Alternating current is, much like the name suggests, the flow of electrons which constantly changes direction. All home and business power grids worldwide are using sine wave AC current because it is easier to generate and much cheaper to distribute, except very few long distance applications (mainly when connecting different country power grids over sea) which benefit from the lower power losses of very high voltage DC (HVDC) systems.

Unfortunately AC current complicates things dramatically for an amateur to clearly understand how it works and makes the “water circuit” model obsolete; however it can still be visualized as water rapidly changing the direction of its flow, even though nobody would ever understand how water would accomplish anything useful by doing this. AC current and voltage constantly changes direction; how quickly is defined by the frequency of the application (measured in Hz) and for residential power grids it usually is 50/60Hz, which means that the voltage and current will change direction *50/60 times per second*. Calculating the active (RMS) voltage and current is fairly easy with sine wave systems; simply divide the peak by

In the above graph you can see a random, imaginary AC power load. As you can see not only the current (i) and voltage (v) are constantly alternating, but they also are out of phase (unsynchronized). The vast majority of AC power loads will cause a phase difference. This means that you need to apply vector mathematics even for the most simple of calculations; it is not possible to simply add, subtract or perform any other scalar mathematics operations when working with vectors. With DC current we would say that if 5A were transferred to a point from one cable and 2A were transferred to the same point from another cable, that would equal 7A delivered to that point; with AC current that would not be true because the end result would depend on the direction of the vectors.

The active (or true) power of an AC powered load can be calculated with the simple

type,

where *φ* is the angle between the voltage and the current and is also commonly known as the *power factor*. The active power is all that home/business consumers care (and pay) but it does *not* equal the total power coming through the conductors (cables) to the load; apparent (or complex) power is the total power transferred to the load and can be calculated with the type

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