How Do You Determine the Equivalent Capacitance in Complex Circuits?

AI Thread Summary
To determine the equivalent capacitance in complex circuits, it's essential to correctly identify capacitors in series and parallel configurations. Capacitors are in parallel if they share two nodes on both sides, while those in series share only one node on one side. The discussion highlights confusion around the series and parallel combinations, particularly regarding the current flow through capacitors. It is clarified that the current is the same on both sides of a capacitor, as the movement of electrons on one side affects the other. Understanding these principles is crucial for accurately reducing the circuit to a single equivalent capacitor.
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Homework Statement


Reduce the circuit below into a single equivalent capacitor at terminals a,b. Assume all initial voltages at t = 0 are zero.


Homework Equations





The Attempt at a Solution


Okay, this is the circuit I had in mind when I made this thread earlier
https://www.physicsforums.com/showthread.php?p=4684447#post4684447

My first thought was to take all the capacitors that to me look to be in parallel and combine them. I said that they are in parallel because they share at least 2 nodes on both sides of the components.

Then, I said the capacitors on the left side are in series. There is a lot of doubt in my decision here. I say that because they all 3 share the same node on only one side of their component, so I called them in series.

Then, after that the rest are clearly in series so I combined them.

Also, I wonder why it matters what terminals I choose to find the equivalent capacitance between, and what would happen if I chose different terminals?
 

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Your understanding of series and parallel combination is still wrong. After you combined the parallels, you say the left 3 are in series.. how is that? If you have gone through the thread you have linked, it contains an answer to the trick.
 
I say they are in series because they all share one node on one side of the component.
 
Alright, I redid it saying the 2C capacitors were in series. However, how do I know the current is the same? I mean, the charges land on the capacitor and don't go to the other side, is the current on a capacitor the same on both sides of the capacitor for one component?
 

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Maylis said:
I say they are in series because they all share one node on one side of the component.

That's where you have gone wrong. Only two of them can share a point in series.
 
Maylis said:
is the current on a capacitor the same on both sides of the capacitor for one component?
Yes. That's why it is 'current through a capacitor'
 
Maylis - Your answer in #4 looks correct.

Alright, I redid it saying the 2C capacitors were in series. However, how do I know the current is the same? I mean, the charges land on the capacitor and don't go to the other side, is the current on a capacitor the same on both sides of the capacitor for one component?

Yes. Electrons going I one side repel electrons out of the other side.
 

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