Capacitor in Series and Parallel combination

[carnot cycle]

Homework Statement

Compute the equivalent capacitance for the network between points A and B.

Homework Equations

1/(Ceq) = 1/C1 + 1/C2 + 1/C3... (series)
Ceq = C1 + C2 + C3... (parallel)
C1 = 6.9 nF
C2 = 4.6 nF

The Attempt at a Solution

I have been getting stuck on a lot of these questions. A few issues I'm having:

1) Not being able to decide if a capacitor is in series or parallel for complex problems like these that involve both.
2) Not knowing where to place an equivalent capacitor after I have combined two or three capacitors.

For this problem, I started by combining the three C1 capacitors on the right side of the problem that are in series with one another.

However, after this, I was unable to decide which are in series or parallel. I am unsure if the two C2 capacitors are in parallel with the equivalent capacitor that I have found after combining the three C1 capacitors that are in series with one another.

Any help/problem solving strategies are greatly appreciated. Thanks!

 

[rude man]

Can you not see that the three right-most C1 capacitors in series are in parallel with the right-most C2?
C1/3 is in parallel with C2?

 

[carnot cycle]

Yes I see that, but why is it not also parallel to the left most C2 capacitor?

EDIT: Also, how did you know to place the C1/3 equivalent capacitor such that it is parallel to the C2?

 

[gneill]

Yes I see that, but why is it not also parallel to the left most C2 capacitor?

Because it's not connected to that C2; there are a pair of C1 capacitors between the nodes where the C1/3 connects and the nodes where that C2 connects. For components to be connected in parallel they must be wired to each other without any other components in between (in the wiring).

EDIT: Also, how did you know to place the C1/3 equivalent capacitor such that it is parallel to the C2?

Because the three series C1 capacitors were connected there before (nodes c and d in the diagram), and the C1/3 equivalent capacitor just replaces them.

 

[carnot cycle]

So does this mean that the two C1 capacitors between nodes A and C are also in parallel?

 

[gneill]

So does this mean that the two C1 capacitors between nodes A and C are also in parallel?

No! They don't both share the same two nodes. Each of them has an open connection (node a, node b) and there's a C2 (and other stuff in parallel with that C2) in between their other connections.

For two components to be in parallel they must share the same potential difference. That is, they must each be connected to the same pair of nodes.

 

[rude man]

So does this mean that the two C1 capacitors between nodes A and C are also in parallel?

To review:
1. let
C2r = right-hand C2
C2l = left-hand C2

then
C2r → C2r' after combining with three C1 in series
C2l → C2l' after combining with C2r' and two C1's
C1 + C2l' + C1 are then in series across a and b.

 

[CWatters]

EDIT: Also, how did you know to place the C1/3 equivalent capacitor such that it is parallel to the C2?

The equivalent capacitor is connected to the same place (see red dots)...

This shows the first two steps only. The process repeats. If you look at the right hand side of the bottom drawing you can see it's similar to the right hand side of the top drawing.

 

[carnot cycle]

Thanks everyone for the help! I've tried a few more problems and seem to be able to solve them now.

 

[carnot cycle]

Well just when I thought I understood these types of problems, I came across one that has left me confused for a while :(

The textbook states that when the switch is closed, the two capacitors shown are connected in parallel. However, I don't understand why they are connected in parallel, and not in series. Aren't the left side and right side of the circuit just connected together when the switch is closed?

The center part of the switch is an insulating handle.

 

[CWatters]

The general rule (for components with two terminals) is that:

They are in series if both components share one common node with each other, but no other component.

They are in parallel if they share two common nodes.

In this case the two capacitors will be connected to each other at both terminals so they are considered to be in parallel.

See also..

http://www.ee.buffalo.edu/faculty/paololiu/edtech/roaldi/References/sp.htm