In electrical and electronic systems, reactance is the opposition of a circuit element to a change in current or voltage, due to that element's inductance or capacitance. A built-up electric field resists the change of voltage on the element, while a magnetic field resists the change of current. The notion of reactance is similar to electrical resistance, but it differs in several respects.
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In phasor analysis, reactance is used to compute amplitude and phase changes of sinusoidal alternating current going through a circuit element. It is denoted by the symbol
Capacitive reactance
A capacitor consists of two conductors separated by an insulator, also known as a dielectric.
Capacitive reactance is an opposition to the change of voltage across an element. Capacitive reactance
There are two choices in the literature for defining reactance for a capacitor. One is to use a uniform notion of reactance as the imaginary part of impedance, in which case the reactance of a capacitor is a negative number:
Another choice is to define capacitive reactance as a positive number,
In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e.
At low frequencies a capacitor is an open circuit so no current flows in the dielectric.
A DC voltage applied across a capacitor causes positive charge to accumulate on one side and negative charge to accumulate on the other side; the electric field due to the accumulated charge is the source of the opposition to the current. When the potential associated with the charge exactly balances the applied voltage, the current goes to zero.
Driven by an AC supply (ideal AC current source), a capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge is returned to the source. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current.
Inductive reactance
Inductive reactance is a property exhibited by an inductor, and inductive reactance exists based on the fact that an electric current produces a magnetic field around it. In the context of an AC circuit (although this concept applies any time current is changing), this magnetic field is constantly changing as a result of current that oscillates back and forth. It is this change in magnetic field that induces another electric current to flow in the same wire, in a direction such as to oppose the flow of the current originally responsible for producing the magnetic field (known as Lenz’s Law). Hence, inductive reactance is an opposition to the change of current through an element.
For an ideal inductor in an AC circuit, the inhibitive effect on change in current flow results in a delay, or a phase shift, of the alternating current with respect to alternating voltage. Specifically, an ideal inductor (with no resistance) will cause the current to lag the voltage by a quarter cycle, or 90°.
In electric power systems, inductive reactance (and capacitive reactance, however inductive reactance is more common) can limit the power capacity of an AC transmission line, because power is not completely transferred when voltage and current are out-of-phase (detailed above). That is, current will flow for an out-of-phase system, however real power at certain times will not be transferred, because there will be points during which instantaneous current is positive while instantaneous voltage is negative, or vice versa, implying negative power transfer. Hence, real work is not performed when power transfer is “negative”. However, current still flows even when a system is out-of-phase, which causes transmission lines to heat up due to current flow. Consequently, transmission lines can only heat up so much (or else they would physically "sag" too much), so transmission line operators have a “ceiling” on the amount of current that can flow through a given line, and excessive inductive reactance can limit the power capacity of a line.
Inductive reactance
The average current flowing through an inductance
Because a square wave has multiple amplitudes at sinusoidal harmonics, the average current flowing through an inductance
making it appear as if the inductive reactance to a square wave was about 19% smaller
Any conductor of finite dimensions has inductance; the inductance is made larger by the multiple turns in an electromagnetic coil. Faraday's law of electromagnetic induction gives the counter-emf
For an inductor consisting of a coil with
The counter-emf is the source of the opposition to current flow. A constant direct current has a zero rate-of-change, and sees an inductor as a short-circuit (it is typically made from a material with a low resistivity). An alternating current has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency.
Impedance
Both reactance
where:
When both a capacitor and an inductor are placed in series in a circuit, their contributions to the total circuit impedance are opposite. Capacitive reactance
where:
Hence:
Note however that if
but the ultimate value is the same.
Phase relationship
The phase of the voltage across a purely reactive device (a capacitor with an infinite resistance or an inductor with a resistance of zero) lags the current by
The origin of the different signs for capacitive and inductive reactance is the phase factor
For a reactive component the sinusoidal voltage across the component is in quadrature (a