Equivalent Circuit: Rotating for Equality

  • Context: Undergrad 
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    Circuit Equivalent
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Discussion Overview

The discussion revolves around the equivalence of two electrical circuits after a rotation, exploring the reasons behind their identical nature. Participants examine the connections between circuit elements and nodes, focusing on the implications of circuit representation and simplification.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks for clarification on why two circuits are considered identical after rotation, referencing a textbook statement.
  • Another participant asserts the truth of the equivalence by pointing out the connections at each node.
  • A third participant elaborates that the circuits are equivalent due to the same connections between the same elements at nodes a and b, regardless of their visual representation.
  • One participant suggests combining all resistors to demonstrate equivalence, while another agrees but notes that this approach may be unnecessary given previous explanations.

Areas of Agreement / Disagreement

Participants generally agree on the equivalence of the circuits based on their connections, though there is some debate about the necessity of combining resistors to prove this point.

Contextual Notes

Some assumptions about the definitions of equivalence and circuit representation may not be explicitly stated, and the discussion does not resolve whether visual representation impacts understanding.

darksyesider
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In my textbook, the text says that the following two circuits are identical after rotating it…can someone explain why this is true?
 

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Obviously, it' true, just look at what's connected to each node.
 
The circuits are equivalent because they have the same connections between the same elements. In each diagram look at the circuit elements connected to node a, and in each diagram look at the circuit elements connected to node b. In both cases the same elements have the same connections so the circuits are the same regardless of how they are drawn.
 
Combine all the resistors and you'll see that they are the same
 
HomogenousCow said:
Combine all the resistors and you'll see that they are the same

Yes, that would work, but it is a completely unnecessary effort. Reread posts 2 and 3.
 

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