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# Alternating current

Alternating current (AC) is electric current which repeatedly changes polarity from negative to positive and back again. The most commonly used form of alternating current does so in a sine wave pattern.

Alternating-current electric power is a form of electrical energy that uses alternating currents to supply electricity commercially as electric power. The system was devised by Nikola Tesla in 1882 and overcomes the limitations imposed by using direct current, as found in the system that Thomas Edison first used to distribute electricity commercially. The first long-distance transmissions of alternating current were in 1891 near Telluride, Colorado, followed a few months later in Germany. Thomas Edison strongly advocated the use of direct current (DC), having many patents in that technology, but eventually alternating current came into general use. Charles Proteus Steinmetz of General Electric solved many of the problems associated with generation and transmission of electricity by alternating current.

Unlike DC, AC can be stepped up by a transformer to a higher voltage. Because of Ohm's law, electrical energy losses are dependent on current flow, not on energy flow. By using transformers, the voltage of the power can be stepped up to a high voltage[?] to that the power may be distributed over long distances at low currents and hence low losses. The voltage can then be stepped down again so that it is safe for domestic supply.

Three-phase electrical generation is very common and is a more efficient use of conductors. Three-phase power is common only in industrial premises and many industrial electric motors are designed for it. Three current waveforms are produced that are 120 degrees out of phase with each other. At the load end of the circuit the return legs of the three phase circuits can be coupled together at the neutral point[?], where the three currents sum to zero. This means that the currents can be carried using only three cables, rather than the six that would otherwise be needed.

In many situations only a single phase is needed to supply street lights[?] or residential consumers. When distributing three-phase electric power, a fourth or neutral cable is run in the street distribution to provide a complete circuit to each house. Different houses in the street are placed on different phases of the supply so that the load is balanced, or spread evenly, across the three phases when a lot of consumers are connected.

For safety, a fifth wire is often connected between the individual electrical appliances in the house and the main electric switchboard[?] or fusebox. The fifth wire is known in Britain and most other English-speaking countries as the earth wire, whereas in America it is the ground wire. At the main switchboard the earth wire is connected to the neutral wire and also connected to an earth stake or other convenient earthing point (to Americans, the "grounding point") such as a water pipe. In the event of a fault, the earth wire can carry enough current to blow a fuse and isolate the faulty circuit. The earth connection also means that the surrounding building is at the same voltage as the neutral point and prevents a person from receiving an electric shock from the appliance. As many parts of the neutral system are connected to the earth, balancing currents, known as earth currents, may flow between the generator and the consumer and other parts of the system, which are also earthed, to keep the neutral voltage at a safe level. This system of earthing the neutral point to balance the current flows for safety reasons is known as a multiple earth neutral system.

Alternating currents are usually associated with alternating voltages. An AC voltage v can described mathematically as a function of time by the following equation:

$v(t)=A \times\sin(\omega t),$

where

A is the amplitude in volts (also called the peak voltage),
ω is the angular frequency in radian/second, and
t is the time in seconds.

Since angular frequency is of more interest to mathematicians than to engineers, this is commonly rewritten as:

$v(t)=A \times\sin(2 \pi f t),$

where

f is the frequency in hertz.

The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of sin(x) is +1 and the minimum value is -1, an AC voltage swings between +A and -A. The peak-to-peak voltage, written as VP-P, is therefore (+A)-(-A) = 2×A.

The size of an AC voltage is also sometimes stated as a root mean square (rms) value, written Vrms. For a sinusoidal voltage:

$V_{rms}={A \over {\sqrt 2}}.$

Vrms is useful in calculating the power consumed by a load. If a DC voltage of VDC delivers a certain power P into a given load, then an AC voltage of Vrms will deliver the same power P into the same load if Vrms = VDC.

To illustrate these concepts, consider the 240 V AC mains used in the UK. It is so called because its rms value is (at least nominally) 240 V. This means that it has the same heating effect as 240 V DC. To work out its peak voltage (amplitude), we can modify the above equation to:

$A=V_{rms} \times \sqrt 2.$

For our 240 V AC, the peak voltage VP-P or A is therefore 240 V × √2 = 339 V (approx.). The peak-to-peak value of the 240 V AC mains is even higher: 2 × 240 V × √2 = 679 V (approx.)

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