Simple Nodal Analysis Problem Solution and Explanation

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SUMMARY

The discussion focuses on solving a nodal analysis problem using Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL). The user initially struggles with the relationship between voltages V2 and V3, questioning if they are equal due to being in parallel. The solution clarifies that V3 is indeed V2 and emphasizes the importance of simplifying the analysis by using a single voltage variable for the supernode. The correct approach involves recognizing that the potential difference across the 4-ohm resistor is V1 - 21 volts.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Understanding of Kirchhoff's Current Law (KCL)
  • Familiarity with nodal analysis techniques
  • Basic knowledge of electrical circuit components (resistors, voltage sources)
NEXT STEPS
  • Study advanced nodal analysis techniques in electrical engineering
  • Learn about supernodes and their applications in circuit analysis
  • Explore the implications of parallel and series resistor configurations
  • Practice solving circuit problems using KVL and KCL with various configurations
USEFUL FOR

Electrical engineering students, circuit designers, and anyone looking to enhance their skills in circuit analysis and problem-solving using KVL and KCL.

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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