## Introduction

The alternating current (which can be abbreviated as CA, or AC, for Alternating Current in English, being however often used) is an electric current which changes direction.

This alternating current is said to be periodic if it changes direction regularly and periodically.

A periodic alternating current is characterized by its frequency, measured in hertz (Hz). This is the number of “round trips” that the electric current makes in one second. A periodic alternating current of 50 Hz performs 50 “round trips” per second, that is, it changes direction 100 times (50 round trips and 50 returns) per second.

The most widely used form of alternating current is sinusoidal current, primarily for the commercial distribution of electrical energy.

The frequency of the electric current distributed by networks to individuals is generally 50 Hz in Europe and Morocco, 60 Hz in North America.

We must distinguish:

- Purely alternating currents whose average value (direct component) is zero, which can supply a transformer without danger.
- Alternating currents with a non-zero direct component which cannot under any circumstances supply a transformer.

## Historical

In the United States, physicist Nikola Tesla in 1882 designed the three-phase alternator. At the same time, in France, Lucien Gaulard invents the transformer. These two inventions make it possible to overcome the limitations imposed by the use of direct current for the distribution of electricity then recommended by Thomas Edison who had filed numerous patents relating to this technology (and had direct current distribution networks) .

The advantages provided by the transport and distribution of electrical energy by alternating currents are undeniable. The industrialist Westinghouse, holder of the patents, ended up imposing it on the United States.

## Sinusoidal alternating currents

Example of sinusoidal signals

A sinusoidal alternating current is a sinusoidal signal of a size homogeneous to a current (expressed in amperes). Strictly, its DC component must be zero to qualify it as an alternative, the sinusoid will therefore have an average value equal to zero.

### From a mathematical point of view

The current therefore has an equation of the type:, or, since, with the amplitude of the signal, the period of the signal expressed in seconds, and the phase shift, or phase at the origin, expressed in radians.

Generally we summarize this equation to, with the pulsation (expressed in rad / s) which therefore corresponds to our or.

Strictly speaking, a sinusoidal alternating current has as much time (T / 2) positive as negative, which implies that its DC component is zero. The sinusoid will therefore oscillate in a balanced way around 0, implying an average value (mathematically) zero, and an effective value (electrically) of.

These two signals are said to be identical but phase-shifted by π. Between their two equations, there is therefore only the phase shift (or phase at the origin) which differs.

In reality, the important thing is that the difference of the phases at the origin is equal to an odd integer, since such a phase shift (π radians corresponding to 180 degrees) corresponds to an offset of half a turn on the trigonometric circle. We therefore associate a signal with the opposite value of the other, because sin (x + z.π) = – sin (x). When blue signal is at maximum, red is at minimum, etc. We therefore notice that the two signals are opposite, that is to say symmetrical by the x-axis