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Are the resistors in series vs in parallel?

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  1. Nov 15, 2016 #1
    1. The problem statement, all variables and given/known data
    A metal wire of resistance R is cut into two pieces of equal length. The two pieces are connected together side by side. What is the resistance of the two connected wires?

    2. Relevant equations
    RSeries = R1 + R2 + ...
    RParallel = (1/R1 + 1/R2 + ...)-1

    3. The attempt at a solution
    Initially I thought that, being connected side by side, the same current would be passing through both halves of the wire thus making them resistors in series. However, the answer turns out to be R/4 as a because they are apparently in parallel. Can someone explain how we know?
     
  2. jcsd
  3. Nov 15, 2016 #2

    phinds

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    Uh ... we know because that's the DEFINITION of parallel (which you seem to have backwards)? Seems like you need to go back to the basics and get solid on what's serial and what's parallel.
     
  4. Nov 15, 2016 #3
    Perhaps I'm not visualizing it correctly? This is how I interpret the set up of the problem which would be series...

    Capture.JPG
     
  5. Nov 15, 2016 #4

    phinds

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    Does that look like "side by side" to you? If one person is standing on another person's head, would you say they are side by side?
     
  6. Nov 15, 2016 #5
    So then the only problem is semantics. If you view the wires from behind (so that you are looking at their length and the exact point that they are connected) then yes, that does look like "side by side". If you are behind two people walking shoulder-to-shoulder you would say they are side by side, which is exactly how I visualized this wire. But if I was supposed to "see" the wire from the end of the wire (just as you would "see" the profile of people walking shoulder-to-should) then I can understand how this wouldn't be side by side.
     
  7. Nov 15, 2016 #6

    davenn

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    No, it isn't semantics, you are visualising incorrectly

    look at these 2 ....

    Capture.JPG

    Capture1.JPG

    can you see any difference electrically in the way they are connected ?


    now what about this version .....

    Capture2.JPG

    what can you tell me about the difference compared to the first 2 variations ?

    which resistors are connected in series and which are connected in parallel ?



    Dave
     
  8. Nov 15, 2016 #7
    There isn't a difference between how the first two are connected, no. But that's my point is that if you rotate the second picture you get the first one and that can be phrased as side by side (at least with general objects). So are you saying that in electrical circuits "side by side" always conveys the 3rd picture you posted (which is obviously in parallel)?
     
  9. Nov 15, 2016 #8

    davenn

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    if the 2 ends of the components ... those resistors, or capacitors etc ... BOTH share a common connection
    we call this a node. then they are in parallel
    you can see that the top 2 images the side by side or one above the other is ONLY a drawing depiction of 2 resistors in series

    they could be drawn as ......

    Capture3.JPG

    but since they share only a SINGLE common node, they are still in series



    D
     
  10. Nov 16, 2016 #9

    phinds

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    You can use whatever definition of words you like in your presonal life but not in science and if you expect other people to understand what you are talking about, you need to use common terminonology. I GUARANTEE you that if you ask any electrical engineer to interpret your problem statement, you will get exactly the same results as from me.
     
  11. Nov 16, 2016 #10

    CWatters

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    Forget about the resistance for a moment. Just think about the wire as a physical bit of metal...

    If you cut a wire in two and then rejoin the two parts back together like that then nothing has actually changed.
     
  12. Nov 16, 2016 #11

    jbriggs444

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    This seems to be a problem with ordinary English. "side by side" is properly interpreted to mean that the flat sides of the wires are next to one another. The alternative would have been called "end to end".

    In context, "side" was intended to denote the side of the wire as opposed to its end. It was not intended to denote right or left on workbench where the wires are placed. One can know that this is the intended meaning because it is the only meaning that makes the phrase convey a useful meaning.
     
  13. Nov 21, 2016 #12
    I realize this, and clearly you didn't understand what my problem was. My initial initial interpretation of "side by side" was flawed hence why I did not understand the problem--I get that now. That's the whole reason I posted my question. It would be a lot more constructive to simply inform me that the standard is to read "side by side" in this way rather than give rhetorical and condescending replies to an obvious homework help question from a student trying to learn.
     
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