Circuits consisting of just one
battery and one load resistance are very simple to analyze, but they are

not
often found in practical applications. Usually, we find circuits where more
than two components are connected together

There are two basic ways in which
to connect more than two circuit components:

*series*and*parallel*. First, an example of a series circuit
Here, we have three resistors
(labeled R

_{1}, R_{2}, and R_{3}), connected in a long chain from one terminal of the battery to the other. (It should be noted that the subscript labeling -- those little numbers to the lower-right of the letter "R" -- are unrelated to the resistor values in ohms. They serve only to identify one resistor from another.) The defining characteristic of a series circuit is that there is only one path for electrons to flow. In this circuit the electrons flow in a counter-clockwise direction, from point 4 to point 3 to point 2 to point 1 and back around to 4
Now, let's look at the other type
of circuit, a parallel configuration

Again, we have three resistors, but
this time they form more than one continuous path for electrons to flow.
There's one path from 8 to 7 to 2 to 1 and back to 8 again. There's another
from 8 to 7 to 6 to 3 to 2 to 1 and back to 8 again. And then there's a third
path from 8 to 7 to 6 to 5 to 4 to 3 to 2 to 1 and back to 8 again. Each
individual path (through R

_{1}, R_{2}, and R_{3}) is called a*branch*
The defining characteristic of a
parallel circuit is that all components are connected between the same set of
electrically common points. Looking at the schematic diagram, we see that
points 1, 2, 3, and 4 are all electrically common. So are points 8, 7, 6, and
5. Note that all resistors as well as the battery are connected between these
two sets of points

And, of course, the complexity
doesn't stop at simple series and parallel either! We can have circuits that
are a combination of series and parallel, too

In this circuit, we have two loops
for electrons to flow through: one from 6 to 5 to 2 to 1 and back to 6 again,
and another from 6 to 5 to 4 to 3 to 2 to 1 and back to 6 again. Notice how
both current paths go through R

_{1}(from point 2 to point 1). In this configuration, we'd say that R_{2}and R_{3}are in parallel with each other, while R_{1}is in series with the parallel combination of R_{2}and R_{3}.
This is just a preview of things to
come. Don't worry! We'll explore all these circuit configurations in detail,
one at a time!

The basic idea of a "series" connection is that components are connected end-to-end in a line to form a single path for electrons to flow

The basic idea of a "parallel" connection, on the other hand, is that all components are connected across each other's leads. In a purely parallel circuit, there are never more than two sets of electrically common points, no matter how many components are connected. There are many paths for electrons to flow, but only one voltage across all components

Series and parallel resistor configurations have very
different electrical properties. We'll explore the properties of each
configuration in the sections to come

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