Find v in electric circuit (nodal analysis, superposition)

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Discussion Overview

The discussion revolves around finding the voltage across a 5 Ohm resistor in a given electric circuit using techniques such as nodal analysis and superposition. Participants explore various methods to approach the problem, including circuit simplifications and the application of fundamental circuit laws.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant expresses uncertainty about starting the problem and questions the feasibility of converting a current source into a voltage source due to the presence of a node between two resistors.
  • Another participant suggests replacing the 9 volt source with a short circuit to simplify the circuit by combining the 20 and 15 Ohm resistors into an equivalent resistance, and then calculating the voltage across the equivalent resistors.
  • A subsequent reply raises a concern about the contribution of the voltage source once it is reintroduced into the circuit analysis.
  • Another participant clarifies that the superposition principle involves calculating the contributions from each source separately: first with the voltage source shorted and then with the current source open-circuited.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to solve the problem, as there are multiple methods proposed and some uncertainty expressed regarding the contributions of the sources in the circuit.

Contextual Notes

Participants discuss various assumptions related to circuit simplifications and the application of superposition, but specific limitations or dependencies on definitions are not fully explored.

Who May Find This Useful

This discussion may be useful for students or individuals learning about circuit analysis techniques, particularly those interested in applying superposition and nodal analysis in electrical engineering contexts.

The_Lobster
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Homework Statement


Find the voltage v across the 5 Ohm resistor as shown in the attached drawing.


Homework Equations


Ohm's law, V=IR


The Attempt at a Solution


I have done plenty of these using different techniques, superposition/source transformation, nodal or mesh analysis, etc. But what puts me off with this one is that I don't really see where I should start. Am I right that I cannot turn the current source on the left into a voltage source because the two resistors in parallel have a node in between them?

What I have done so far is to devise two equations for the current in the two loops two the right of the drawing, disconnecting the current source (superposition), and I get: (I_1 = upper mesh)
Upper mesh:
0 = -9V + 35 I_1
Lower mesh:
0 = 9V + 15I_2

If I know put the current source back in place, and remove the voltage source, how would I then proceed to find the current through the 5 ohm resistor from th ecurrent source?
 

Attachments

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Replace the 9 volt source with a short; then the 20 and 15 ohm resistors will be in parallel and can be replaced with their equivalent. The 10 and 5 ohm resistors are similarly in parallel and can be replaced with a single equivalent. Solve that circuit for the voltage across the equivalent resistors. Now backtrack; you know the voltage across each parallel combination, and you can easily calculate the current in each resistor that makes up the combinations because you know the voltage across them.
 
Thank you!

But what about the contribution from the voltage source once we put that back?
 
This is superposition.

You calculate the contribution from the current source with the voltage source shorted, and add that to the contribution from the voltage source with the current source open circuited.
 

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