Equivalent Circuit: Rotating for Equality

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The discussion centers on the equivalence of two circuit diagrams after rotation, emphasizing that they are identical due to the same connections between elements. Participants highlight that examining the elements connected to specific nodes, such as node a and node b, reveals their equivalence. The conclusion is that the circuits maintain the same functionality regardless of their orientation. Some participants suggest that combining resistors to demonstrate equivalence is unnecessary, reinforcing the idea that the connections alone suffice to prove the circuits are the same. Ultimately, the focus is on the importance of node connections in determining circuit equivalence.
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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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