# Struggling to find the equivalent capacitance of this circuit

• naftacher
In summary, the conversation is about the correct interpretation of series and parallel connections in a circuit, specifically in relation to the components C3, C4, and C5. The original assertion was that these components are in series, but upon further examination, it was found that they are not, as there is an intermediate connection between C3 and C5. The conversation also discusses the importance of understanding series and parallel connections in circuit analysis.
naftacher
Homework Statement
I have attached an image of this circuit. I must:
1. find the equivalent capacitance of the circuit
2. find the charge on each capacitor
3. find the potential drop on each capacitor
Relevant Equations
equivalent capacitance in series: 1/Cseries = 1/C1 ...
equivalent capacitance in parallel: Cparallel = C1 + C2...

I asserted C3, C4, and C5 to be in series. **I found the capacitance of "C3-4-5" to be 1.67x10-6 F. This I did by using 1/C = 1/C3 + 1/C4 + 1/C5

Then I noticed that I had another series circuit of "C3-4-5" and C1, and C2. Again, I used a similar formula. I obtained an equivalent capacitance of 1.0x10-6 F. This number is not 8x10-6F as told by the answer key.

I have been told that: I am incorrectly interpreting who is in series and who is in parallel. This is frustrating. The common image from any physics textbooks would make it seem that C3, C4, and C5 appear to be in series. Likewise, the common series definition "components directly adjacent to one another" applies to C1, C2, and C3.

I do not understand where my logic is wrong to begin with.

Delta2
Take two nodes A and B. A set of components are said to be connected in series if the components are joined end to end with no intermediate connections, starting from A and ending at B.

A set of branches is said to be connected in parallel if all of the branches in that set have their endpoints connected to the same two nodes.

Now you are asking why ##C_3, C_4, C_5## are not connected in series. Well, if we start at the bottom left node between ##C_3## and ##C_4## and trace the loop clockwise, we see there is an intermediate connection between ##C_5## and ##C_3##. These three components are thus not in series!

We might say that ##C_4## and ##C_5## are connected in series, and furthermore that ##C_3## is connected in parallel with this previous branch.

Last edited by a moderator:
etotheipi said:
Take two nodes A and B. A set of components are said to be connected in series if the components are joined end to end with no intermediate connections, starting from A and ending at B.

A set of components are said to be connected in parallel if all of the components in that set have their endpoints connected to the same two nodes.

Now you are asking why ##C_3, C_4, C_5## are not connected in series. Well, if we start at the bottom left node between ##C_3## and ##C_4## and trace the loop clockwise, we see there is an intermediate connection between ##C_5## and ##C_3##. These three components are thus not in series!

We might say that ##C_4## and ##C_5## are connected in series, and furthermore that ##C_3## is connected in parallel with this previous branch.

Isn't there that same intermediate connection between C4 and C5 (that horizontal)? Therefore, C4 and C5 could not be in series with each other? I am so sorry. This never made sense to me.

You might be getting thrown off by how it looks. Here's an equivalent re-drawing of the circuit between those two nodes:

Can you see that ##C_4## and ##C_5## are connected in series, and ##C_3## is connected in parallel with the above branch?

naftacher said:
Isn't there that same intermediate connection between C4 and C5 (that horizontal)? Therefore, C4 and C5 could not be in series with each other? I am so sorry. This never made sense to me.

By "intermediate connection" I mean a junction of some sort, with a branch out to another different part of the circuit. Between ##C_4## and ##C_5## is just a wire.

etotheipi said:
By "intermediate connection" I mean a junction of some sort, with a branch out to another different part of the circuit. Between ##C_4## and ##C_5## is just a wire.

Thank you for your redrawing. I do see that C4 and C5 are in series. and the intermediate connection C3 experiences with C4 and C5. However, in the original image I posted, this intermediate is just not obvious at all. Starting from the lower left node between C3 and C4, what is that intermediate connection that you see? I can see this in the redraw, but not in the original image.

naftacher said:
I asserted C3, C4, and C5 to be in series ... The common image from any physics textbooks would make it seem that C3, C4, and C5 appear to be in series.
No and no.

naftacher, getting straight on what's "series" and what's "parallel" is the most basic part of circuit analysis. You clearly haven't got it yet so I strongly suggest that you get straight on that before you attempt to solve ANY circuit problem. It can be confusing at first but until you have it down pat, you'll continue to be frustrated.

Equivalently, you can think of it like this: in a series connection between two nodes A and B, there is only one possible path through which the current can flow.

Delta2
phinds said:
No and no.

naftacher, getting straight on what's "series" and what's "parallel" is the most basic part of circuit analysis. You clearly haven't got it yet so I strongly suggest that you get straight on that before you attempt to solve ANY circuit problem. It can be confusing at first but until you have it down pat, you'll continue to be frustrated.

this I understand. I just don't see "it", pardon the low IQ. This I cannot change. Somebody above did help me see the nodal definition of what is in series and what is in parallel. However, this was a redraw. From the original sketch, I would not have understood this.

It is very important in circuit analysis to be able to pick out pairs of nodes in a circuit and determine if there are sets of components connected in parallel between those nodes, or if there is a series branch between those nodes, or even if there are multiple series branches themselves connected in parallel between those nodes!

Build up from simpler problems. Really the only way to gain familiarity with circuits is to see and practice with lots of different types of, well, circuits!

etotheipi said:

It is very important in circuit analysis to be able to pick out pairs of nodes in a circuit and determine if there are sets of components connected in parallel between those nodes, or if there is a series branch between those nodes, or even if there are multiple series branches themselves connected in parallel between those nodes!

Build up from simpler problems. Really the only way to gain familiarity with circuits is to see and practice with lots of different types of, well, circuits!
I just wish that this absurd simple thing was not THIS dense to me.

Make no mistake, circuit analysis is hard! Determining parallel and series connections is one of the first pieces of the jigsaw puzzle you need to put together. It will click eventually, with practice. Try and not focus on how the circuit is set out on the page, just focus on the ideas of nodes and paths.

Can I trace through this path with my finger between these two start and end nodes, and there are no other (intermediate) connections sprouting off in the middle? Then it's a serial path, also known as a 'daisy-chain' path.

Do these two serial paths have their start and end points at the same nodes? If so, then these two serial paths are connected in parallel!

## 1. How do I determine the equivalent capacitance of a circuit?

To find the equivalent capacitance of a circuit, you need to first identify all the capacitors in the circuit and their values. Then, you can use the formula 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn to calculate the equivalent capacitance, where C1, C2, C3, etc. are the individual capacitances. Alternatively, you can use the series or parallel combination formulas for capacitors, depending on the circuit's configuration.

## 2. What is the purpose of finding the equivalent capacitance in a circuit?

Finding the equivalent capacitance in a circuit allows us to simplify the circuit and make calculations easier. It also helps us understand the overall behavior of the circuit and how it will respond to different inputs. Additionally, knowing the equivalent capacitance can help us choose the appropriate components for a circuit.

## 3. Can the equivalent capacitance of a circuit be negative?

No, the equivalent capacitance of a circuit cannot be negative. Capacitance is a physical quantity that represents the ability of a capacitor to store charge, and it is always a positive value. If you get a negative value when calculating the equivalent capacitance, it is likely due to an error in the calculations.

## 4. How does the arrangement of capacitors affect the equivalent capacitance?

The arrangement of capacitors in a circuit can affect the equivalent capacitance in two ways: series and parallel combination. In series, the equivalent capacitance is always less than the individual capacitances, while in parallel, it is always greater than the individual capacitances. Therefore, the arrangement of capacitors can significantly impact the overall capacitance of a circuit.

## 5. Are there any limitations to calculating the equivalent capacitance of a circuit?

Yes, there are some limitations to calculating the equivalent capacitance of a circuit. The formulas and methods used assume ideal conditions, such as perfect capacitors and no external factors affecting the circuit. In reality, these conditions may not always be met, so the calculated equivalent capacitance may not be entirely accurate. Additionally, the formulas may not apply to complex circuits with non-linear elements.

• Introductory Physics Homework Help
Replies
27
Views
3K
• Introductory Physics Homework Help
Replies
12
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
19
Views
1K
• Introductory Physics Homework Help
Replies
11
Views
3K
• Introductory Physics Homework Help
Replies
108
Views
9K
• Introductory Physics Homework Help
Replies
8
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
4K
• Introductory Physics Homework Help
Replies
1
Views
4K