How can I prevent "Stuck on Circuits" problems in the future?

To prevent "Stuck on Circuits" problems, it is important to properly design and build the circuit using high-quality components. Regular maintenance and inspections can also help to identify any potential issues before they become major problems. It is also important to follow safety protocols and handle circuits with care to avoid any accidental damage that could lead to a "Stuck on Circuits" problem.

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