Simplifying Circuit Diagrams: Understanding Topology and Resistor Placement

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The discussion centers on simplifying circuit diagrams for MCAT preparation, specifically regarding the arrangement of resistors and wiring. Participants clarify that as long as the connections at nodes remain unchanged, the circuit's topology is preserved, allowing for flexibility in wire placement. Concerns about altering series and parallel configurations are addressed, confirming that moving wires does not affect the circuit as long as resistors are not repositioned. The importance of understanding topology in circuit simplification is emphasized, noting that this principle applies primarily to DC circuits. Overall, the conversation reinforces the idea that wire movement is permissible without altering circuit functionality.
johnj7
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Homework Statement


This is not a homework problem, but I'm studying for the mcat, and had some trouble figuring out how to simplify a circuit. Could someone look at the attached picture pdf? (the diagram is painless, i promise) Are the circuits I have drawn the same?

Thank you!
 

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It may take awhile to get your attachment approved. I would suggest uploading the diagram to a photobucket account (or something of the sort), and posting the link.
 
johnj7 said:

Homework Statement


This is not a homework problem, but I'm studying for the mcat, and had some trouble figuring out how to simplify a circuit. Could someone look at the attached picture pdf? (the diagram is painless, i promise) Are the circuits I have drawn the same?

Thank you!

All the resistors with values are connected to the same node in your drawing. Why wouldn't they be the same?
 
hmm, well i just thought it was a bit confusing, i didn't know you could move wires around like that, because maybe that would change which resistors are in series or in parallel. but i guess that's not true at all.

so bottom line is, you can move the wires however you like as long as its just wire and no resistors are moved/replaced?
 
johnj7 said:
hmm, well i just thought it was a bit confusing, i didn't know you could move wires around like that, because maybe that would change which resistors are in series or in parallel. but i guess that's not true at all.

so bottom line is, you can move the wires however you like as long as its just wire and no resistors are moved/replaced?

The key is topology as to which components are connected to which nodes. If you change that - you changed the circuit. But so long as the terminals are connected together at any node ... it really doesn't matter. (In high speed digital circuit layouts, it might for different reasons, like speed and noise. But for these kinds of DC circuits not.)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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