5.1. What are "series" and "parallel" circuits?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 lowerright 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 counterclockwise 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 endtoend 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.
