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# Alternating current

An alternating current (AC) is an electrical current, where the magnitude and direction of the current varies cyclically, as opposed to direct current, where the direction of the current stays constant. The usual waveform of an AC circuit is generally that of a sine wave, as this results in the most efficient transmission of energy. However in certain applications different waveforms are used, such as triangular or square waves.

Used generically, AC refers to the form in which electricity is delivered to businesses and residences. However, audio and radio signals carried on electrical wire are also examples of alternating current. In these applications, an important goal is often the recovery of information encoded (or modulated) onto the AC signal.

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## History

William Stanley Jr designed one of the first practical coils to produce alternating currents. His design was an early precursor of the modern transformer, called an induction coil. From 1881 to 1889, the system used today was devised by Nikola Tesla, George Westinghouse, Lucien Gaulard, John Gibbs , and Oliver Shallenger . These systems overcame 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 transmission of alternating current took place 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 (see War of Currents). Charles Proteus Steinmetz of General Electric solved many of the problems associated with electricity generation and transmission using alternating current.

## Distribution and domestic power supply

Unlike DC, AC can be stepped up or down by a transformer to a different voltage. Voltage conversion is possible for DC using rotating machines or inverters. However these tend to be more expensive and less efficient than transformers, or did not exist when Edison, Westinghouse and Tesla were designing their power systems. See HVDC.

Use of a higher voltage leads to more efficient transmission of power. The power losses in the conductor are due to the current and are described by the formula P = I2R, implying that if the current is doubled, the power loss will be four times greater. Therefore it is advantageous when transmitting large amounts of power to convert the power to extremely high voltages (sometimes as high as hundreds of kilovolts). However high voltages also have disadvantages, the main ones being the increased danger to anyone who comes into contact with them, the extra insulation required, and generally increased difficulty in their safe handling. Therefore power for general use is stepped down to a relatively low level, generally around 200 V to 500 V phase-phase and 100 V to 250 V phase-neutral.

Three-phase electrical generation is very common and is a more efficient use of commercial generators. Electrical energy is generated by rotating a coil inside a magnetic field, in large generators with a high capital cost. However, it is relatively simple and cost effective to include three separate coils in the generator stator (instead of one). These sets of coils are physically separated and at an angle of 120° to each other. Three current waveforms are produced that are 120° out of phase with each other, but of equal magnitude.

Three-phase systems are designed so that they are balanced at the load; if a load is correctly balanced no current will flow in the neutral point . Also even in the worst case unbalanced (linear) load the neutral current will not exceed the highest of the phase currents. For three-phase at low (normal mains) voltages a four-wire system like this is normally used reducing the cable requirements by one-third over using a separate neutral per phase. When stepping down three-phase a transformer with a Delta primary and a Star secondary is often used so there is no need for a neutral on the supply side.

For smaller customers (just how small varies by country and age of install) only a single phase and the neutral are taken to the property. For larger installs all three phases and the neutral are taken to the main board. From a three-phase main board both single and three-phase circuits may lead off (and in some cases also circuits with two phases (not to be confused with two-phase) and a neutral are led off).

Split phase systems (single phase centre tapped to give two hots 180° out of phase) are useful in situations where only one or two high-voltage phases are available, but the demand exceeds what can easily be supplied as single phase at the normal voltage. This system is only common in North America where almost all homes have it, and it is normal to connect higher power appliances across the hots. A similar method is used for a different reason on construction sites in the UK. Small power tools and lighting are supposed to be supplied by a local center-tapped transformer with a voltage of 55V between each power conductor and the earth. This significantly reduces the risk of electrocution in the event that one of the live conductors becomes exposed through an equipment fault whilst still allowing a reasonable voltage for running the tools.

A third wire is usually (should be always but there are many older, non-compliant, or third world installs where it is not) connected between the individual electrical appliances in the house and the main consumer unit or distribution board. The third wire is known in Britain and most other English-speaking countries as the earth wire, but in North America it is the ground wire. Exactly what happens to the ground wire before the main board varies, but there are three main possibilities, which are listed here by their European names:

• TT (customer's earth not connected to neutral at all)
• TN-S (neutral and earth run back separately to the transformer star point)
• TN-C-S (neutral and earth are joined at the intake position).

There is also TN-C where neutral and earth are joined right through the install, but this is much less common than the others and requires special procedures to make it safe.

A system should be designed so that in the event of a short to earth on any part of the system some form of fuse or breaker will make the system safe. In a TT system the high earth loop impedance means that a Residual-Current Device (RCD) must be used. In other earthing systems this can be covered by the normal overcurrent protention systems. RCDs may still be used on such systems though as they can protect against small earth faults such as through a person.

## AC frequencies by country

Most countries in the world have standardised their electricity supply systems to one of two frequencies: 50 hertz or 60 hertz. The list of 60 hertz countries, most of them in the New World, is shorter, but this is not to say that 60 hertz is less common. The 60 hertz countries are: American Samoa, Antigua and Barbuda, Aruba, Bahamas, Belize, Bermuda, Canada, Cayman Islands, Colombia, Costa Rica, Cuba, Dominican Republic, El Salvador, French Polynesia, Guam, Guatemala, Guyana, Haiti, Honduras, South Korea, Marshall Islands, Mexico, Micronesia, Montserrat, Nicaragua, Northern Mariana Islands, Palau, Panama, Peru, Philippines, Puerto Rico, Saint Kitts and Nevis, Suriname, Taiwan, Trinidad and Tobago, Turks and Caicos Islands, United States, Venezuela, Virgin Islands (U.S.), Wake Island.[1]

The following countries have a mixture of 50 Hz and 60 Hz supplies: Bahrain, Brazil (mostly 60 Hz), Japan (60 Hz used in western prefectures), Liberia (now officially 50 Hz, formerly 60 Hz and many independent 60 Hz generating plants still exist). [2]

It is generally accepted that Nikola Tesla chose 60 hertz as the lowest frequency that would not cause street lighting to flicker visibly. The origin of the 50 hertz frequency used in other parts of the world is open to debate but seems likely to be a rounding off of 60hz to the 1 2 5 10 structure popular with metric standards.

Other frequencies were somewhat common in the first half of the 20th century, and remain in use in isolated cases today, often tied to the 60 Hz system via a frequency changer . 25 Hz power was used in most of Ontario, Quebec and the northern USA. In the 1950's, much of this electical system, from the generators right through to household appliances, was converted and standardised to 60 Hz. Some 25 Hz generators are still in use at Niagara Falls for large industrial customers who did not want to replace existing equipment. The lower frequency eases the design of low speed electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type motors for electric traction applications such as railways, but also causes a noticeable flicker in incandescent lighting.

Most countries have chosen their television standard to match their mains supply frequency.

Off-shore, textile industry, marine, computer mainframe, aircraft and spacecraft applications sometimes use 400Hz, for technical benefits of reduced weight of apparatus or higher motor speeds. 16.67 Hz power is still used in some European rail systems, such as in Sweden and Switzerland.

AC-powered appliances can give off a characteristic hum at the multiples of the frequencies of AC power that they use.

## Mathematics of AC voltages

Alternating currents are usually associated with alternating voltages. An AC voltage v can be 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 radians per 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 can also be stated as a root mean square (rms) value, written Vrms. For a sinusoidal voltage:

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

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 average power P into the same load if Vrms = VDC. Because of this fact rms is the normal means of measuring voltage in mains (power) systems.

To illustrate these concepts, consider the 240 V AC mains used in the UK (it should be noted that the UK is now officially 230 V +10% −6% but in reality voltages are still closer to 240 V than 230 V in most cases). 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:

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

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

Note that non-sinusoidal waveforms have a different relationship betweeen their peak magnitude and effective (RMS) value. This is of practical significance when working with non-linear circuit elements that produce harmonic currents.

The European Union (including the UK) have now officially harmonized on a supply of 230 V 50 Hz. However they made the tolerance bands very wide at ±10%. Some countries actually specify stricter standards than this for example the UK specifies 230 V +10% −6%. Most supplies to the old standards therefore conform to the new one and do not need to be changed.