Are the resistors in series vs in parallel?

[bryyo357]

Homework Statement

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?

Homework Equations

R_Series = R₁ + R₂ + ...
R_Parallel = (1/R₁ + 1/R₂ + ...)^-1

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?

 

[phinds]

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.

 

[bryyo357]

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.

Perhaps I'm not visualizing it correctly? This is how I interpret the set up of the problem which would be series...

 

[phinds]

Perhaps I'm not visualizing it correctly? This is how I interpret the set up of the problem which would be series...

View attachment 108983

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?

 

[bryyo357]

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?

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.

 

[davenn]

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.

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

look at these 2 ...

can you see any difference electrically in the way they are connected ?now what about this version ...

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

 

[bryyo357]

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

look at these 2 ...

View attachment 108985

View attachment 108986

can you see any difference electrically in the way they are connected ?now what about this version ...

View attachment 108987

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

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)?

 

[davenn]

So are you saying that in electrical circuits "side by side" always conveys the 3rd picture you posted (which is obviously in parallel)?

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 ...

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

 

[phinds]

So then the only problem is semantics.

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.

 

[CWatters]

Perhaps I'm not visualizing it correctly? This is how I interpret the set up of the problem which would be series...

View attachment 108983

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.

 

[jbriggs444]

Perhaps I'm not visualizing it correctly? This is how I interpret the set up of the problem which would be series...

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.

 

[bryyo357]

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.

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.