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With all the complexity of electrical circuits and the myriad components that we can put
into them, it turns out there are certain types of connections about which we can generalize.
If components connected in certain ways behave in a predictable fashion, we can use that
fact to simplify our analysis of electrical circuits. Today we will talk about two of
those types of connections, series and parallel.
Series and parallel connections are the same time a simple concept, yet sometimes confusing.
I've been teaching this stuff for < mumble> years and have found these concepts the source
of many errors for students learning circuit analysis. So let's see if we can come up with
some definitions and some techniques that will make it less likely for us to make errors.
Let's start with series connections.
A series connection occurs when two terminal components are:
1. connected so that they share one node and 2. they have the same exact current going
through them. I do not mean they have the same amount of current, but I mean the actual
electrons pass from one component to the next.
We might write the definition as:
Components are in series if they share one node and have the same current going through
them.
Let's start with two components, resistors to be specific. If I connect these two resistors
so that they share a node, and if a current, Iin, enters this pair of resistors we can
see that, by Kirchhoff's current law, that current has to pass through the wire that
connects them and come out at the other end. Since they are connected so that they share
a node and have the same current going through them, they are in series.
The same would be true if we increased that to three resistors. Each pair of resistors
shares a node, and if current enters the combination it has to leave the combination. That means
these three resistors are in series.
I think you can see that no matter how many resistors I connect in this fashion, they
would all be in series. They all share a single node between each pair, and the current that
enters the combination leaves the combination.
I think some of the confusion, or misapplication, occurs when synonyms are introduced into the
definition. For example, series does not mean in a line.
If we look at this arrangement of resistors, we see each pair of resistors shares a node.
If a current enters the bottom resistor, it will pass through the wire that connects it
to the next resistor through that resistor to the next wire and out the top resistor.
That means these three resistors are in series, even though they are not in a line.
Here's an example of resistors connected so that they share one node. However, these resistors
are not in series. Because if current enters the left-hand resistor some of it will go
down through the bottom resistor and some will go through the right-hand resistor. This
means the currents through the resistors are not equal, so there are no series connections
in the arrangement.
Let's move on to parallel connections.
Components are in parallel if they share two nodes and have the same voltage across them.
Now this is a little bit redundant because a voltage is a difference in potential between
two points, or nodes, so if components share two nodes, they necessarily have the same
voltage across them.
Continuing...
If we take two resistors and connect them so that they share two nodes, each of these
components will have the same voltage across them. That means these resistors are in parallel.
If we increase the number of resistors between these two nodes to three, since there are,
still, only two nodes, we still only have one voltage. That means all three of these
resistors share two nodes and have the same voltage across them, so all three resistors
are in parallel.
When the components are side by side this is very easy to see. However, I think the
same thing happens with language here when people substitute the phrase side-by-side
for 'share two nodes'.
For example, these two resistors, though they are not side-by-side, still share two nodes.
Since there are only two nodes, there is still be only one voltage, so these components are
in parallel.
To look at and negative example, here we see three resistors connected to each other. Each
of the resistors on the right are in a position that we called parallel to the resistor on
the left in the previous examples. Two of those resistors, also, appear to be
side-by-side. But, when we mark the nodes, we see there are three separate nodes in this
circuit. If there are three nodes, we have voltages between all three of them, so we
have three separate voltages in the circuit. So, in this circuit there are no individual
components in parallel.
This whole series parallel thing, by the way, is why I started encouraging students to highlight
the nodes. I cannot recall a single time when somebody correctly outlined the nodes and
then went on to make any series or parallel mistake.
I hope this clearly defines series and parallel and the difference between them.
So today, we covered the definition of series and parallel.
Components are in series if they share one node and have the same current going through
them.
Components are in parallel if they share to nodes and have the same voltage across them.
Next time we will look at series and parallel resistors and see how this can help us to
simplify circuits.
Until next time, go out and make it a great one.