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In electrical circuits, reactance is the opposition presented to
alternating current Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating current is the form in w ...
by
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
and
capacitance Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...
. It's measured in Ω (Ohms). Along with resistance, it is one of two elements of impedance; however, while both elements involve transfer of electrical energy, no dissipation of electrical energy as heat occurs in reactance; instead, the reactance stores energy until a quarter-cycle later when the energy is returned to the circuit. Greater reactance gives smaller current for the same applied
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
. Reactance is used to compute
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
and phase changes of sinusoidal alternating current going through a circuit element. Like resistance, reactance is measured in
ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (1 ...
s, with positive values indicating ''inductive'' reactance and negative indicating ''capacitive'' reactance. It is denoted by the symbol X. An ideal
resistor A resistor is a passive two-terminal electronic component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active e ...
has zero reactance, whereas ideal reactors have no shunt conductance and no series resistance. As
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
increases, inductive reactance increases and capacitive reactance decreases.


Comparison to resistance

Reactance is similar to resistance in that larger reactance leads to smaller currents for the same applied voltage. Further, a circuit made entirely of elements that have only reactance (and no resistance) can be treated the same way as a circuit made entirely of resistances. These same techniques can also be used to combine elements with reactance with elements with resistance but
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
s are typically needed. This is treated below in the section on impedance. There are several important differences between reactance and resistance, though. First, reactance changes the phase so that the current through the element is shifted by a quarter of a cycle relative to the phase of the voltage applied across the element. Second, power is not dissipated in a purely reactive element but is stored instead. Third, reactances can be negative so that they can 'cancel' each other out. Finally, the main circuit elements that have reactance (capacitors and inductors) have a frequency dependent reactance, unlike resistors which have the same resistance for all frequencies, at least in the ideal case. The term ''reactance'' was first suggested by French engineer Édouard Hospitalier in ''L'Industrie Electrique'' on 10 May 1893. It was officially adopted by the
American Institute of Electrical Engineers The American Institute of Electrical Engineers (AIEE) was a United States–based organization of electrical engineers that existed from 1884 through 1962. On January 1, 1963, it merged with the Institute of Radio Engineers (IRE) to form the Inst ...
in May 1894.


Capacitive reactance

A capacitor consists of two conductors separated by an insulator, also known as a
dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...
. ''Capacitive reactance'' is an opposition to the change of voltage across an element. Capacitive reactance X_C is
inversely proportional In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio. The ratio is called ''coefficient of proportionality'' (or ''proportionality ...
to the signal
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
f (or
angular frequency In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...
\omega) and the
capacitance Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...
C.Irwin, D. (2002). ''Basic Engineering Circuit Analysis'', page 274. New York: John Wiley & Sons, Inc. 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 the negative number,Glisson, T.H. (2011). ''Introduction to Circuit Analysis and Design'', Springer, p. 408 :X_C = -\frac = -\frac . Another choice is to define capacitive reactance as a positive number,Hughes E., Hiley J., Brown K., Smith I.McK., (2012). ''Hughes Electrical and Electronic Technology'', 11th edition, Pearson, pp. 237-241Robbins, A.H., Miller W. (2012). ''Circuit Analysis: Theory and Practice'', 5th ed., Cengage Learning, pp. 554-558 :X_C = \frac = \frac . In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e. Z_c=-jX_c. At f=0, the magnitude of the capacitor's reactance is infinite, behaving like an open circuit (preventing any current from flowing through the dielectric). As frequency increases, the magnitude of reactance decreases, allowing more current to flow. As f approaches \infty, the capacitor's reactance approaches 0, behaving like a
short circuit A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit that allows a current to travel along an unintended path with no or very low electrical impedance. This results in an excessive current flowing through the circuit ...
. The application of a DC voltage across a capacitor causes positive charge to accumulate on one side and negative charge to accumulate on the other side; the
electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
due to the accumulated charge is the source of the opposition to the current. When the
potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...
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 (counter-EMF), 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, due to the heat expanding the metal transmission lines), 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. Power providers utilize capacitors to shift the phase and minimize the losses, based on usage patterns. Inductive reactance X_L is proportional to the sinusoidal signal
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
f and the
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
L, which depends on the physical shape of the inductor: X_L = \omega L = 2\pi f L. The average current flowing through an
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
L in series with a sinusoidal AC voltage source of RMS
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
A and frequency f is equal to: :I_L = = . Because a
square wave Square wave may refer to: *Square wave (waveform) A square wave is a non-sinusoidal waveform, non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same ...
has multiple amplitudes at sinusoidal
harmonic In physics, acoustics, and telecommunications, a harmonic is a sinusoidal wave with a frequency that is a positive integer multiple of the ''fundamental frequency'' of a periodic signal. The fundamental frequency is also called the ''1st har ...
s, the average current flowing through an
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
L in series with a square wave AC voltage source of RMS
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
A and frequency f is equal to: :I_L = = making it appear as if the inductive reactance to a square wave was about 19% smaller X_L = f L than the reactance to the AC sine wave. Any conductor of finite dimensions has inductance; the inductance is made larger by the multiple turns in an
electromagnetic coil An electromagnetic coil is an electrical Electrical conductivity, conductor such as a wire in the shape of a wiktionary:coil, coil (spiral or helix). Electromagnetic coils are used in electrical engineering, in applications where electric curre ...
. Faraday's law of electromagnetic induction gives the counter- emf \mathcal (voltage opposing current) due to a rate-of-change of magnetic flux density \scriptstyle through a current loop. :\mathcal = - For an inductor consisting of a coil with N loops this gives: :\mathcal = -N. The counter-emf is the source of the opposition to current flow. A constant
direct current Direct current (DC) is one-directional electric current, flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor (material), conductor such as a wire, but can also flow throug ...
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 Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating current is the form in w ...
has a time-averaged rate-of-change that is proportional to frequency, this causes the increase in inductive reactance with frequency.


Impedance

Both reactance and resistance are components of impedance . :\mathbf = R + \mathbfX where: *\mathbf is the complex impedance, measured in
ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (1 ...
s; *R is the resistance, measured in ohms. It is the real part of the impedance: *X is the reactance, measured in ohms. It is the imaginary part of the impedance: *\mathbf is the square root of negative one, usually represented by \mathbf in non-electrical formulas. \mathbf is used so as not to confuse the imaginary unit with current, commonly represented by \mathbf. 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 X_C and inductive reactance X_L contribute to the total reactance X as follows: : where: *X_L is the inductive reactance, measured in ohms; *X_C is the capacitive reactance, measured in ohms; *\omega is the angular frequency, 2\pi times the frequency in Hz. Hence: *if \scriptstyle X > 0, the total reactance is said to be inductive; *if \scriptstyle X = 0, then the impedance is purely resistive; *if \scriptstyle X < 0, the total reactance is said to be capacitive. Note however that if X_L and X_C are assumed both positive by definition, then the intermediary formula changes to a difference: : but the ultimate value is the same.


Phase relationship

The phase of the voltage across a purely reactive device (i.e. with zero parasitic resistance) ''lags'' the current by \tfrac radians for a capacitive reactance and ''leads'' the current by \tfrac radians for an inductive reactance. Without knowledge of both the resistance and reactance the relationship between voltage and current cannot be determined. The origin of the different signs for capacitive and inductive reactance is the phase factor e^ in the impedance. :\begin \mathbf_C &= e^ = \mathbf\left(\right) = \mathbfX_C \\ \mathbf_L &= \omega Le^ = \mathbf\omega L = \mathbfX_L\quad \end For a reactive component the sinusoidal voltage across the component is in quadrature (a \tfrac 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.


See also

* Magnetic reactance *
Susceptance In electrical engineering, susceptance () is the imaginary part of admittance (), where the real part is conductance (). The reciprocal of admittance is impedance (), where the imaginary part is reactance () and the real part is resistance ( ...


References

* Shamieh C. and McComb G., ''Electronics for Dummies,'' John Wiley & Sons, 2011. * Meade R., ''Foundations of Electronics,'' Cengage Learning, 2002. *


External links


National magnet lab, inductive reactance
{{DEFAULTSORT:Reactance Electrical resistance and conductance Physical quantities