Simple Nodal Analysis Problem Solution and Explanation

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Discussion Overview

The discussion revolves around a nodal analysis problem related to an electrical circuit involving resistors and a voltage source. Participants are attempting to solve the problem using Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL), focusing on the relationships between voltages and currents at various nodes in the circuit.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses uncertainty about whether V3 equals V2 due to their parallel arrangement and questions the interpretation of the current from the voltage source.
  • Another participant suggests simplifying the analysis by using a single voltage variable instead of multiple variables for the nodes.
  • A later reply confirms that V3 is indeed V2, suggesting that they represent the same node and emphasizes the need to express the current through the 4Ω resistor in terms of the voltage across it.
  • One participant acknowledges the clarification regarding the potential difference across the 4Ω resistor, indicating that this information was helpful for their understanding.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between V3 and V2, but there remains some uncertainty regarding the correct application of KCL and the interpretation of the circuit elements. The discussion does not reach a consensus on the overall solution to the problem.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in the nodal analysis, and there are assumptions about the circuit configuration that may affect the analysis.

Magnawolf
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Homework Statement



cDpzcYo.png


Homework Equations



KVL and KCL

The Attempt at a Solution



Let V = V1 and the Voltage across the 2 ohm resistor be V2 just for reference.

Step 1: KCL @ Supernode: V1/3 + V2/2 + 21/4 + V3/6 = 0

I think my problem is here somewhere. Does V3 = V2 because they're in parallel? Also, am I wrong to say that 21/4 is a current going out of the supernode?

Step 2: V2-V1 = 9 (pretty sure this is right)

I can't get the correct answer. Any help is appreciated.
 
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Magnawolf said:

Homework Statement



cDpzcYo.png


Homework Equations



KVL and KCL

The Attempt at a Solution



Let V = V1 and the Voltage across the 2 ohm resistor be V2 just for reference.

Step 1: KCL @ Supernode: V1/3 + V2/2 + 21/4 + V3/6 = 0

I think my problem is here somewhere. Does V3 = V2 because they're in parallel? Also, am I wrong to say that 21/4 is a current going out of the supernode?

Step 2: V2-V1 = 9 (pretty sure this is right)

I can't get the correct answer. Any help is appreciated.

The 2 and 6 Ohm resistors are in parallel so they must share the same potential difference. If V1 is the potential at the top of the 3 Ohm resistor then the potential difference across the 4 Ohm resistor must be V1 - 21.

If you make a supernode of the nodes either side of the 9 V source, then really you need only one voltage variable to write the equation. Suppose you chose v to be that variable (after all it's already specified in the circuit diagram). Then on one side of the source the potential is v and on the other side it's v+9. No need to introduce V2 or V3 etc.
 
Hi. Your V3 is V2, it's the one and the same node. Keep it as just V2.

The current through the 4Ω is given by (voltage across the 4Ω resistor itself) / 4

So what is the voltage across that 4 ohm resistor? Hint: the expression will involve a subtraction
 
gneill said:
If V1 is the potential at the top of the 3 Ohm resistor then the potential difference across the 4 Ohm resistor must be V1 - 21.
This. This is what I needed. Thanks so much!
 

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