Equivalent capacitance, circular arrangement

AI Thread Summary
The discussion focuses on determining the equivalent capacitance between two nodes, A and B, in a circuit with capacitors arranged in a circular layout. Participants clarify that while some capacitors may appear to be in series or parallel, the arrangement's topology is what matters for calculating equivalent capacitance. The conversation emphasizes that visualizing the circuit correctly, regardless of its orientation, is crucial for understanding the connections and solving the problem. Additionally, it is noted that labeling terminals does not require applying voltage; they serve primarily as reference points for analysis. Ultimately, the goal is to simplify the circuit into an equivalent representation for easier calculations.
gracy
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Mentor's note: Post moved to new thread since it's a new problem.

One more problem

Homework Statement


CAJ.png


Find the equivalent capacitance between A and B.

Homework Equations



The Attempt at a Solution


I think all the Capacitors are in series but according to my book only three capacitors are in series.How?
 
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When the problem named and labelled the two nodes A and B between which you are to determine the capacitance, it effectively implied connection terminals for the circuit. These terminals provide a favored point of view for you to interpret the circuit.

Fig1.png
 
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How did you switch from one figure to the other,wire A and wire B seems flipped and how you decided that 2 μF location?
 
Your original figure is just rotated to bring the terminal leads horizontal. The two circuits are mirrored about the center where the arrow is. Follow outwards from the center and confirm that you find the corresponding components in the same (mirrored) locations.
 
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gneill said:
The two circuits are mirrored about the center where the arrow is
When it is mirrored, left would come in right one's place and right would go in left one's place.Similarly, the vertical flip would occur, right?
 
gneill said:
Follow outwards from the center and confirm that you find the corresponding components in the same (mirrored) locations.
Sorry, I did not understand.
 
gracy said:
When it is mirrored, left would come in right one's place and right would go in left one's place.Similarly, the vertical flip would occur, right?

That's not important ... the point is the circular and square arrangements are the same circuit layouts
and it is now easier to visualise and to solve the problem

so now have a go at solving the total capacitance value between points A and BDave
 
Mirrors reverse front to back, not top to bottom. Otherwise you'd be looking at your feet in the mirror rather than your eyes :smile:

Surely you can see the symmetry between the two circuits? Confirm that all the components of both circuits make the same connections to each other.
 
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Gracy if you don't mind, from yr many questions I have got the impression you are working hard and putting pressure on yourself but it feels like you have your eyes frowning four inches (10 cm) from the book. And that you need to relax, take somehow a cool distant look at these problems (and no doubt the texts of the corresponding books) and ask yourself what is this about? What does the question mean? What principles/equations do I have to use? (They are probably in the text preceding the excercise)... etc.

Questions are made for verification of understanding but not usually intended to be fiendish.

You're asked the capacitance between A and B. What is there between A and B? One way there is one capacitor, the other way there are three capacitors in series. No big deal to alternatively draw them as in #2.
 
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  • #10
If the question would have asked just equivalent capacitance of the circuit rather than the equivalent capacitance between A and B then all the capacitors would be in parallel, Right?
 
  • #11
gneill said:
Follow outwards from the center
Which center?
 
  • #12
gracy said:
If the question would have asked just equivalent capacitance of the circuit rather than the equivalent capacitance between A and B then all the capacitors would be in parallel, Right?
For the most part such a question does not make sense if it's not specified how the group of capacitors are to connected to some external circuit,

They definitely can;t be considered to all be in parallel. That would require having only two nodes, which you should know. In some sense they are all in series, if taken in isolation from any other circuit, but then equivalent capacitance makes no sense.

gracy said:
Which center?
gneill meant: from the center of the figure, outward, i.e. from a point between the two circuit diagrams.
 
  • #13
SammyS said:
In some sense they are all in series,
gracy said:
I think all the Capacitors are in series
I knew it, I don't know what happened to me as I wrote in parallel.
 
  • #14
SammyS said:
but then equivalent capacitance makes no sense.
What does equivalent capacitance mean?
 
  • #15
gracy said:
What does equivalent capacitance mean?
What do you suppose it (equivalent capacitance) means? After all, this whole thread has to do with finding the equivalent capacitance.

Does your textbook or do your notes show how the formulas for equivalent capacitance are derived for capacitors in parallel and those in series?
 
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  • #16
gracy said:
What does equivalent capacitance mean?
The original network of capacitors are connected into a circuit, or to a battery.
Equivalent capacitance between point A and B is the capacitance of the single capacitor you replace the whole network between A and B with, so as nothing changes in the voltages and charges in the external network.
 
  • #17
@gracy, have you seen real capacitiors and resistors? Such things like in the picture? I guess, you have seen batteries.

http://getmfg.com/wp-content/uploads/2014/10/rsz_eck-10pct20leanpct20electronicspct20componentspct20-960x650.jpg

You can make a network/circuit from these components by joining the terminals and connect it to a battery,
It is as making a necklace from beads. You need a thread to connect the beads and enclosures at the ends.
In A, the beads are connected in series. In B, the beads are parallel. How are the beads of different color connected in C?
Here you can see real necklaces. Can you see, where are only series and where are both series and parallel connections? http://www.fortheloveof.net/how-to-make-an-earthy-beaded-necklace/
 

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  • #18
ehild said:
How are the beads of different color connected in C?
Both series and parallel connections.
 
  • #19
gracy said:
Both series and parallel connections.
Yes!
 
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  • #20
But why gneill rotated my diagram in OP 90 degrees to the right?
 
  • #21
It does not matter. I guess, you have a necklace. Is it the same necklace if you rotate it, turn it over, make the threads differently curved, fold it? Throw it up into the air, or hold it in your hand or around your neck?

People working with electric circuits like to draw the terminal points vertically, one below the other.
 
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  • #22
gracy said:
But why gneill rotated my diagram in OP 90 degrees to the right?

Why do you care? You are obsessing on things that do not matter, and doing that is interfering with your ability to learn and understand!. All that matters is the "topology", not the shape or the orientation.
 
  • #23
And what about mirror image,is it necessary?
 
  • #24
gracy said:
And what about mirror image,is it necessary?

What do YOU think? Do you think it matters? If you do, why do you think it?
 
  • #25
Ray Vickson said:
What do YOU think? Do you think it matters? If you do, why do you think it?
I don't know.But if I'll take example of necklace,I would say No!
 
  • #26
I think the only thing that's important to do here is showing connection terminals A and B.Is converting this circular arrangement into normal circuit like arrangement necessary?
 
  • #27
gracy said:
I think the only thing that's important to do here is showing connection terminals A and B.Is converting this circular arrangement into normal circuit like arrangement necessary?
No, it is not necessary. But makes it easier to handle for those, who usually draw circuits that way.
 
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  • #28
gracy said:
I think the only thing that's important to do here is showing connection terminals A and B
Right?
 
  • #29
gracy said:
Right?
showing connections between components and connections to the terminals.
 
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  • #30
gracy said:
But why gneill rotated my diagram in OP 90 degrees to the right?

Because he thought nothing of it, because it was so obvious to him he didn't need to think about it, because he thought only of the essential of the situation which is represented by a diagram you can draw in various equivalent ways, because he is not glued to the page like a liferaft, relax, do the same yourself on occasion. :oldsmile:
 
  • #31
gracy said:
What does equivalent capacitance mean?

In a sense, nothing. If they had asked just the capacitance between A and B it would have been the same question. I.e. The total of positive charges in all the capacitors added together per unit potential difference between A and B.

But then it will often be convenient to replace in a mathematical treatment a circuit that has a part like that of the problem with one in which all those capacitors are condensed into a single capacitor, which is called an "equivalent circuit". E.g. Say some more complicated circuit contained the circuit of the problem, then you could for purposes of calculation replace that part with a single capacitor between A and B with capacitance you are caLculating here, which would be called the "equivalent capacitance".

Done practically whenever possible for purpose of simplifying problems to their essences.
 
  • #32
  • #33
gneill said:
When the problem named and labelled the two nodes A and B between which you are to determine the capacitance, it effectively implied connection terminals for the circuit.
If there is connection terminals already there then?
If 100 volts of potential difference is applied between a and b in the circuit .Find the potential difference between c and d.
OLU.png


There are terminals a and b and now we have to find potential of c and d hence we have to fix terminals in there so now should i proceed with 2 pairs of potential terminals?
 
  • #34
Terminals a and b were added because the original problem statement wanted you to consider the equivalent capacitance as viewed across the labeled nodes. The added terminals just make the situation obvious.

You have formulated a new problem where, given an applied potential difference across ab, you wish to find the resulting potential difference across nodes c and d. In this case c and d are just nodes that you don't plan on doing anything with except perhaps measure their potentials. There are no special procedures required. Labeling these nodes doesn't alter the circuit or impose any new conditions.
 
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  • #35
Should not I fix terminals at c and d?like this

ter.png
 
  • #36
gracy said:
Should not I fix terminals at c and d?like this

View attachment 92900
You can if you want to. It doesn't change the circuit operation in any way if you don't connect anything to the new terminals. Open terminals won't pass any current.
 
  • #37
What connection terminal means?
 
  • #38
gracy said:
What connection terminal means?
I think it provides a point of connection to external circuits.So there should be some supplied voltage.
 
  • #39
gracy said:
I think it provides a point of connection to external circuits.So there should be some supplied voltage.
There can be output voltage also.
 
  • #40
Gracy, have you constructed circuits and measured voltage at various places in the circuit?
 
  • #41
gneill said:
You can if you want to. It doesn't change the circuit operation in any way if you don't connect anything to the new terminals.
don't connect anything means?not even voltage source?
 
  • #42
gracy said:
I think it provides a point of connection to external circuits.So there should be some supplied voltage.
Not necessarily. You don't have to connect anything if you don't want to. Sometimes terminals are just provided for test points to make it convenient to connect test equipment like voltmeters.

Unless you connect something to a circuit it doesn't affect the circuit.

In many instances "output terminals" are drawn in order to draw your attention to where you should consider the circuit output to be. They don't affect the operation of the circuit just by being there.
 
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  • #43
gracy said:
don't connect anything means?not even voltage source?
Right.

I mean, you could connect a voltage source there or anywhere else you wanted for that matter. But then you'd be changing the circuit and creating a different problem to analyze.
 
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  • #44
gneill said:
When the problem named and labelled the two nodes A and B between which you are to determine the capacitance, it effectively implied connection terminals for the circuit.
In such cases we should not apply voltage ?As we can see you did not apply voltage but made A and B connection terminals there when the question asked to find equivalent potential between A and B

fig1-png.92577.png


Right?
 
  • #45
gracy said:
In such cases we should not apply voltage ?As we can see you did not apply voltage there when the question asked to find equivalent potential between A and B
You don't have to apply anything if the terminals are just serving as labels to identify certain nodes or specify a point of view (way of looking at the circuit).

The problem did not say to apply a voltage across AB. So don't.
 
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  • #46
gracy said:
If 100 volts of potential difference is applied between a and b in the circuit .Find the potential difference between c and d.
In this question I should apply voltage i.e 100 volts in between A and B but no voltage in between C AND D Because it would be wrong.Right?
 
  • #47
gracy said:
In this question I should apply voltage i.e 100 volts in between A and B but no voltage in between C AND D Because it would be wrong.Right?
Like this!(sorry capacitor and voltage source symbols look alike)
ki.png


Here C1 and C2 are not in series ,right?
 
  • #48
gracy said:
Here C1 and C2 are not in series ,right?
Right.
 
  • #49
please answer my #46
 
  • #50
Is current direction correct?
From positive terminal of battery to the rest of the circuit.
direction.png
 
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