Electrical reactance

The reactance ( reactance also ) is a quantity of electrical engineering, an alternating current is limited by building an AC voltage and causes a temporal phase shift between voltage and current. The value of the reactance is frequency dependent. The addition of "blind" comes from the fact that electrical power to the reactances indeed transported, but not where it is converted into thermal, mechanical or chemical energy.

Reactance in the complex AC circuit analysis

The reactance is a physically real quantity for existing operations in AC technology. A mathematical treatment of sinusoidal operations is possible with trigonometric functions, but often tedious. To facilitate the calculation can be mathematically elegant performed with complex quantities, after which the results are to be transferred in real quantities.

The reactance is in the complex AC circuit analysis of the imaginary part of the complex impedance (impedance). The real part of is referred to as resistive. The Pythagorean sum of active and reactive resistance is called impedance. Complex variables are in this bill, the instantaneous values ​​of voltage and current.

The unit of reactance is - just as with the effective resistance - the ohm with the unit symbol Ω.

General:

It follows for the reactance:

Or

Inductive and capacitive reactance

Capacitors and inductors are energy storage. The flow of current creates a capacitor to an electric field; upon application of a voltage to a coil it builds up a magnetic field. A current or voltage source is removed during this time electrical energy. This energy may, however, be recirculated in a reversal of the direction of the current or voltage source, - in contrast to an active resistor. The course of the energy transport is determined by the course of the voltage or the current.

The most commonly studied course in electrical engineering is that of sinusoidal alternating quantities. In this case, the following charge and discharge of the energy store by means of a sinusoidal periodic voltage waveform and a phase-shifted sinusoidal current flow ( " reactive current "). The ratio between the voltage and the duration of a quarter period shifted current is referred to as reactance, the oscillating energy between the source and the energy storage as the reactive energy.

In a transient, one-time charging or discharging the course of the captured or emitted energy of an exponential function. Can be determined this time courses in particular by solving differential equations.

Reactance of sinusoidal signals

The derivation of the following equations can be found under the headings of complex AC circuit analysis and electrical resistance.

Coil

For an ideal coil with the inductance is its impedance

Where j is the imaginary unit.

Your reactance, also called inductance, is the imaginary part of the impedance:

It is a linear reactance (of voltage or current independent ) alternating current resistance, but increases with the frequency (or increasing angular frequency ). A calculation example for the inductive resistance is seen here.

Capacitor

For an ideal capacitor of capacitance is its impedance

Its reactance, historically referred to as capacitance, is the imaginary part of the impedance:

The reactance of an ideal capacitor is also an AC linear resistance whose magnitude with increasing frequency but smaller.

Reactance with non-sinusoidal signals

In a non- sinusoidal waveform of voltage or current can not specify a clear reactance. Any periodic signal can be represented by a sum of sinusoidal signals of different frequencies, which is the basis of the Fourier analysis. This in addition to the sinusoidal fundamental vibration occurring harmonics have to be observed each for themselves and their reactances are determined. A single reactance value can not be given, but it is a superposition of different reactances at different frequencies and different voltage and current amplitudes to be determined. Thus, the current waveform is distorted with respect to the voltage curve. This occurs, for example, in non-linear loads such as switching power supplies, or inductive components, which are in magnetic saturation on.

Reactances in DC

The derivation in DC requires a different mathematical approach than for reactances, which presupposes sinusoidal alternating quantities. Nevertheless, the result comes out right when you can strive against the frequency ω the limit zero. A frequency of 0 Hz corresponds to a time constant value.

This is found to be in DC for the coil reactance:

Resulting in a vanishingly small resistance at an ideal coil. Practically, this means that a coil in a DC circuit generates a direct connection or a short circuit; leaving only the wire resistance is not included in the final equation.

Accordingly, the reactance of a capacitor results in DC to:

What the ideal capacitor results in an infinitely high resistance. In practice this means, that a capacitor in the dc circuit generates an interrupt; it flows only in the last equation is not contained very low leakage current.

Reactance of an electrical load to the mains

An ideal linear reactance caused only reactive power in the network, but it consumes no active power. The need for setting up and dismantling of electric or magnetic fields, electrical energy is returned to the producer, but charged the lines.

However reactances never occur alone, as there are no lossless circuits in practice. So reactances are always associated with active resistors that actually implement performance.

Predominates in a consumer the inductive reactance compared to the capacitive, the consumer is called a resistive- inductive, resistive- capacitive otherwise than.

Example: The series reactor under fluorescent and gas discharge lamps is an inductive resistor ( reactance ) for current limiting and therefore causes over a resistor only small losses (resistive and magnetic losses).

The following loads are resistive- inductive usually:

• Electric motors
• Transformers
• Fluorescent and gas discharge lamps with conventional ballast, if not compensated
• Sagittarius

The following loads are resistive- capacitive usually:

• Switching power supply without power factor correction (English: Power Factor Correction PFC), including many computer power supplies
• Capacitor power supplies
• Frequency without PFC
• Lamps with a series arrangement of inductor and capacitor ( used for reactive power compensation of lighting fixtures without this series circuit )
• Capacitors for reactive power compensation ( separate cabinets or incorporated into luminaires and other inductive loads )

The first two capacitive loads are - if they have no switching measures for power factor correction - due to the input rectifier and non-linear loads; they not only produce reactive power, therefore, harmonics in the supply network.