Are these 2 resistors in parallel?

Question

So I had a circuit to analyse and I needed to find the equivalent resistor and then I arrived to a confusion. Are R1 and R3 in parallel? Here is the circuit.

schematic

^{simulate this circuit – Schematic created using CircuitLab}

It is common to draw the voltage source on the left hand side. If you draw R1 in the middle and V1 and R2 to the left, it becomes more obvious. — Dampmaskin, Oct 15 '19 at 14:50

score 48 · Accepted Answer · answered Oct 15 '19 at 15:15

Redrawing schematics is a great way to analyze circuits, but also an exercise in why schematics are drawn in particular ways — to more clearly communicate to other engineers.

schematic

^{simulate this circuit – Schematic created using CircuitLab}

The rearrangement above should be a little more clear. If you trace a path from one terminal of the battery to the other, you can hopefully see that there are two paths (the split occurs at the junctions on either side of R1).

Series means one-after-another current flow (like a series of events or a television serial). Parallel means that current flows through two or more components at the same time (proportional to the component values).

Just as when you measure voltage, where the value depends on your reference point, components can be series or parallel depending on what you are comparing them to:

You could say:

R2 is in series with the voltage source, or
R2 forms a series-parallel circuit with R1 and R3, or
R1 and R3 are parallel with each other, or
R1 and R3 are parallel with a voltage source and some resistance R2

score 12 · Answer 2 · answered Oct 15 '19 at 15:01

12

I see a few answers already, but none provides the definition of "parallel":

Two two-pins components are in parallel when the voltage across them is the same

Conversely, with "series", you have:

Two two-pins components are in series when the current through them is the same

Bear in mind that "the same" literally means "the same" in this context. If you have two resistors with two different voltage generators connected to them, and the generators provide the same voltage, then the voltage across the resistors will numerically be the same, but it won't be the same voltage.

The definitions above also solve the confusion if you only have two components, as highlighted in the comments to this answer. In that case, the components are both in series and in parallel, since the voltage across them and the current through them is the same.

Being in series and in parallel with something else at the same time is not impossible, a very common example can be a voltage generator and its load.

answered Oct 15 '19 at 15:01

Vladimir Cravero

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While the statements you make about voltage in parallel and current in series being "the same" are true, these are necessary but not sufficient conditions - there are circuits where components which are not in parallel nevertheless have the same voltage drop across them. – Stobor Oct 16 '19 at 06:32
@Stobor I disagree, at least for my definition of "the same". The same *numeric* voltage can appear across various components, without them being in parallel; but if the voltage is the same as in the same physical phenomenon, then they are in parallel indeed. – Vladimir Cravero Oct 16 '19 at 07:00
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This seems like an awfully roundabout way of saying things. Why say "A and B are parallel if the difference-in-potential-between-the-two-termini-of-A is the difference-in-potential-between-the-same-two-termini as the difference-in-potential-between-the-two-termini-of-B" when you could just say "A and B are parallel if the two termini of A are the same two termini as the two termini of B"? If the termini matter and the voltage doesn't matter, why mention the voltage at all? – Cassie Swett Oct 16 '19 at 17:02
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This is a confusing way to look at it, especially for a beginner. In a beginner's mind, I could see easy confusion with your definition that would make R2 seem to be parallel. Yes, the voltage across them is the same and yes, it comes from the same separation of charge, but that's just the result of them sharing terminals. How can you differentiate between the voltage drop across two identical resistors in two identical circuits without it being arbitrary in order ensure that they aren't "the same"? The better definition, in which they share terminals, doesn't require anything arbitrary. – gormadoc Oct 16 '19 at 20:14
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Another issue is that it doesn't work for non-parallel loads that don't have any voltage drop. In both cases the voltage is exactly the same, both in magnitude and origin. Saying R1's separation of no charge is different from R2's separation of no charge requires a look at their terminals, necessitating the easier definition again. – gormadoc Oct 16 '19 at 20:16
In my first comment, it should be "Yes the voltage across R1 and R3 are the same". I inserted the previous sentence after writing the next one. – gormadoc Oct 16 '19 at 20:44
Remove the generators, every component is now both in series and in parallel with every other component, according to your definition. – Eric Duminil Oct 17 '19 at 06:56
I read the comments and I understand your points. If we want to discuss how beautiful or easy to understand the definition is, then let me add that I personally like it because, with the series definition, it highlights once more the omnipresent dualism of linear circuits. It can be confusing, but it is a definition, and it is right, so either take it, or leave it. I find the "share both terminals" somewhat less precise, so I guess it is at least debatable. – Vladimir Cravero Oct 17 '19 at 07:03
@gormadoc I fail to understand why you think that "my" definition would make R2 to seem in parallel. The voltage across it is not the same as R1 or R3, so there's that. Moreover, if loads do not have any voltage drop across them and the origin is the same, either they are in parallel or they are shorted - I probably fail to understand your example, can you elaborate? – Vladimir Cravero Oct 17 '19 at 07:05
@EricDuminil if you remove the generators all the resistors are in parallel, but certainly not in series, because it is not true that the same current flows through all of them. – Vladimir Cravero Oct 17 '19 at 07:07
@VladimirCravero : Exactly 0A everywhere. Isn't it the same current? – Eric Duminil Oct 17 '19 at 07:10
@EricDuminil I am not talking of a particular solution of the circuit. Same current means that IR1= IR2 = IR3 = a_certain_i, which is not always true for three resistors in parallel. – Vladimir Cravero Oct 17 '19 at 07:13
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Because you delineate between "same" voltage and "equal" voltage in an unnatural manner. To a beginner, they see one voltage source and that it's doing all the work. In my experience with Intro to Circuits students, they don't always see that the voltage across one component is different from another when they are hooked up differently. For a more clear explanation, consider removing R3 and making R1=R2. Now the voltages are the same, exactly V/2. The source is the same. They are still not in parallel. – gormadoc Oct 17 '19 at 17:12
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As for my second comment, your interpretation is wrong. Take one resistor and short the leads. Now do it again with another resistor, but leave them unconnected to each other. There is no voltage drop and the origin is the same in that there is no separation of charge or the origin is the same in that there isn't one. Either way it clearly can't be true: hook up a power source to one and it has no effect on the other, which can't be true if they were in parallel. If you exclude either of the definitions, however, you also exclude two resistors actually hooked up in parallel. – gormadoc Oct 17 '19 at 17:20

score 4 · Answer 3 · answered Oct 15 '19 at 14:31

4

Yes, because there are two different flows:

V1 -> R2 -> R1 -> V1
V1 -> R2 -> R3 -> V1

R2 and the combination (R1, R3) are in series, but R1 and R3 are in parallel.

answered Oct 15 '19 at 14:31

Michel Keijzers

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score 1 · Answer 4 · answered Oct 15 '19 at 14:35

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R1 and R2 have their ends connected to the same nodes.

schematic

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. Remove R2 and V1 and it becomes very obvious that R1 is in parallel with R3.

answered Oct 15 '19 at 14:35

Transistor

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Yes but no, if you remove R2 and V1 it becomes ambiguous. It also looks like R1 and R3 are in series. :) – Dampmaskin Oct 15 '19 at 14:42
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How is a drawing with single path suppose to show parallelism, something that requires more than one paths? – ikegami Oct 16 '19 at 05:32
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It's easier to see for some people that, but removing the voltage source from a network makes all definitions about serial and parallel meaningless, so it's likely to add more confusion than clarification. Topological transformations (like moving the middle branch to the left) are much more helpful. – toolforger Oct 16 '19 at 07:46

score 0 · Answer 5 · edited Oct 18 '19 at 17:26

Yes, R1 and R3 are in parallel. Both their ends land at the same places. As a mains electrical guy I'm not supposed to presume wires are zero ohms, but if I do, this becomes a fairly simple matter. Conductance = 1/resistance.

R1 (50.5 ohms) has a conductance of 0.01980198 siemens.
R2 (55.83 ohms) has a conductance of 0.01791152 siemens.

In parallel, conductances simply add. So 0.0377135 siemens.
Stated in resistance, R1/3 is 26.52 ohms.

R1/3 and R2 are in series. In series, resistances simply add. 26.52+1.54 = 28.06 ohms.

This shunts a 10V constant-voltage supply, so we can plug 10V into Ohm's Law and done.

Are these 2 resistors in parallel?

5 Answers5

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