Having trouble with some review circuits using nodal analysis

In summary, the conversation discusses a problem with review circuits using nodal analysis. The individual is trying to find node voltages for v1, v2, and v3, with a given current of 3.1A. They provide their method for solving the problem and have derived three equations with three unknown variables. They ask for reassurance on their answers and mention other possible methods for solving the problem. Ultimately, they verify their answers with a more precise solution given by another individual.
  • #1
mitchapalooza
2
0
Having trouble with some review circuits using nodal analysis :(

Homework Statement


I'm trying to find node voltages for v1, v2, and v3.
I = 3.1A

Homework Equations


V=IR


The Attempt at a Solution


My method of going about and solving this was fairly straight forward I thought. The way the question is set up, I believe nodal analysis is already ready to go. So I started with
KCL(v1): 2 + 3.1 + (v1-v2)/3Ω = 0
KCL(v2): (v2-v1)/3 + v2/2 + (v2-v3)/4 = 0
KCL(v3): (v3-v2)/4 + v3/3 - 3.1 = 0

Now it's been a while since I've done this (nodal analysis), but I now have 3 eqns and 3 unknown variables. The answer I have is -21.2V -5.87V and 2.8V respectively.

It's one of those, "I've tried all my guesses, need some reassurance before I commit to my last chance" scenarios.

Any helpful on this would be great! Thanks :D

Note that I haven't tried the brute force method of just solving for everything, or the mesh current method.
 

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  • #2


Hi mitchapalooza, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

mitchapalooza said:
The answer I have is -21.2V -5.87V and 2.8V respectively.
Have you substituted those back into the equations to verify they are the solution? The equations look right.
 
Last edited by a moderator:
  • #3


Have they taught you the superposition theorem? That way you could handle the problem one current source at a time ...
 
  • #4


I solved the system and found v1 = -20.78V, v2 = -5.78V and v3 = 2.67V
 
  • #5


I got
V1 = - 21.17
V2 = -5.87
V3= +2.80
so we're close.
 
  • #6


Well, I got:
V1 = -127/6
V2 = -88/15
V3 = 14/5

which is the exact solution. :cool:

The 12 digit floating point approximation would be:

V1 = -21.1666666667
V2 = -5.86666666667
V3 = 2.80000000000
 

1. What is nodal analysis and how is it used in circuit analysis?

Nodal analysis is a method used in circuit analysis to determine the voltage and current at each node (junction point) in a circuit. It involves writing Kirchhoff's Current Law (KCL) equations at each node and solving for the unknown variables using simultaneous equations. This method is useful for analyzing more complex circuits with multiple voltage sources and resistors.

2. Why am I having trouble with nodal analysis in circuit reviews?

Nodal analysis can be challenging for beginners because it requires a good understanding of KCL and how to write and solve simultaneous equations. It also requires a thorough understanding of circuit theory and the ability to visualize and analyze complex circuits. Practicing and reviewing fundamental concepts can help improve your understanding and ability to apply nodal analysis in circuit reviews.

3. What are some common mistakes to avoid when using nodal analysis?

Some common mistakes to avoid when using nodal analysis include not properly labeling nodes, incorrectly applying KCL equations, and making errors in solving simultaneous equations. It is important to double-check your work and make sure all equations are properly set up and solved accurately.

4. Can nodal analysis be used for all types of circuits?

Nodal analysis can be used for most circuits, but it is most effective for circuits with multiple voltage sources and resistors. It may not be the most efficient method for simpler circuits with only one voltage source and a few resistors. In these cases, other methods such as Ohm's Law or Kirchhoff's Voltage Law may be more appropriate.

5. Are there any tips for improving my nodal analysis skills?

Practicing and reviewing fundamental circuit theory concepts is key to improving your nodal analysis skills. It may also be helpful to break down complex circuits into smaller sections and analyze each section individually before combining them. Additionally, using software or online tools to simulate and analyze circuits can also be useful in developing your nodal analysis skills.

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