Equivalent capacitance, circular arrangement

[gracy]

Mentor's note: Post moved to new thread since it's a new problem.

One more problem

Homework Statement

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?

 

[gneill]

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.

 

[gracy]

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?

 

[gneill]

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.

 

[gracy]

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?

 

[gracy]

Follow outwards from the center and confirm that you find the corresponding components in the same (mirrored) locations.

Sorry, I did not understand.

 

[davenn]

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

 

[gneill]

Mirrors reverse front to back, not top to bottom. Otherwise you'd be looking at your feet in the mirror rather than your eyes

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.

 

[epenguin]

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.

 

[gracy]

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?

 

[gracy]

Follow outwards from the center

Which center?

 

[SammyS]

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.

Which center?

gneill meant: from the center of the figure, outward, i.e. from a point between the two circuit diagrams.

 

[gracy]

In some sense they are all in series,

I think all the Capacitors are in series

I knew it, I don't know what happened to me as I wrote in parallel.

 

[gracy]

but then equivalent capacitance makes no sense.

What does equivalent capacitance mean?

 

[SammyS]

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?

 

[ehild]

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.

 

[ehild]

@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/

 

[gracy]

How are the beads of different color connected in C?

Both series and parallel connections.

 

[ehild]

Both series and parallel connections.

Yes!

 

[gracy]

But why gneill rotated my diagram in OP 90 degrees to the right?

 

[ehild]

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.

 

[Ray Vickson]

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.

 

[gracy]

And what about mirror image,is it necessary?

 

[Ray Vickson]

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?

 

[gracy]

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!

 

[gracy]

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?

 

[ehild]

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.

 

[gracy]

I think the only thing that's important to do here is showing connection terminals A and B

Right?

 

[ehild]

Right?

showing connections between components and connections to the terminals.

 

[epenguin]

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.

 

[epenguin]

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.

 

[gracy]

I understood .Thanks @gneill and@ehild

 

[gracy]

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.

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?

 

[gneill]

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.

 

[gracy]

Should not I fix terminals at c and d?like this