# Alternating current

Alternating current denotes electrical current that changes its direction (polarity) in regular repetition and in which positive and negative instantaneous values ​​complement each other in such a way that the current is zero on average over time. The alternating current must be distinguished from direct current , which does not change over time (apart from switching processes or influencing effects), and mixed current as a superposition of the two.

All over the world, the electrical energy supply is most often made with sinusoidal alternating current. The reasons for this preference are the simple generation and simple transformation of the alternating voltage . Single-phase alternating current is common in households . There is also an advantageous concatenation as a three-phase alternating current system. For the energy transmission, the active and reactive current components of the alternating current must be observed.

Internationally, alternating current is often referred to in English as alternating current or with the abbreviation AC , which is also used for alternating voltage . In contrast, DC stands for direct current, which is used to identify both direct current and direct voltage .

law: Your square sinusoidal as well but a DC component containing mixed size

## generation

### Temporal course

Above: Mixed current created from sinusoidal current through rectification
Below: Its alternating current component

The simplest conceivable form of alternating current is created by constantly changing polarity reversal of a direct current source . Although this alternating current is technically useful, it is not used for large-scale energy supply . The reason is the extended frequency spectrum of such a voltage curve, which includes additional, significantly higher frequencies than just the basic frequency . This very high proportion of harmonics would cause a high expenditure of energy in the transformation and long-distance transmission of the electrical current. For the same reason, it is not allowed to send with square wave voltage in radio technology because the very intense harmonics would interfere with other radio services. The rectangular shape is used in small devices such as switched-mode power supplies in computers or choppers for generating high voltage from batteries, because it can be produced technically very easily with switching components of power electronics . Small devices can be shielded in such a way that the harmonics do not interfere with other devices.

"Sinusoidal alternating current" is used almost exclusively in the energy supply because it does not have any undesired harmonic oscillations. It gets its name from the fact that the instantaneous values ​​over a full period with a positive and a negative half-oscillation correspond exactly to the values ​​of the sine angle function over a full circle (0-360 °), the graphical representation on a time axis gives the typical sine curve.

Other graph shapes, such as triangular shapes, only occur with very little power in measurement technology , impulse technology , electronic sound generation or analog communications technology .

### Multi-phase alternating current

Sinusoidal oscillations in a three-phase system

In addition to alternating current as a single-phase conductor current , interlinked alternating currents offset in their phase angles are used to supply energy in the rotating electrical machines . The generator coils required for this are evenly distributed around the circumference. With three phase angles of 120 ° each, this special form of alternating current is known as three-phase alternating current and colloquially as "three-phase current".

The individual alternating currents of the three-phase system can be used independently of one another as a single system for small consumers. The three external conductor currents , which are shifted against each other in time, have the advantage, among other things, that the total conductor cross-sections can be reduced with the same transmitted power and the long-distance transmission with high-voltage alternating current becomes less lossy due to the interlinking. In addition, inexpensive and robust three-phase asynchronous motors can be built - but with the disadvantage that their speed can only be changed in rough steps without a frequency converter .

In addition, there are other multiphase alternating current systems, such as two-phase alternating current or, in general, multiphase alternating current systems, which, however, are of no essential importance in public electrical energy supply. AC systems with more than three phases are used in special electrical drive systems based on synchronous motors , among other things . The multi-phase alternating current is obtained from the three-phase system by means of an inverter and an intermediate circuit.

## Calculation quantities

### Frequency and period

The frequency describes the number of oscillations of a periodic process related to the time interval for which this number applies. It is specified in the unit Hertz with the unit symbol Hz.

A period is the smallest spatial or temporal interval after which the process repeats. This time interval is called the period . With an alternating current, a period is e.g. B. a successive positive and negative half oscillation. The period is equal to the reciprocal of the frequency${\ displaystyle T}$${\ displaystyle f}$

${\ displaystyle T = {\ frac {1} {f}}}$ .

The best-known AC frequency is 50 Hz, the network frequency of the public electrical energy supply in the European Union. This alternating current has a period of

${\ displaystyle T_ {50} = {\ frac {1} {50 \; \ mathrm {Hz}}} = {\ frac {1} {50}} \ mathrm {s} = 20 \; \ mathrm {ms} }$ .

For an overview of the energy supply in other countries, see country overview of plug types, mains voltages and frequencies .

The angular frequency is preferably used for theoretical calculations, such as in complex AC calculations: ${\ displaystyle \ omega}$

${\ displaystyle \ omega = 2 \ pi \ cdot f}$ .

With an alternating current with a frequency of 50 Hz

${\ displaystyle \ omega _ {50} = 2 \ pi \ cdot 50 \; \ mathrm {Hz} \ approx 314 \; \ mathrm {s} ^ {- 1}}$ .

The lowest alternating current frequency, which is used to a certain extent in Germany, Austria, Switzerland, Sweden and Norway, is found in traction current at 16.7 Hz.

The highest frequency for alternating current is given by the possibilities and requirements in radio technology and is in the order of magnitude of 300 GHz.

### Characteristic values ​​of the current strength

The representation for sinusoidal alternating voltage applies accordingly to the current intensity.
1 = peak value , here also amplitude
2 = peak-valley value
3 = effective value
4 = period duration

The time-dependent course of the alternating current causes problems when specifying the current strength.

• Instantaneous values or instantaneous values are unsuitable for characterization.${\ displaystyle i}$
• The peak value is the highest (independent of the polarity) achievable current strength, it is representative as a special instantaneous value only in the case of a sinusoidal shape and is then referred to as the amplitude ; too often the current is not sinusoidal. Measuring it with an oscilloscope is often difficult (if only for grounding reasons).
• The mean value is defined to be equal to zero.
• The rectified value is the most easily measurable quantity, but has little meaning outside of measurement technology .
• The rms value is the preferred value when energy conversion is important.

The effective value of an alternating current corresponds to the value of a direct current that generates the same heat in an ohmic resistor . It can be measured with an ammeter that generates effective values. The amplitude of  a sinusoidal alternating current can be calculated from the rms value and the crest factor √2 ${\ displaystyle {\ hat {\ imath}}}$

${\ displaystyle {\ hat {\ imath}} = {\ sqrt {2}} \ cdot I _ {\ mathrm {eff}}}$ .

In the case of non-sinusoidal alternating current, there is a different relationship between peak value and rms value, depending on the shape of the curve. For example, if the square-wave alternating current changes after the same times between and : ${\ displaystyle + {\ hat {\ imath}}}$${\ displaystyle - {\ hat {\ imath}}}$

${\ displaystyle {\ hat {\ imath}} = I _ {\ mathrm {eff}}}$ .

Unless otherwise specified, AC currents and AC voltages always refer to the rms values. For example, a current drawn from the power grid with the specification "maximum 2.0 A" may rise

${\ displaystyle {\ hat {\ imath}} = I _ {\ mathrm {eff}} \ cdot {\ sqrt {2}} \ approx 2 {,} 0 \ \ mathrm {A} \ cdot 1 {,} 414 \ approx 2 {,} 8 \ \ mathrm {A}}$ .

### AC resistors

Capacitive phase shift between current and voltage
Inductive phase shift between current and voltage

The linear resistances for alternating current are ohmic resistance , capacitor and coil . Capacitors and coils behave differently with alternating current than with direct current . With sinusoidal alternating currents, they can be treated like resistors, but they also shift the phase angle between the current and voltage curves. In order to distinguish it from ohmic resistance, the term impedance is used here . - Almost all semiconductors behave as non-linear resistors. ${\ displaystyle {\ underline {Z}}}$

• Ohmic resistance with alternating current: An ohmic resistance does not cause a phase shift. In an alternating current circuit with purely ohmic resistances, the current and voltage are in phase. The impedance is equal to the DC resistance .${\ displaystyle {\ underline {Z}} _ {R}}$${\ displaystyle R}$
• Alternating current capacitor: With direct current, a capacitor lets a current flow while charging; in the process, it increasingly builds up a counter-voltage until it interrupts the flow of current. With alternating current, current flows constantly due to the constant charge reversal of the metallic plates, which causes a phase-shifted voltage. A sinusoidal charging current builds up a likewise sinusoidal voltage on the capacitor, delayed by 90 °. The impedance of a "capacitive" load is . Here is the capacitance of the capacitor, the angular frequency and the imaginary unit .${\ displaystyle {\ underline {Z}} _ {C} = (\ mathrm {j} \ omega C) ^ {- 1}}$${\ displaystyle C}$${\ displaystyle \ omega}$${\ displaystyle \ mathrm {j}}$
• Coil with alternating current: In a lossless coil, the voltage leads the current by 90 °, because self-induction (see Lenz's rule ) creates a counter-voltage in the coil, which only allows the current to increase gradually. The impedance of an "inductive" load is through . Where is the inductance of the coil.${\ displaystyle {\ underline {Z}} _ {L} = \ mathrm {j} \ omega L}$${\ displaystyle L}$

For the calculation, reference is made to the complex AC calculation . All measurable physical quantities such as current and voltage are real; the use of complex quantities is purely a mathematical method that simplifies calculations.

### Performance parameters

Time curve of voltage , current strength and power with a purely ohmic consumer${\ displaystyle u}$${\ displaystyle i}$${\ displaystyle p}$

With the voltage and the current , which change over time , applies to the instantaneous value of the power${\ displaystyle u}$${\ displaystyle i}$${\ displaystyle t}$${\ displaystyle p}$

${\ displaystyle p = u \ cdot i}$

In the case of periodic processes, there are time-independent power quantities, namely the real power , the reactive power or the apparent power . ${\ displaystyle P}$ ${\ displaystyle Q}$ ${\ displaystyle S}$

Have to a resistor and always the same sign, so the instantaneous power is always positive, as the picture shows. The current through an ohmic resistor always generates “effective” energy, which is released to the outside as Joule heat ; this energy per time is called real power. It stands for the average performance over time. ${\ displaystyle u}$${\ displaystyle i}$${\ displaystyle p}$

Time curve of voltage , amperage and power with a purely inductive consumer${\ displaystyle u}$${\ displaystyle i}$${\ displaystyle p}$

If coils (inductances) or capacitors (capacitances) are contained in a circuit, phase shifts occur with sinusoidal values . In the case of an ideally inductive consumer, the energy supplied by the voltage source is used to build up the magnetic field. The energy is initially stored in the magnetic field, but with the periodic change in the sign of the voltage, the field is reduced again and the energy is fed back into the network, as the picture shows with negative values ​​of . The same applies to capacitive consumers. The mean over time shows that an ideal reactance does not draw any real power. The energy per time that oscillates in the network is called the displacement reactive power. ${\ displaystyle p}$${\ displaystyle p}$

The apparent power is a quantity formed from the effective values ​​of voltage and current, in which the temporal relationships between and are ignored. ${\ displaystyle u}$${\ displaystyle i}$

For the exact definitions and further details, reference is made to the three articles of the performance parameters mentioned.

## history

Michael Faraday created the basic requirements for today's “electricity from the socket” in 1831 with his investigations into electromagnetic induction. His basic research made it possible to convert mechanical power into electrical power .

The magnetoelectric machines of the first epoch, such as those of the Anglo-French Societé anonyme de l'Alliance based on Floris Nollet , operating in Belgium , were bulky and uneconomical with their permanent magnets. Around the middle of the century, however, the dynamo-electric principle was discovered, which replaced the previously used steel magnets with self-inducing electromagnets and therefore led to greater economic efficiency. The first discoverer, the Dane Søren Hjorth , had his generator patented in England in 1854. The next builder of such a machine, Ányos Jedlik , did not fully understand it and hoped for further development to the perpetual motion machine . Werner Siemens was the third and achieved an economic breakthrough in 1866 with the dynamo-electric generator.

The historical development of different systems is described under current warfare . An essential component for the widespread dissemination and application of alternating current technology was the development of the transformer , in which several researchers, engineers and businessmen in different countries were significantly involved between 1870 and 1910, some of them independently of one another.

With the Reichenhall electricity works , the wood pulp manufacturer Konrad Fischer built Germany's first public alternating current power station in Bad Reichenhall , which went into operation on May 15, 1890. It was the first hydropower plant in Germany and the first public power plant in Bavaria. A countershaft having two conical wheels and a belt drive , a rendered jonval turbine hydropower 600 min -1 to an alternating current generator from Oerlikon in Zurich , the 2000V voltage developed and a maximum of 30 amperes. At the time of commissioning, the plant was able to supply 1200 light bulbs in Reichenhall, Karlstein and Kirchberg .

The operators of the Niagara hydropower plant are offering a \$ 100,000 prize to anyone who develops a solution to transmit electrical power over long distances. The decision was made in 1893 in favor of the alternating current system developed by Nikola Tesla and George Westinghouse .

## Consideration in high frequency technology

At a mains frequency of 50 Hz, the wavelength is 6000 km, which is considerably larger than Germany. In most AC components, it can therefore be neglected that the AC current is a wave. At higher frequencies, such as in the high frequency range , the skin effect (current displacement) occurs, which leads to a restriction of the actually conductive layer to the outer areas of a conductor. At 50 Hz this penetration depth is 12 mm for aluminum and 10 mm for copper. While this is not relevant for lines in domestic use, lines for highest currents, e.g. B. in generators, sometimes designed as a waveguide (such a conductor can also be used to guide coolant). When transmitting energy via overhead lines , a combination of steel and aluminum is often used as the conductor cable. Steel as a core for tensile strength surrounded by aluminum for electrical conductivity.

## Biological effect on humans

The effect and possible dangers of electricity on the human body arises in part from the influence of the conduction system of the heart : There excitations are transmitted as electrical impulses, leading to the orderly contraction of the heart muscle. Electricity supplied from the outside interferes with this spread of excitation, especially when it excites cells of the heart during the so-called vulnerable phase . In this phase, parts of the heart are still excited - that is, they cannot be re-excited - while other parts are already on the way to the non-aroused state, that is to say they are partially excitable again. If additional excitation is triggered in the vulnerable phase, this can lead to disordered excitation of the heart muscle cells, known as ventricular fibrillation . Blood can no longer be pumped due to the uneven, rapid contractions of the heart muscle cells.

The particular danger of alternating current compared to direct current arises from the fact that alternating current is more likely to hit the vulnerable phase due to the rapid change in polarity .

The consequences of an electrical accident with alternating current on people depend on various factors, in particular the type and frequency of the current (see above) and the length of time that the current affects the body. This explains why, for example, an electric shock caused by an electric pasture fence has no lasting effects on people or animals, as the current pulses are too short to excite the nerve cells. Finally, the path that the current takes through the body also plays a role, with the vertical path through which the current flows through all vital organs being the most dangerous.

Ultimately, the current strength per area, i.e. the current density , as well as its duration of action determine the effects. For example, high currents at the entry and exit points cause burns to the skin, which are called current brands . The following table provides an indication of the expected effects on the human body. However, these values ​​are strongly dependent on the current path and only apply if the current is distributed in the body via the skin resistance and not e.g. B. focused on the heart muscle . For the heart muscle itself, 0.01 mA is sufficient to trigger ventricular fibrillation . If, for example, electrodes are implanted under the skin or even in the vicinity of the heart or other sensitive organs, the magnitudes of leakage currents that are comparatively permissible in normal household appliances can be life-threatening.

varies greatly according to the current path and exposure time
Amperage effect
below 0.5 mA imperceptible (may be perceptible with the tongue )
10 ... 25 mA Contractions of the finger muscles (release limit), increase in blood pressure, no effect on the cardiac conduction system, possibly already fatal for children
25 ... 80 mA Unconsciousness, arrhythmia , increase in blood pressure
80 mA… 3 A Respiratory arrest, circulatory arrest due to ventricular fibrillation or asystole

The corresponding specification of touch voltages is only possible (see Ohm's law ) if the corresponding body resistance is known. For example, in the case of the house power connection (230 V) and a body resistance of approximately 3 kΩ (with a current path between a fingertip of the left hand and a fingertip of the right hand under different conditions ), the result is a current of approx. 75 mA, which corresponds to the above reactions mentioned and can lead to death as a result. Damp or wet skin can massively reduce body resistance. Touching objects under low voltage ( <50 V) is not considered to be life-threatening for adults. ${\ displaystyle U _ {\ sim}}$

## literature

• Klaus Lunze: Theory of alternating current circuits: textbook. Verlag Technik, Berlin 1991, ISBN 3-341-00984-1 .
• Heinz Rieger: Alternating voltage, alternating current. Publicis Corporate Publishing, Erlangen 1992, ISBN 3-8009-4036-1 .
• Paul Vaske: Calculation of AC circuits. Teubner, Stuttgart 1985, ISBN 3-519-20065-1 .
• Gert Hagmann: Fundamentals of electrical engineering. 15th edition. AULA publishing house. Wiebelsheim, ISBN 978-3-89104-747-7

Wiktionary: Alternating current  - explanations of meanings, word origins, synonyms, translations
Commons : alternating current  - collection of pictures, videos and audio files

## Individual evidence

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4. ^
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