Identifying series and parallel connections

[gracy]

Homework Statement

In the arrangement shown,find the equivalent capacitance between A and B.

Homework Equations

Capacitance in parallel
$C$=$C_1$+$C_2$

The Attempt at a Solution

Supplied solution says
As,we can clearly see that ,capacitors 10μF and 20μF are connected between same points $C$ and $B$(Parallel combination)

They can be replaced by a single capacitor of capacitance given by
$C$=10μF+20μF=30μF
Thus circuit can be shown by (b).
Now ,the capacitors 15μF and 30μF are arranged in a row(sweries combination)
the equivalent capacitance is given by C such that
$\frac{1}{C}$=$\frac{1}{15}$+$\frac{1}{30}$=$10$μF
What I did not understand is
They can be replaced by a single capacitor of capacitance given by
Why can't I replace them as fllows

 

[gneill]

Are you asking if there is a difference between these two?

Electrically, no: There is no difference. You can arrange circuit components in any way you wish on paper, draw wires or components at angles, make wires long or short, have wires wander all over the page, etc., and it will make no difference to the circuit. What matters is the topology of the network (what connects to what).

 

[gracy]

Can you please provide me easy tip for identifying which capacitors are in parallel connection and which are not?I can identify in simple cases but when it is complicated ,I can't.

 

[gneill]

Parallel components share two nodes for their connections. Series components have one node that they share exclusively (no other connections at that junction).

A simple visual aid for finding parallel components is to color each node a different color (that includes all the wiring that makes up a given node). Components that are in parallel will connect to the same two color pairs. An example from a recent thread involving simplifying a resistor network is demonstrative:

All the resistors that connect to the same color pairs are in parallel. Note that all the horizontally drawn resistors have the color pair (Blue, Red), so they are all in parallel despite how complex the network appears.

 

[gracy]

Parallel components share two nodes for their connections.

What is exact definition of node in context of circuits.

 

[gneill]

What is exact definition of node in context of circuits.

You should check your course text or notes for an official definition.

But in simple terms, a circuit node is a conducting "island" in a circuit that is all at the same potential with respect to some fixed reference. Typically it is a conductive path (wire) that two or more components connect to.

 

[gracy]

Typically is a conductive path (wire) that two or more components connect to.

Here component can be capacitor,resistance ,keys ,switch ,bulb etc?

 

[gneill]

Here component can be capacitor,resistance ,keys ,switch ,bulb etc?

Resistors, capacitors, inductors, diodes,...: yes. Things like switches and keys: no.

Switches and keys can serve to change the domain of a node by extending or curtailing the conductor-connected region, but they are not electronic components in the intended sense of the word. They physically change the circuit topology when they are operated.

A (light) bulb is just a fancy name for a special purpose resistor

 

[gracy]

Resistors, capacitors, inductors, diodes,...: yes. Things like switches and keys: no.

What about batteries?

 

[gracy]

Are (1) and 2 two different (separate)nodes?

 

[gracy]

Are 1,2,3,4,5,6,7,8 nodes?If yes ,are 1,2,3 three different (separate)nodes?are 5,6,7,8 four different (separate)nodes?

 

[SammyS]

Are 1,2,3,4,5,6,7,8 these nodes?If yes ,are 1,2,3 three different (separate)nodes?are 5,6,7,8 three different (separate)nodes?
View attachment 92458

In case gneill is busy.

Everything in blue is part of the same node. It's all made of ideal conductor.

Everything in red is part of the same node. - a node different from the blue node.

 

[gneill]

Are (1) and 2 two different (separate)nodes?
View attachment 92457

No. They are both on the same wire path. Everything with the same color belongs to one node.edit: Ha! SammyS snuck in there while I was otherwise occupied

 

[gracy]

Are 1,2,3,4,5,6,7,8 nodes?

 

[SammyS]

Are 1,2,3,4,5,6,7,8 nodes?

No.

In post #11:

The entire blue wire constitutes a single node. Points 1, 2, and 3 are all located on this same node.

Points 5, 6, 7, and 8 are located on the red node.

Point 4 is on the yellow node.

 

[gracy]

Resistors, capacitors, inductors, diodes,...: yes. Things like switches and keys: no.

What about batteries?

 

[gracy]

Are component 1,2,3 underlined in blue in series? I think yes because they share a common node as highlighted by pink circle.

 

[gneill]

What about batteries?

Yes: batteries and other voltage sources, also current sources, are components.

 

[gracy]

And please answer my post#17

 

[gneill]

Are component 1,2,3 underlined in blue in series? I think yes because they share a common node as highlighted by pink circle.

View attachment 92477

No they are not in series. A pair of components in series share a single node exclusively (all alone, with nothing else connected to that node: Just one wire each from two components). The red and blue nodes have a lot of component connections, not two. That section of wire "A" alone that you've identified has four components connected to it!

Besides, those components were identified as being in parallel earlier in the thread. The only case where components can be both in series and in parallel is when there are only two components in the circuit. Then their connections will agree with both definitions:

 

[gracy]

That section of wire "A" alone that you've identified has four components connected to it!

Which four?

 

[gneill]

Which four?

Sorry, I think that's a frivolous question. Surely you can see which resistors have wires touching wire segment A? (Include its bottom end!).

 

[gracy]

(all alone, with nothing else connected to that node: Just one wire each from two components)

But this implies three components can never be in series.

 

[gracy]

Did you mean if thee are two components in series (that's why you used"pair of component)then othing else connected to that node: Just one wire each from two components)
and if component are in series then only three components should be connected to that node but A has 4 components connected to it,hence it is wrong!Right?

 

[gracy]

Are component 1,2,3 ,4 underlined in blue in series? I think yes because they share a common node "A"as highlighted by pink circle.

 

[gneill]

But this implies three components can never be in series.

No it does not. For any number of components in series the connections between the components are exclusive -- only two components connect at any node along the path. There is a single path for current to follow through the string of components. No current can leave the path, and no current can join.

Did you mean if thee are two components in series (that's why you used"pair of component)then othing else connected to that node: Just one wire each from two components)...

Yes.

...and if component are in series then only three components should be connected to that node but A has 4 components connected to it,hence it is wrong!Right?

No, only two components can be connected to any node along a series-connected path. Wire segment "A" has four components connected to it, so none of the components connected there are in series with any of the other components connected there. And, segment "A" is only a small portion of the overall node that is colored in blue. The entire connected path colored in blue is one node, and there are even more components connected to it.

 

[gneill]

Are component 1,2,3 ,4 underlined in blue in series? I think yes because they share a common node "A"as highlighted by pink circle.
View attachment 92482

No! There are more than two connections at that node. It is not exclusively shared by exactly two components.

 

[gracy]

so none of the components connected there are in series with any of the other components connected there

Not even 1 & 2?

 

[gneill]

Not even 1 & 2?

No. Their connection is not exclusive.

Gracy, there is only one series connection in that entire circuit. That is the resistor and battery in the bottom left corner. They share an exclusive connection.

 

[gracy]

Extremely Sorry,if I am irritating you.
But I am unable t understand if this is the case

No, only two components can be connected to any node along a series-connected path

how is it possible to have more than 2 connections in series?

 

[gneill]

Extremely Sorry,if I am irritating you.
But I am unable t understand if this is the case

how is it possible to have more than 2 connections in series?

 

[gracy]

Here capacitor,and the two resistance are in series,Right?

 

[gracy]

Gracy, there is only one series connection in that entire circuit. That is the resistor and battery in the bottom left corner. They share an exclusive connection.

You mean the two connections of yellow node?
If yes that means I understood series connection.

 

[gneill]

Here capacitor,and the two resistance are in series,Right?

Right.

 

[gneill]

You mean the two connections of yellow node?
If yes that means I understood series connection.

Yes.