Identifying series and parallel connections

[gracy]

No, any number of components can be in parallel and share the same pair of nodes (only two nodes are required for any number of parallel components).

Here node implies highlighted pink portion "A "or complete blue portion(if we refer image in post #17)

 

[gneill]

Here node implies highlighted pink portion "A "or complete blue portion(if we refer image in post #17)

As an example, yes. The blue wire segment is one node. The red wire segment is another node. The highlighted pink portion is just a portion of the blue node, it is not a separate node.

Components that share both of those nodes (red, blue) for their connections are in parallel.

 

[gracy]

By isolated node (that you used in explanation of series connection)means
orange portion "a" here
it appears like a single line

 

[gracy]

Resistors 1,2,3,4, and 5 are in parallel connection.

 

[gracy]

Resistors 1,2,3,4, and 5 are in parallel connection.

And there are no other components in parallel connection.
Right?

 

[gracy]

Gracy, it should not be necessary to enumerate every possible permutation of connections in order to understand the concept.

Sorry but it gives me confident to move further.As I am satisfied that till here my all concepts are clear and I should move forward.

 

[gneill]

Resistors 1,2,3,4, and 5 are in parallel connection.
View attachment 92490
And there are no other components in parallel connection.
Right?

Correct.

 

[gracy]

please answer my post #53

 

[gneill]

By isolated node (that you used in explanation of series connection)means
orange portion "a" here
it appears like a single line
View attachment 92489

No, it is not isolated. It is a small portion of the larger whole (blue network) which has other connections.

 

[gracy]

On a serious note I want to ask one thing
How do you decide to bring new wire in I mean switching to yellow from blue,I faced this problem while drawing circuits in post #38 and #40.

I've explained that a node is isolated, contiguous wiring. If you follow a continuous wire path between two points, then they belong to the same node.

Each colored "island" in the diagram is contiguous wiring.

Based on my observation of our diagram
A node can not cross any component,right?
I mean it will be wrong if I will replace green wire with yellow wire because by doing thatyellow wire will crss the component(battery)

 

[gneill]

Correct.

 

[gracy]

No, it is not isolated. It is a small portion of the larger whole (blue network) which has other connections.

Oh,yes.
But I think it should be correct that
isolated node appears like a single line(linear; no branches)

 

[gracy]

Correct.

Was it the answer of my post#60?

 

[gneill]

Oh,yes.
But I think it should be correct
isolated node appears like a single line(linear; no branches)

Shape, angle, length, etc., make no difference. Isolated means no way out except via a component. Contiguous wires, bounded only by components, are a single node.

 

[gneill]

Was it the answer of my post#60?

Yes.

 

[gracy]

And a node will continue until any component comes in it's way .I mean it would be wrong if I will replace blue with yellow wire like this

If my constant questions are bothering you,please answer them later.I am ready to wait.

 

[gneill]

And a node will continue until any component comes in it's way .I mean it would be wrong if I will replace blue with yellow wire like this

Yes. That would be wrong.

 

[gracy]

"shorted out" means that there is a low (usually zero) resistance path

When we say components are shorted out in spite of presence of some (non zero )resistance?when there is resistance of 0. something ohm?Or sometimes even 1 or 2 ohms of resistance ?
My friend says even if there is 1 or 3 ohms of resistance the components are shorted out.I am asking for theoretical purpose (on paper)not laboratory.
My actual question is what is low resistance?Range for low resistance?

 

[gneill]

When we say components are shorted out in spite of presence of some (non zero )resistance?when there is resistance of 0. something ohm?Or sometimes even 1 or 2 ohms of resistance ?
My friend says even if there is 1 or 3 ohms of resistance the components are shorted out.I am asking for theoretical purpose (on paper)not laboratory.
My actual question is what is low resistance?Range for low resistance?

Technically a "short circuit" is any path that bypasses an intended or normal path of a circuit. It diverts current that would otherwise flow through the intended path when the circuit is operating normally. The particular value of the shorting resistance is technically unimportant.

However, it is common to speak of a short circuit as usually being of zero resistance, since placing a wire across a portion of a circuit to aid in analysis of the circuit is a common practice and is referred to as "shorting" the component or path. So it is common to think of a short circuit as being a zero resistance path unless otherwise specified.

"Low resistance" is a relative term. It implies low with respect to the other resistances in the surrounding circuit. There's no strict definition. You can take it to mean any value that would measurably alter the operating behavior of a circuit.

 

[gracy]

If there is 4 ohm resistance in an intended or normal path of a circuit and there is an optional path where 3 ohm resistance is present.Then current will take route where there is 3 ohm resistance.Will it be called short circuit or greater difference in resistance is required?

 

[gneill]

If there is 4 ohm resistance in an intended or normal path of a circuit and there is an optional path where 3 ohm resistance is present.Then current will take route where there is 3 ohm resistance.Will it be called short circuit or greater difference in resistance is required?

If the 3 Ohm resistance was not an intentional part of the original circuit then it is technically a short circuit.

If someone were to tell you to place a short circuit across the 4 Ohm path without any other details, then you would place zero Ohms (a wire) across it, because that is the conventional implication.

I can't provide a definition for "low" here. It depends on too many arbitrary or unspecified factors.

 

[gracy]

Ok.Thanks for all the answers @gneill .God bless you,give you all happiness in your life.Take care.
You made my day!I was having great difficulty in identifying parallel and series connections.Hope ,this thread helps many students who are facing same problem.

 

[gracy]

Here wires are arranged like a square

In this only second and third capacitors (from right)are in series.If these square like arrangement of wire is not there ALL the capacitors are in series.Here I have not used wires of different color that I should have used.

Here I could not find any capacitors in parallel as there are no capacitors sharing two nodes.But according to my book three capacitors are in parallel.The book however does not mention which three.

 

[gneill]

You haven't identified the nodes properly. Any wire segments that touch must be the same node (color). In your diagram I can see orange touching blue, red touching green, green touching pink. Make another attempt.

 

[azizlwl]

When drawing a node, example the green note, keep on following the lines until block by resistor, capacitor or any other components. Trace all branches till blocked.

 

[gracy]

You haven't identified the nodes properly. Any wire segments that touch must be the same node (color). In your diagram I can see orange touching blue, red touching green, green touching pink. Make another attempt.

If I will replace blue with red,it will be wrong as red will be crossing the capacitor then.

 

[gneill]

Why didn't you replace blue with orange? If you started coloring on the left end with orange, you should stay with orange until you run out of wires that are connected. When you switch to red for the wire between the two capacitors on the left, stay with red until all wire segments that are connected to it are the same color, and so on.

 

[gracy]

I think this would be correct

 

[gracy]

And if we look at the above pic,it is clear that first three capacitors from left (from end p)are parallel to each other as the share 2 common nodes orange and red.
Right?
But we can see there was orange wire then a capacitor came in between then there was red and again orange,Will it be okay?

 

[gneill]

And if we look at the above pic,it is clear that first three capacitors from left (from end p)are parallel to each other as the share 2 common nodes orange and red.
Right?

Right.

But we can see there was orange wire then a capacitor came in between then there was red and again orange,Will it be okay?

Yes it's fine. So long as you identified the nodes properly (which you did this time) then whatever sequence appears must be correct.

If you had some other circuit where you discovered that both leads of a component ended up with the same color, then you would have to worry. The circuit would either be "wrong" or it's a trick question, since that component would be "shorted out" by the wiring and would not be doing anything useful in the circuit.

 

[gracy]

How can I simplify this circuit I mean how can I remove the square like arrangement of wires how to replace the square like arrangement of wires with some simple wiring?

 

[gneill]

How can I simplify this circuit I mean how can I remove the square like arrangement of wires how to replace the square like arrangement of wires with some simple wiring?

1. Identify the parallel components.
2. For each set of parallel components that you identify erase all but one and replace that one with the parallel value.
3. Clean up superfluous wires.

 

[gracy]

But one square is still remaining!

If I will replace the black wire with yellow then this remaining one wire will be not there.And all the three capacitors would be in parallel.Resultant capacitance would be 5C(All six capacitors had capacitance C)

3. Clean up superfluous wires.

I think by this you meant use least number of wires that's why I replaced black with yellow wire.

 

[gneill]

I didn't see your intermediate steps but I think something went wrong, probably an inadvertent change in the circuit when you were reducing the wiring. That 3c capacitor should not have ended up where you show it, and if it did it would be in parallel with the one beside it (so one or the other should not be there at this point).

Here's how I see the reduction taking place. I've replaced the orange color with green for better contrast with the red:

 

[gracy]

Thanks infinitely for your diagram.Neat and tidy!
I did not understand What exactly we have to erase?

 

[gracy]

In my book answer is given to be $\frac{3C}{4}$
And explanation is given as follows
First three capacitors are in parallel and next two are short circuited.
I don't know if there is no trace of resistance how did they know it is short circuited?

 

[gneill]

Thanks infinitely for your diagram.Neat and tidy!
I did not understand What exactly we have to erase?

Erase all but one capacitor in each parallel grouping.

 

[gneill]

In my book answer is given to be $\frac{3C}{4}$
And explanation is given as follows
First three capacitors are in parallel and next two are short circuited.
I don't know if there is no trace of resistance how did they know it is short circuited?

A wire is a equivalent to a zero valued resistance. The parallel pair on the right was shorted by the wire going over/around it. Using the method I've outlined this combined pair becomes an isolated capacitor automatically, so you don't need to do any other analysis to find the shorted (and thus redundant) components.

 

[gracy]

Note that "this capacitor "becomes isolated !so "so this parallel pair "was not doing anything in the circuit.
one of your lines from the immaculate diagram .

"this capacitor" you meant capacitor having capacitance C (first capacitor from right hand side)?
"so this parallel pair "
Which pair?you meant the second and third capacitors from right side.?
was not doing anything in the circuit.You meant there was no utility of them?
If yes,what does an isolated capacitor has to do with the pair's utility?

 

[gneill]

Note that "this capacitor "becomes isolated !so "so this parallel pair "was not doing anything in the circuit.
one of your lines from the immaculate diagram .

"this capacitor" you meant capacitor having capacitance C (first capacitor from right hand side)?

No. Why would you think that? The note in the diagram points to the isolated capacitor which was formed from the parallel pair at that location. The far right capacitor was never touched by the reductions as it was not part of a parallel group.

"so this parallel pair "
Which pair?you meant the second and third capacitors from right side.?

Of course. It's a pair of capacitors in the original circuit, and we found them to be parallel.

was not doing anything in the circuit.You meant there was no utility of them?
If yes,what does an isolated capacitor has to do with the pair's utility?

The parallel pair was reduced to one capacitor. The reduction process left it with only one lead connected to the circuit.

Without both leads connected a component cannot carry current. Charge cannot move onto or off of a capacitor through one wire alone. The capacitor thus has no influence, no utility, as far as the circuit is concerned. This means that the original pair was also of no utility (a correct circuit simplification cannot change the circuit's externally-viewed behavior in any way).

 

[gracy]

A wire is a equivalent to a zero valued resistance

Wires will always be there in a circuit,then this means all the circuits short circuited.Of course not,what am I missing?

 

[gracy]

I now understand how tha answer came out to be $\frac{3C}{4}$
But I am still facing difficulty in comprehending the following

A wire is a equivalent to a zero valued resistance. The parallel pair on the right was shorted by the wire going over/around it.

 

[gneill]

Wires will always be there in a circuit,then won't this all the circuits are short circuited?Of course not,what am I missing?

Go back to the discussion of what a "short circuit" means. It means a bypass (either intentional or accidental) of a normal circuit path. Wires (paths) that are supposed to be there to interconnect components are just doing what they were meant to do.

In the circuit under discussion two of the capacitors are bypassed by a wire. Whether this was intentional (i.e. a "trick" for you to discover) or an accident (the author of the problem made a mistake) cannot be known for sure, but because it is not a proper situation to have for a practical circuit (why would one design a circuit with parts that do nothing?) we call that path a short circuit: the subcircuit comprising the two capacitors is shorted. Current will not flow in that subcircuit due to the bypass.