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Voltage Conversion and Inversion
As discussed here, there are two types of electricity: direct current and alternating current. Each has its advantages and disadvantages, and most types of devices will only run on one or the other. Therefore, it would be useful to be able to change electricity from one form to the other. Fortunately, devices have been created that enable us to do exactly that.
The process of changing AC into DC is called conversion (actually, this is an imprecise term because "conversion" also refers to changing one DC voltage to another, and other things as well, but it will do for our purposes.) Devices that perform this process are called converters, but are also sometimes called adapters, and if being used for charging batteries, they are often just called chargers. Changing DC into AC is the opposite process and is called inversion. A device that does this is, of course, called an inverter.
Most people use converters on a daily basis even if they don't realize it, while inverters are used only for special applications. The reason for this is pretty simple: most people have AC power in their houses and therefore have little need for a device that creates AC from a DC source. However, inverters are useful for a wide range of applications, including letting you run small 115 VAC household appliances from your car's battery or electrical system, which is DC. In the PC world, inverters are a major component in uninterruptible power supplies, changing stored battery energy into a form your AC-powered PC power supply can use.
Another important thing to keep in mind is that every time you convert or invert electricity, there is some loss of energy due to waste heat in the components. The very best inverters are only about 90% efficient, meaning 10% of the energy is lost during the inversion; cheaper ones are less efficient. Converters can be as efficient as inverters, but are often much worse, often being no better than 50% efficient--half the power input to them is radiated as heat.
Next: External Power Problems