Equivalent Capacitance

In summary, the goal is to reduce the given circuit into a single equivalent capacitor at terminals a and b, assuming all initial voltages at t=0 are zero. One approach is to combine capacitors that appear to be in parallel, followed by those that are in series. However, it is important to correctly identify which components are in series and which are in parallel. It is also important to note that the current through a capacitor is the same on both sides of the component.
  • #1
gfd43tg
Gold Member
950
50

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?
 

Attachments

  • 6.5.png
    6.5.png
    10.9 KB · Views: 441
  • 6.5 attempt 1.pdf
    144.6 KB · Views: 399
  • 6.5 attempt 1.jpg
    6.5 attempt 1.jpg
    10.7 KB · Views: 425
Last edited:
Physics news on Phys.org
  • #2
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.
 
  • #3
I say they are in series because they all share one node on one side of the component.
 
  • #4
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?
 

Attachments

  • 6.5 attempt 2.jpg
    6.5 attempt 2.jpg
    12.7 KB · Views: 408
  • 6.5 attempt 2.pdf
    159.4 KB · Views: 183
  • #5
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.
 
  • #6
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'
 
  • #7
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.
 

What is equivalent capacitance?

Equivalent capacitance is a measure of the combined capacitance of two or more capacitors in a circuit. It represents the total amount of charge that can be stored in the capacitors when they are connected in a specific configuration.

How do you calculate equivalent capacitance?

The formula for calculating equivalent capacitance depends on the specific configuration of the capacitors. In series, the equivalent capacitance is equal to the reciprocal of the sum of the reciprocals of each individual capacitance. In parallel, the equivalent capacitance is equal to the sum of all individual capacitances.

Why is equivalent capacitance important?

Equivalent capacitance is important because it helps simplify complex circuits with multiple capacitors into a single equivalent capacitor. This makes it easier to analyze the behavior of the circuit and make calculations.

How does equivalent capacitance affect the overall capacitance of a circuit?

The equivalent capacitance of a circuit is always equal to or less than the individual capacitances of the capacitors in the circuit. This means that the overall capacitance of the circuit will decrease when capacitors are connected in series, and increase when they are connected in parallel.

Can the equivalent capacitance ever be greater than the individual capacitances?

No, the equivalent capacitance can never be greater than the individual capacitances in the circuit. This is because when capacitors are connected in parallel, the equivalent capacitance is the sum of all individual capacitances, which cannot be greater than the largest individual capacitance.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
746
  • Introductory Physics Homework Help
Replies
5
Views
840
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
2
Replies
67
Views
8K
  • Introductory Physics Homework Help
Replies
19
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
6K
Back
Top