Equivalent capacitance, circular arrangement

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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.
  • #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.
 
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  • #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
 
  • #51
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?
Right. It would be wrong for the problem that you posed to apply another source between C and D. It would change the circuit and create a different problem.
 
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  • #52
gracy said:
please answer my #46
That's right too. Here, 100V is input and Vcd is the output voltage.
 
  • #53
gracy said:
Is current direction correct?
From positive terminal of battery to the rest of the circuit.
View attachment 92905
Correct conventionally.
 
  • #54
gracy said:
Is current direction correct?
From positive terminal of battery
View attachment 92905
Your indicated currents look fine for the instant that the circuit is first assembled. Since there are no resistances in the circuit it will reach steady-state essentially instantaneously though, and all current flow will cease leaving the capacitors with some charge values.
 
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  • #55
gneill said:
all current flow will cease leaving the capacitors with some charge values. [/QUOTE]

I did not understand.

gneill said:
Since there are no resistances

capacitors have resistance,right?
 
Last edited:
  • #56
Capacitor 'plates' have resistance, which is negligible since they are metallic.
 
  • #57
Ideal components that aren't specifically resistances are considered to have no resistance. In a circuit diagram, unless otherwise specified, components are taken to be ideal. Capacitors, inductors, and wires are considered to be ideal components, and so have no inherent resistance.
 
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  • #58
gneill said:
and all current flow will cease leaving the capacitors with some charge values.
I don't understand.
 
  • #59
gracy said:
I don't understand.
Once the capacitors are charged, the currents will cease. This will happen really very fast as there is no resistance in the circuit.
 
  • #60
batteries/voltage source have resistance,right?
 
Last edited:

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