The string of Christmas lights on this tree may have cost $5 or $25, depending on how its circuit is constructed. One possibility is that the lights are connected along a single path, in a series circuit. In this case, if the filament in one of the bulbs were to burn out, then all the lights would go out. You wouldn't be able to tell which one malfunctioned, unless you go through the string and replace each bulb one at a time. The only advantage to such a design is that it is inexpensive. Alternatively, each bulb could be placed in its own separate branch of the circuit. Since there are now multiple paths by which charge can travel through the circuit, a burnt out bulb would not affect the rest of the lights, and it’d be obvious which one would need to be replaced. Of course, a string of lights with this design, known as a parallel circuit, would cost much more than the first. In this chapter, we will examine and learn the mathematics involved in series circuits, parallel circuits, and those that are a combination of both.
Series circuits are simple and comparatively inexpensive to design, but require every resistor or device in the circuit to be functional in order for the rest to work. Parallel circuits are more complex and expensive, but they have some advantages that may be worth the cost. There are applications for each type of circuit. More commonly, a combination of both types is used, which can offer capabilities and advantages that neither type can provide individually. Ammeters and voltmeters are tools used to evaluate the flow of current through a circuit and must be connected to the circuit appropriately in order to measure the flow without significantly changing it.