How Do I Correctly Apply Nodal Analysis in This Circuit Problem?

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Discussion Overview

The discussion revolves around the application of nodal analysis to a circuit problem presented in a homework assignment. Participants explore the setup of equations based on a circuit diagram, addressing challenges in understanding the method and the implications of current directions.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant expresses difficulty in understanding the textbook and attempts to set up nodal equations but is unsure about the correct approach.
  • Another participant suggests labeling the circuit with assumed current directions to clarify the setup of equations for each node.
  • Subsequent posts include attempts to formulate equations based on the circuit, with some participants expressing uncertainty about their correctness.
  • There is a discussion about how to account for the fixed potential of the battery in the equations, with emphasis on the importance of consistent current direction assumptions.
  • One participant notes that the direction of currents can be guessed based on the source's position, but consistency in the equations is more critical than the assumed directions.

Areas of Agreement / Disagreement

Participants generally agree on the need to set up equations based on current directions and the fixed potential from the battery. However, there is no consensus on the correctness of the specific equations being proposed, and uncertainty remains regarding the application of nodal analysis.

Contextual Notes

Some participants mention confusion regarding the setup of equations and the interpretation of current directions, indicating a potential lack of clarity in the underlying assumptions or definitions used in nodal analysis.

Who May Find This Useful

This discussion may be useful for students learning about nodal analysis in circuit theory, particularly those struggling with the application of the method in homework problems.

pat666
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Homework Statement



See attached picture.

Homework Equations


The Attempt at a Solution



I really suck at this and am having trouble understanding the textbook we have. here's my attempt:

I'm calling node 1 v1 and 2 v2.
so
0=(v1-v2)/4k7+v1/10k+(v2-v1)/1k
0=(v2-v1)/1k+v2/470+v2/1

I know I have to do something with the 10V but I'm not sure what?? I've been trying questions with current sources and can sometimes get the answer right with them after ages of playing...

I can solve this equation easily but I'm sure that the setup is wrong. I really need help with this, I know its supposed to be easy but something hasn't clicked and I don't understand these questions yet.

Thanks for any help
 

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You might find things to be a bit clearer if you were to label the circuit diagram with some assumed current directions (see attached figure). Then when you write the equation for a given node, you take the voltage difference across the components according to the assumed current directions (current flows from + to -).

The battery fixes the potential at the left end of R1. Treat that point as if it were a neighboring node to NODE 1, but a node that you don't need to write separate equations for (since it already has a completely specified voltage as fixed by the battery).
 

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So
0=10/4k7-(v1)/10k-(v2-v1)/1k
0=(v2-v1)/1k-v2/470-v2/1k

Just a guess, I'm still having trouble understanding what I should be doing.

Thanks
 
Using the assumed currents, you can see that the potential difference across R1 would be 10V - V1. So the current entering NODE 1 through R1 would be (10V - V1)/R1.

Similarly, the potential difference across R3 is V1 - 0V (0V because the bottom end of R3 is the "ground" node, which is always assumed to be at 0V potential). So the current leaving NODE 1 via R3 is V1/R3.

The current leaving NODE 1 via R2 is (V1 - V2)/R2.

Sum them up and set equal to zero for the equation for NODE 1. Then do the same for NODE 2.
 
0=(10-V1)/R1-V1/10K-(V1 - V2)/R2
0=(V1 - V2)/R2-V2/470-V2/1k
?
If that is right (?) would you mind telling me how to find the current directions?

Thanks for your help!
 
pat666 said:
0=(10-V1)/R1-V1/10K-(V1 - V2)/R2
0=(V1 - V2)/R2-V2/470-V2/1k
?
If that is right (?) would you mind telling me how to find the current directions?

Thanks for your help!

That looks fine.

You can usually make an educated guess about the current directions based upon the values and positions of the sources. In this case, the only source is the 10V supply, so it should have the highest potential in the circuit, and everything should "go downhill" from there.

HOWEVER! It doesn't really matter what directions you assume for the currents! As long as you are consistent about using them as you write the equations, the math will take of everything and you'll arrive at the same results.
 
Thanks for your help.
 

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