AC and DC current: Fundamental differences and a simple explanation
Much like the name suggests once again, alternating current is the flow of electrons which constantly changes direction. Ever since the late 19th century, nearly all home and business power grids worldwide are using sine wave AC current because it is easier to generate and much cheaper to distribute, with the exception of very few long distance applications which benefit from the lower power losses of the newly developed very high voltage DC systems.
AC has another great advantage, it allows for transfer of energy from the consumption point back into the grid as well as from the grid to the consumption point. This is very beneficial for buildings and installations that now produce more energy than they consume, which is quite possible when using alternate energy sources such as solar panels and wind turbines. The fact that AC allows the two-way flow of energy is the main reason why alternate power sources are becoming extremely popular and affordable.
When things come down to the technical level, 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 √2. In layman's terms, when AC current changes directions 50 times per second (50Hz), it means that the incandescent lights of your house are being turned on and off 50 times per second. The human eye cannot perceive it and your brain simply believes that the lights are constantly turned on.
Random AC Current / Voltage (230V) waveform
In the above graph you can see a random, imaginary AC power load connected to a 230V AC outlet. 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.
Random 3-phase load AC RMS Voltage/Current vector diagram
The active (or true) power of an AC powered load can be calculated with the simple P = V_RMS * I_RMS * cos(φ) (Watts) 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 S = V_RMS * I_RMS (VA).
As you can see, calculations are becoming far more complex with AC current compared to DC current. It takes at least mediocre knowledge of vector mathematics to even perform the most simple of calculations.