3 resistors in parallel: how to get there

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Discussion Overview

The discussion revolves around understanding the equivalent resistance of a circuit with three resistors, specifically how to interpret their configuration as being in parallel. Participants explore the reasoning behind this classification and clarify the relationships between the resistors in the circuit.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about how the circuit with three resistors can be considered equivalent to a parallel configuration, despite their professor's explanation.
  • Another participant suggests re-drawing the circuit to clarify the arrangement of the resistors, indicating that R1 and R2 are in parallel, and questions the placement of R3.
  • A subsequent reply elaborates on the relationships between the resistors, suggesting that R1 and R2, R2 and R3, and R1 and R3 can all be viewed as being in parallel under certain interpretations.
  • Further clarification is provided by another participant, who encourages visualizing the circuit differently to understand how the resistors are connected.
  • A later post indicates that the original poster has gained clarity on the problem after the discussion.
  • One participant notes that this type of circuit problem is commonly encountered in educational contexts to test understanding of series and parallel resistor configurations.

Areas of Agreement / Disagreement

Participants generally agree on the parallel nature of the resistors, but there is some confusion regarding the explanation and visualization of the circuit. The discussion includes multiple interpretations of how to approach the problem, indicating that some uncertainty remains.

Contextual Notes

The discussion reflects limitations in the initial understanding of circuit configurations and the need for visual aids to clarify relationships between components. There are unresolved aspects regarding the exact nature of the connections and the implications of short circuits in the circuit layout.

Granger
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Homework Statement


2. Homework Equations [/B]

Hi! So I was given the following circuit with R=15k

ATTACH]
Ypbs6Ki.png


I was asked to calculate the equivalent resistance between A and B.

The Attempt at a Solution


[/B]
According to my professor this circuit is equivalent to a circuit with three resistors in parallel, so the resistance is the parallel of the 3 resistances R (= 5k).

However I don't understand how it is equivalent.

My professor explanation was that no matter what pad we choose for a current it will pass only through a resistor (which I totally understand why!). However I don't see how that means mathematically that they are in parallel. Can someone help me clarify it?.

Thanks!
 
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The easiest way for me on this problem is to re-draw the circuit. Start with A at the top and B at the bottom, and label the resistors in the original figure R1, R2, R3 from left-to-right. Then you can see that R1 and R2 are in parallel going from A at the top to B at the bottom. Do you now see where R3 goes?
 
berkeman said:
The easiest way for me on this problem is to re-draw the circuit. Start with A at the top and B at the bottom, and label the resistors in the original figure R1, R2, R3 from left-to-right. Then you can see that R1 and R2 are in parallel going from A at the top to B at the bottom. Do you now see where R3 goes?

Starting with A we go through R1 and then the circuit parts into R2 and a short circuit (so R1 and R2 are in parallel). After that we have B and R3 (so R1 and R3 are in parallel). Then after R2, we have the same situation (R2 and R3 in parallel).

So if R1 and R2 are in parallel, R2 and R3 and then R1 and R3 then the 3 resistors are in parallel?
 
Granger said:
So if R1 and R2 are in parallel, R2 and R3 and then R1 and R3 then the 3 resistors are in parallel?
Yes, but I didn't follow your description, sorry. Start by "pulling" A up to the top of the circuit, which pulls the left of R1 up and the right end of R2 up toward A. Do you see how you can do this because those two ends of R1 and R2 are shorted together by the wire? Then do similar things rotating the rest of the circuit...
 
berkeman said:
Yes, but I didn't follow your description, sorry. Start by "pulling" A up to the top of the circuit, which pulls the left of R1 up and the right end of R2 up toward A. Do you see how you can do this because those two ends of R1 and R2 are shorted together by the wire? Then do similar things rotating the rest of the circuit...

Oh I finally got it! Thank you very much !
 
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Just FYI, that circuit has appeared here on PF numerous times. It is a standard problem to make sure students really understand series/parallel concepts and that they can redraw a circuit to make things more clear.
 

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