This may sound dumb but I'm really confused. How do you determine whether two components are in series or parallel? I know about the fact that if current has only one path to go from one component to the other, they are in series and if there is a junction in between, they are in parallel. But as the no of components increases, this gets really tricky and accuracy drops miserably. can anyone suggest any other trick? Thanks.

 

The question doesn't necessarily have an answer for every arrangement of more than two components. For example, look up delta and wye configurations of three components.

 

This may sound dumb but I'm really confused. How do you determine whether two components are in series or parallel? I know about the fact that if current has only one path to go from one component to the other, they are in series and if there is a junction in between, they are in parallel. But as the no of components increases, this gets really tricky and accuracy drops miserably. can anyone suggest any other trick? Thanks.

If a two-terminal device (call them terminal A and B) is connected to another two-terminal device (call them terminal C and D) such that A is connected to C and B is connected to D, they are in parallel.

If two such devices have only one terminal connected to each other (for example, A to C), then that common connection point will have no other components connected there, when the two devices are in series.

If you can't say two devices are connected according to the definitions above, then the devices are not in series, nor are the in parallel.

There is a special case for two devices in parallel, with no other components. In such a case the devices are also in series with each other, even though more than one terminal is common.

The question doesn't necessarily have an answer for every arrangement of more than two components. For example, look up delta and wye configurations of three components.

Actually, his specific question does have an answer.

He asked,
"How do you determine whether two components are in series or parallel?".

Well, there are ways to determine that, but those ways may reveal that sometimes two devices are not in series, nor in parallel.

 

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There is a special case for two devices in parallel, with no other components. In such a case the devices are also in series with each other, even though more than one terminal is common.

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I disagree with that. If two devices are connected in parallel, then they are not in series. The can't be both. It makes no difference whether they are connected to anything else.

 

I disagree with that. If two devices are connected in parallel, then they are not in series. The can't be both. It makes no difference whether they are connected to anything else.

It's just a matter of definition. If i say I have a circuit with only two components, and these components are in series, you'll know what I'm talking about. I only mentioned this special case because I offered two non-traditional definitions that might help the OP more easily spot the cases in a complex circuit. My definitions are not ideal, but maybe easier for him to apply

There is no law that says it must be classified as only one case and not both, but if you want to choose one only, I would choose to say it's a series circuit and not a parallel circuit.

One accepted definition of a series circuit is, "An electric circuit connected so that current passes through each circuit element in turn without branching".

One accepted definition of a parallel circuit is, "A closed circuit in which the current divides into two or more paths before recombining to complete the circuit".

It seems to me that two components connected into a circuit will certainly meet the definition of a series circuit and fails to meet the parallel definition above. I think it also can be considered parallel, but we must open our minds and not rigidly conform to the above definition.

For example. A battery driving a resistor is best described as a series circuit because the current flows around and does not branch.

 

I believe the most rigorous and useful definitions are:

Two components are in series if and only if current passing through either MUST pass through the other.

Two components are in parallel if and only if any voltage that appears across either MUST appear across the other.

Two isolated components connected together, say a battery and a lightbulb, satisfy both definitions and are hence both in series and in parallel. From a practical standpoint, such arrangements are generally more usefully thought of as being in series, but both descriptions are correct. In fact, when you first look at such a circuit, you probably determine the voltage across the lightbulb not by mentally applying KVL, but by recognizing that the battery voltage appears directly across the lightbulb, which means that you are exploiting the fact that they are in parallel.

@asulikeit: When you said that you knew that "if there is a junction in between, they are in parallel," this is simply wrong. Having a junction between two components is pretty much a guarantee that they are not in series, but says nothing about whether or not they are in parallel.

 

I believe the most rigorous and useful definitions are:

Two components are in series if and only if current passing through either MUST pass through the other.

Two components are in parallel if and only if any voltage that appears across either MUST appear across the other.

I'm curious why you consider these the most rigorous and most useful definitions.

As far as rigor, it is likely that any definitions based on currents and voltages will be open to "hole-poking", since the idea of series or parallel are more topological in nature, and should not require scientific concepts.

For example, if I have a resistor in series with a parallel combination of a resistor and two ideal current sources, and if those current sources are equal in magnitude and opposite in direction, then the currents through the resistors must be equal, yet those resistors are not strictly in series.

Likewise, if I have a resistor in parallel with a series combination of a resistor and two ideal voltage sources, and those voltage sources are equal in magnitude and opposite in direction, then the voltages on those resistors must be equal, yet those resistors are not strictly in parallel.

Note, I haven't even opened up the can of worms by trying to discuss nonconservative fields and path dependent voltages.

I know you can easily shore up any hole-poking, but the point is, why bring physics into any definition that can be based solely on topology? It's a needless complication if the goal is "rigor".

I also think that "usefulness" is too nebulous a notion to really hang our hats on. Usefulness depends on the use at hand.

For example, if I wanted to teach a young child about series and parallel connections, I think I would find it more useful to apply a definition with a topology based description, rather than any explanation based on voltages and currents. I remember wiring up batteries and lightbulbs in 4th grade science demonstrations. I was not in any way ready to understand voltages and currents, but the ideas of series and parallel (even if i didn't know the names) were very clear in my mind, as I remember.

I would tend to say that your definitions are good and useful, but in general, rigorous is often the antithesis of useful, and defining anything in the most rigorous way is often complex. The importance of rigorous definitions tends to be more of an issue in mathematics than science. It is important in science to be as clear as possible, but perfect definitions are not always possible. For example, try to define "life" or "waves", and it is not so easy as it might at first seem. I'm sure the mathematicians have topological definitions of series and parallel that would bore most of us to tears and prove less than useful to anyone first trying to visualize and interpret circuits intuitively.

 

For example, if I have a resistor in series with a parallel combination of a resistor and two ideal current sources, and if those current sources are equal in magnitude and opposite in direction, then the currents through the resistors must be equal, yet those resistors are not strictly in series.

While the currents must be equal in magnitude and consistent in direction, they are not "the same" current, as in the identically same current. I almost put that they have to have the same "symbolic" current and/or voltage, but I find that the concept of symbolic currents and voltages confuses many people without a bunch of clarification.

Likewise, if I have a resistor in parallel with a series combination of a resistor and two ideal voltage sources, and those voltage sources are equal in magnitude and opposite in direction, then the voltages on those resistors must be equal, yet those resistors are not strictly in parallel.

Same clarification.

It should be noted, however, that if these elements are part of a larger circuit and if the constraints still hold, then from a practical standpoint they are in series/parallel.

Note, I haven't even opened up the can of worms by trying to discuss nonconservative fields and path dependent voltages.

Which is good, since KVL goes out the window and you have to step back to more fundamental analysis techniques to begin with.

 

Two components are in series if and only if current passing through either MUST pass through the other.

Two components are in parallel if and only if any voltage that appears across either MUST appear across the other.

i like it but if we are after ultimate definition of parallel vs. serial, this still does not quite work. for example you can have two two-terminal devices wired in such a way that voltage across both is same but they are not in parallel - they could be in antiparallel such as diodes.

what if you have transformers where primaries are either in seris or parallel but secondaries are in antiparallel. the current in secondaries is the same but also the voltage, is this parallel or series?

just trolling

 

for example you can have two two-terminal devices wired in such a way that voltage across both is same but they are not in parallel

Antiparallel is just another word for parallel. OK, a special 'kind' of parallel that we use to describe tricky devices like diodes, but the voltage across them still MUST be the same, so they still obey Steveb's law.

secondaries are in antiparallel. the current in secondaries is the same but also the voltage, is this parallel or series?

The secondaries are in parallel, because the voltages across them MUST be the same. The fact that the currents through each are also the same is just coincidence.
It is no different from having two identical resistors in parallel; the voltage across them MUST be identical. The current through them is also the same, but it does not HAVE to be; it's just an accident of design.

I think Steveb's definitions are solid; they are just examples of Kirchoff's laws.

 

For example, if I have a resistor in series with a parallel combination of a resistor and two ideal current sources, and if those current sources are equal in magnitude and opposite in direction, then the currents through the resistors must be equal, yet those resistors are not strictly in series.

Steveb's laws apply to two components. A parallel combination of a resistor and two ideal current sources is NOT one component, it is several. Now, if you collapsed them into a single equivalent component then you would have to agree that it is indeed in series with the second resistor, since any current in one MUST also flow in the other.

 

Steveb's laws apply to two components. A parallel combination of a resistor and two ideal current sources is NOT one component, it is several. Now, if you collapsed them into a single equivalent component then you would have to agree that it is indeed in series with the second resistor, since any current in one MUST also flow in the other.

OMG, I have laws named after me!

Honestly, I'm not trying to state or endorse any laws or definitions here: neither my own, nor those of others. I just offered a guideline to the OP to try and help in identify series and parallel within complicated topologies, as he asked.

Other than that, I would just say that the concepts of series an parallel are quite simple and do not necessarily need to be tied to circuit laws, or physical laws of any kind. They can be isolated as abstract topological structures. Someone mentioned wye and delta topologies and we can add feedback structures and the bridge structure to the list of important configurations that should be instantly identifiable to a trained and experienced person.

The ability to see and identify topologies is a useful skill in itself, whether we are dealing with circuits, block diagrams, signal flowgraphs, or any of the other myriad of graphical abstraction tools we use in math, engineering and science.

 

Honestly, I stopped reading after post 5 or 6 and decided to bring some levity to this debate; I will ask, Why do the simplest of questions always ignite the fiercest debates?

 

Honestly, I stopped reading after post 5 or 6 and decided to bring some levity to this debate; I will ask, Why do the simplest of questions always ignite the fiercest debates?

I've noticed three different reasons for this. First, often a simple questions gets complicated by semantics. Second, sometimes different people come in with different starting assumptions. In both of these cases, it often takes quite a bit of discussion to figure out that these issues have happened.

Third, and most interesting, is that often what appears to be a simple question, turns out to not be so simple at all.

I won't try to figure out which of these, if any apply here, But, in this case, I don't think the discussion is very fierce. At least, I haven't felt that way about it, and take it all lightheartedly. Sometimes it is interesting to think about and talk about simple ideas that we have taken for granted for a long time.

 

@WBahn: The notes that I was referring to stated that there are only 2 cases: either 2 components are in series or they are in parallel. Which apparently is wrong. Can you please elaborate about components being neither in parallel nor in series. I can't really visualize the case. And well if these components happen to be resistors/capacitors how will you determine the effective resistance/capacitance?

@steveb: What if terminals A and C are connected together and there is a third component connected to the same junction? How will you find the effective resistance/capacitance in such a case?

Thanks.

 

Consider the attached circuit.

The circuit on the left has no components in parallel or series. But that has no effect on there being an equivalent resistance, because these are two different concepts.

First, it's important to understand what is meant by "equivalent resistance" (and then you can extend it to capacitance, inductance, whatever). Resistance characterizes the behavior of a circuit as seen between two particular nodes. What this means is that, assuming such a valid characterization exists at all, that the relationship between the voltage across the two nodes and the current flowing in one node (and out the other) obeys Ohm's Law, namely V=IR. The effective resistance is merely the ratio of the voltage and the current, assuming that this ratio is, in fact, constant; if it isn't constant, then there is no "effective resistance" between those two nodes.

Another way of saying it is is to imagine the following: I take two boxes each of which is identical and has two leads sticking out of it. In one box I but the circuit at the left and in the other I put the single resistor on the right. If there exists a resistor value such that I can use that value resistor for the second box and, as a result, you cannot determine which box has the full circuit and which box has the single resistor, then the single resistor is the effective resistance of the entire circuit on the left.

But notice that, if I connect the two points that you interact with (the ones marked '+' and '-') to different nodes of the circuit, then the equivalent resistance as seen between the new nodes (known as a 'port') will be different. The point is that it is almost nonsensical to ask what the equivalent resistance of something is unless and until the viewpoint is specified (i.e., what is the effective resistance between this node and that node -- or, in the jargon, the effective resistance seen looking into a specific port).

 

@steveb: What if terminals A and C are connected together and there is a third component connected to the same junction? How will you find the effective resistance/capacitance in such a case?

If I'm understanding you correctly, you are describing three similar two-terminal devices (e.g. resistors), with possibly different component values, connected such that one lead of each is connected to the same node.

This is the classic wye topology (also called a tee topology). The concept of equivalent resistance (or capacitance, inductance as the case may be) is more complicated than WBahn's example because there are now three terminals to worry about. This topology can be transformed into a delta topology (also called a pi topology).

So, to answer your question, there is no equivalent resistance, in this case. Note that WBahn's example has wye connections in it, yet he has a more complex circuit that ultimately has two free terminals. Here you can have one net equivalent resistance for the complete circuit. Note that the wye-delta transform can help you find the equivalent resistance of his circuit. However, there is an equivalent circuit to be considered (requiring 3 separate resistors) when you have 3 free terminals, if you desire to make a transformation. Here are two references that discuss this.

http://www.tina.com/English/tina/course/5wye/wye.htm

http://en.wikipedia.org/wiki/Y-Δ_transform

 

Thanks a ton! Doubts cleared! Thank you.