# AC voltage

Alternating voltage is an electrical voltage whose polarity changes in regular repetition, but whose mean value over time is zero according to standardization . The curve shape of the voltage is irrelevant and in no way tied to the sine curve .

Above: Mixed voltage created from sinusoidal alternating voltage by rectification
Below: Its alternating voltage component

## Notation

The symbol for the physical quantity "electrical voltage" is this ; in confusion with DC or pulsating voltage an AC voltage is (terms invention) characterized by the tilde as an index, ie  . Under no circumstances is the unit symbol V for volts to be marked. For an alternating voltage of 230 V. ${\ displaystyle U}$${\ displaystyle U _ {\ sim}}$

${\ displaystyle U _ {\ sim} = \ 230 \; \ mathrm {V}}$

to write. If the tilde can not be used is derived from the Anglo-Saxon world, the index AC (Engl. Alternating current ) used - both current (Engl. Current as well as voltage) (Engl. Voltage ), so  . The addition to the volt as the unit symbol VAC ( volts alternating current ) is, as above, not permissible according to German standards. ${\ displaystyle U _ {\ mathrm {AC}}}$

If the variable is shown as a time-dependent instantaneous value, lowercase letters are used, i.e. for voltage or . ${\ displaystyle u}$${\ displaystyle u (t)}$

## Definitions and delimitations

Temporal progression of changing variables

### definition

In order for an electrical voltage that changes over time to be called alternating voltage, it must meet two criteria in accordance with the standardization mentioned: ${\ displaystyle u (t)}$

• It is periodic and therefore satisfies with the period for all integers${\ displaystyle T}$${\ displaystyle n}$
${\ displaystyle u (t) = u (t + n \ cdot T)}$.
• Their equivalence is zero, so it applies to any point in time${\ displaystyle t_ {1}}$
${\ displaystyle \ int _ {t_ {1}} ^ {T + t_ {1}} u (t) \; \ mathrm {d} t = 0}$,

or equivalent: The area between the curve and the zero line is partly positive and partly negative and complements itself to zero after a period.

### Examples

• The noise is a stochastic process , the time, but periodically does not pass; therefore, the noise voltage is not an alternating voltage. In communications engineering , the noise voltage is sometimes incorrectly equated with the alternating voltage or defined as a special form of alternating voltage if the required properties of alternating quantities (e.g. periodicity ) are insignificant or negligible for the process under consideration.
• A one-time switching process does not meet the criteria of a periodic process either.
• A periodically repeating switching process, which switches between a positive and a negative voltage, then generates an alternating voltage when the equivalence of the voltage thus generated is zero.

## use

The AC voltage best known from everyday life is the mains voltage from the socket. The AC voltage is about the general form of Ohm's law with the AC linked, so it is subject to particular rules of calculation with load resistors for DC resistance even an AC resistance have, see complex alternating current calculation .

In addition to this application for electricity supply , AC voltage is also used in communications engineering. An example of this is the microphone , which generates an alternating voltage that depicts the recorded sound event. In electrical signal processing and measurement technology , it occurs continuously in various forms. If a mixed voltage is fed to an alternating voltage coupling (e.g. by means of a capacitor ), only the alternating voltage component is transmitted.

## Parameters

A sinusoidal alternating voltage.
1 = peak value , here also amplitude ,
2 = peak-valley value,
3 = effective value,
4 = period duration
Nominal value (using the mains voltage as an example)
The nominal value of a voltage, as it is indicated, for example, on nameplates , is its rms value. However, due to losses in the supply lines of the distribution network, the voltage actually available is load-dependent. Through technical advances, the tolerance of the mains voltage has been reduced several times over the course of history. The nominal voltages of 220 V with permissible deviations of +20% / - 10%, 230 V with ± 10% or 240 V with ± 5% are therefore the same supply network whose nominal voltage has been changed by changing the current voltage within the tolerance range of the contractually agreed nominal voltage; see also rated voltage .
Rms value
The effective value (engl. Root mean square , RMS) voltage corresponds mathematically to the root of the mean over the square of the voltage or current function during an integer number of periods. The rms value corresponds to the DC voltage at which the same power is transmitted to an ohmic consumer. The term "230 V" for the AC voltage common in households is an effective value.${\ displaystyle U _ {\ mathrm {eff}}}$
Maximum value, peak value, peak value, amplitude
The peak value (when the AC voltage peak value called for sinusoidal path and amplitude ) is the highest achievable (regardless of the polarity) voltage level. With a given effective value of a defined voltage curve, the peak value can be calculated, but only statistical information is possible for random voltage curves (audio, noise, ...).${\ displaystyle U _ {\ mathrm {s}}}$ ${\ displaystyle {\ hat {u}}}$${\ displaystyle {\ hat {u}}}$
Oscillation range, formerly peak-peak voltage
This peak-to-valley value is the difference between the positive and negative peak values ​​of the voltage function. In the case of sinusoidal voltage, it is twice the amplitude.${\ displaystyle U _ {\ mathrm {ss}}}$
Rectified value
The rectified value is the mean value of the rectified voltage. This is the easiest to measure. Many simple measuring devices measure this value and display it multiplied by the sine form factor 1.11 as the "rms value". The devices therefore only measure correctly if the curve shape is sinusoidal.
Form factor
The form factor indicates the ratio of the rms value to the rectified value. With sinusoidal alternating voltage it is 1.111 (exact  ). In the case of statistical voltage profiles, the form factor, in contrast to the crest factor, is also a unique number if the statistical behavior is defined (e.g. 1.11 for white noise ).${\ displaystyle \ pi / {\ sqrt {8}}}$
Crest factor
The crest factor (engl. Crest factor ) is the ratio of the peak value to the RMS value. This factor can be used to convert the two quantities rms value and peak value. For example, the crest factor of a sinusoidal alternating voltage is 1.414 (exactly  ). However, this only applies to periodic and precisely defined voltage curves; for any voltage curves (measured values, noise, etc.), the crest factor only makes statistical statements about a required amplitude probability (e.g. for noise with a Gaussian distribution )${\ displaystyle {\ sqrt {2}}}$
frequency
The frequency indicates the number of periodically occurring oscillations in relation to the time in which they are counted. In principle, any frequency is possible; in technical use and manageability, alternating voltages are rather rare. In theoretical treatments, especially sinusoidal vibrations, the angular frequency is also used for calculations.${\ displaystyle f> 0}$${\ displaystyle f <16 {\ text {Hz}}}$ ${\ displaystyle \ omega = 2 \ pi f}$

## Specialist literature

• Ernst Hörnemann, Heinrich Hübscher: Electrical engineering specialist training in industrial electronics. 1st edition, Westermann Schulbuchverlag GmbH, Braunschweig 1998, ISBN 3-14-221730-4 .
• Günter Springer: Expertise in electrical engineering. 18th edition, Verlag Europa-Lehrmittel, 1989, ISBN 3-8085-3018-9 .
• Horst Stöcker: Pocket book of physics. 4th edition, Verlag Harry Deutsch, Frankfurt am Main 2000, ISBN 3-8171-1628-4 .
• Wilfried Weißgerber: Electrical engineering for engineers. 4th edition, Verlag Vieweg, 2008, ISBN 978-3834805027 .