- Reactance (electronics)
**Reactance**is a circuit element's opposition to an alternating current, caused by the build up of electric or magnetic fields in the element due to the current. Both fields act to produce counter emf that is proportional to either the rate of change (time derivative), or accumulation (time integral) of the current. In vector analysis, Reactance is theimaginary part ofelectrical impedance , used to compute amplitude and phase changes of sinusoidalalternating current going through the circuit element. It is denoted by the symbol $scriptstyle\{Chi\}$. The SI unit of reactance is the ohm.Both reactance $scriptstyle\{Chi\}$ and resistance $scriptstyle\{R\}$ are required to calculate the impedance $scriptstyle\{\; ilde\{Z$, although in some circuits one of these may dominate: an approximate knowledge of the minor component is useful to determine if it may be neglected.

:$ilde\{Z\}\; =\; R\; +\; jChi$

Both the magnitude $scriptstyle$ and the phase $scriptstyle\{\; heta\}$ of the impedance depend on both the resistance and the reactance.

:$|\; ilde\{Z\}|\; =\; sqrt\{ZZ^*\}\; =\; sqrt\{R^2\; +\; Chi^2\}$

:$heta\; =\; arctan\{left(\{Chi\; over\; R\}\; ight)\}$

The magnitude is the ratio of the

voltage and currentamplitude s, while the phase is the voltage–current phase difference.* If $scriptstyle\{Chi\; >\; 0\}$, the reactance is said to be "inductive"

* If $scriptstyle\{Chi\; =\; 0\}$, then the impedance is purely "resistive"

* If $scriptstyle\{Chi\; <\; 0\}$, the reactance is said to be "capacitive"The reciprocal of reactance is

susceptance .**Physical significance**Determining the voltage-current relationship requires knowledge of both the resistance and the reactance. The reactance on its own gives only limited physical information about an electrical component or network.

# A positive reactance implies that the circuit is inductive, where phase of the voltage "leads" the phase of the current; while a negative reactance implies that the circuit is capacitive, where phase of the voltage "lags" the phase of the current

# A reactance of zero implies the current and voltage are in phase and conversely if the reactance is non-zero then there is a phase difference between the voltage and currentThere are certain specific effects that depend on the reactance alone, for example; resonance in an series

RLC circuit occurs when the reactances "X_{C}" and "X_{L}" are equal but opposite, and the impedance has a phase angle of zero.**Capacitive reactance****Capacitive reactance**$scriptstyle\{Chi\_C\}$**is**inversely proportional to the signalfrequency $scriptstyle\{f\}$ and the capacitance $scriptstyle\{C\}$.:$Chi\_C\; =\; -frac\; \{1\}\; \{omega\; C\}\; =\; -frac\; \{1\}\; \{2pi\; f\; C\}quad$

A capacitor consists of two conductors separated by an insulator, also known as a

dielectric .At low frequencies a capacitor is

open circuit , as no current flows in the dielectric. A DC voltage applied across a capacitor causes charge to accumulate on one side; theelectric field due to the accumulated charge is the source of the opposition to the current. When thepotential associated with the charge exactly balances the applied voltage, the current goes to zero.Driven by an AC supply, a capacitor will only accumulate a limited amount of charge before the potential difference changes sign and the charge dissipates. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current.

**Inductive reactance**Inductive reactance $scriptstyle\{Chi\_L\}$ is

proportional to the signalfrequency $scriptstyle\{f\}$ and the inductance $scriptstyle\{L\}$.:$X\_L\; =\; omega\; L\; =\; 2pi\; f\; Lquad$

An inductor consists of a coiled conductor. Faraday's law of electromagnetic induction gives the back emf $scriptstyle\{mathcal\{E$ (voltage opposing current) due to a rate-of-change of

magnetic flux density $scriptstyle\{B\}$ through a current loop.:$mathcal\{E\}\; =\; -$dPhi_B} over dt}quad

For an inductor consisting of a coil with $N$ loops this gives.

:$mathcal\{E\}\; =\; -N\{dPhi\_B\; over\; dt\}quad$

The back-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 ashort-circuit (it is typically made from a material with a lowresistivity ). Analternating current has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency.**Phase relationship**The phase of the voltage across a purely reactive device (a device with a resistance of zero) "lags" the current by $scriptstyle\{pi/2\}$ radians for a capacitive reactance and "leads" the current by $scriptstyle\{pi/2\}$ radians for an inductive reactance. Note that without knowledge of both the resistance and reactance we cannot determine the voltage--current relationships.

The origin of the different signs for capacitive and inductive reactance is the phase factor in the impedance.

:$ilde\{Z\}\_C\; =\; \{1\; over\; omega\; C\}e^\{j(-\{pi\; over\; 2\})\}\; =\; jleft(-\{1\; over\; omega\; C\}\; ight)\; =\; jChi\_Cquad$

:$ilde\{Z\}\_L\; =\; omega\; Le^\{j\{pi\; over\; 2$ = jomega L = jChi_Lquad

For a reactive component the sinusoidal voltage across the component is in quadrature (a $scriptstyle\{pi/2\}$ phase difference) with the sinusoidal current through the component. The component alternately absorbs energy from the circuit and then returns energy to the circuit, thus a pure reactance does not dissipate power.

**References**# Pohl R. W. "Elektrizitätslehre." – Berlin-Gottingen-Heidelberg: Springer-Verlag, 1960.

# Popov V. P. "The Principles of Theory of Circuits." – M.: Higher School, 1985, 496 p. (In Russian).

# Küpfmüller K. "Einführung in die theoretische Elektrotechnik," Springer-Verlag, 1959.

#**ee also***

Susceptance

*Magnetic reactance **External links*** [

*http://www.magnet.fsu.edu/education/tutorials/java/inductivereactance/index.html Interactive Java Tutorial on Inductive Reactance*] National High Magnetic Field Laboratory

* [*http://www.geocities.com/SiliconValley/2072/elecrri.htm Resistance, Reactance, and Impedance*]

* [*http://www.sweethaven.com/sweethaven/ModElec/dcac/SunShine/LessonMain01.asp?uNum=221 Inductive Reactance: Endless Examples & Exercises*]

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