In electrical circuits, reactance is the opposition presented to
alternating current
Alternating current (AC) is an electric current which 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 whic ...
by
inductance or
capacitance
Capacitance is the capability of a material object or device 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 ar ...
.
Greater reactance gives smaller current for the same applied
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
. Reactance is similar to
resistance in this respect, but does not lead to
dissipation of electrical energy as heat; instead, energy is momentarily stored in the reactance, and a quarter-cycle later returned to the circuit.
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
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
* Phase space, a mathematic ...
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 (b ...
s, with positive values indicating ''inductive'' reactance and negative indicating ''capacitive'' reactance. It is denoted by the symbol
. An ideal
resistor has zero reactance, whereas ideal
inductor
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s and
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
s have zero resistance. As
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
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 fo ...
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 M. 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 Insti ...
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 electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
.
''Capacitive reactance'' is an opposition to the change of voltage across an element. Capacitive reactance
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, which is called the coefficient of proportionality or proportionality constan ...
to the signal
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
(or
angular frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
) and the
capacitance
Capacitance is the capability of a material object or device 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 ar ...
.
[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]
:
.
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. 237-241][Robbins, A.H., Miller W. (2012). ''Circuit Analysis: Theory and Practice'', 5th ed., Cengage Learning, pp. 554-558]
:
.
In this case however one needs to remember to add a negative sign for the impedance of a capacitor, i.e.
.
At
, the magnitude of the capacitor's reactance is infinite, behaving like an
open circuit Open circuit may refer to:
*Open-circuit scuba, a type of SCUBA-diving equipment where the user breathes from the set and then exhales to the surroundings without recycling the exhaled air
* Open-circuit test, a method used in electrical engineerin ...
(preventing any
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
from flowing through the dielectric). As frequency increases, the magnitude of reactance decreases, allowing more current to flow. As
approaches
, the capacitor's reactance approaches
, 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 circui ...
.
The application of a
DC voltage across a capacitor causes positive
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
to accumulate on one side and negative
charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
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
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
is
proportional to the sinusoidal signal
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
and the
inductance , which depends on the physical shape of the inductor:
.
The average current flowing through an
inductance 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 ...
and frequency
is equal to:
:
Because a
square wave has multiple amplitudes at sinusoidal
harmonics, the average current flowing through an
inductance 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 ...
and frequency
is equal to:
:
making it appear as if the inductive reactance to a square wave was about 19% smaller
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.
Faraday's law of electromagnetic induction gives the counter-
emf (voltage opposing current) due to a rate-of-change of
magnetic flux density
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
through a current loop.
:
For an inductor consisting of a coil with
loops this gives:
:
.
The counter-emf is the source of the opposition to current flow. A constant
direct current
Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or eve ...
has a zero rate-of-change, and sees an inductor as 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. ...
(it is typically made from a material with a low
resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
). An
alternating current
Alternating current (AC) is an electric current which 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 whic ...
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 .
:
where:
*
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 (b ...
s;
*
is the
resistance, measured in ohms. It is the real part of the impedance:
*
is the reactance, measured in ohms. It is the imaginary part of the impedance:
*
is the
square root of minus one, usually represented by
in non-electrical formulas.
is used so as not to confuse the imaginary unit with current, commonly represented by
.
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
and inductive reactance
contribute to the total reactance
as follows:
:
where:
*
is the
inductive reactance, measured in ohms;
*
is the
capacitive
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of a c ...
reactance, measured in ohms;
*
is the angular frequency,
times the frequency in
Hz.
Hence:
*if
, the total reactance is said to be inductive;
*if
, then the impedance is purely resistive;
*if
, the total reactance is said to be capacitive.
Note however that if
and
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
In electrical networks, a parasitic element is a circuit element ( resistance, inductance or capacitance) that is possessed by an electrical component but which it is not desirable for it to have for its intended purpose. For instance, a resis ...
) ''lags'' the current by
radians for a capacitive reactance and ''leads'' the current by
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
in the impedance.
:
For a reactive component the sinusoidal voltage across the component is in quadrature (a
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
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particle ...
*
Susceptance In electrical engineering, susceptance (''B'') 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. In SI unit ...
References
* Shamieh C. and McComb G., ''Electronics for Dummies,'' John Wiley & Sons, 2011.
* Meade R., ''Foundations of Electronics,'' Cengage Learning, 2002.
*
External links
Interactive Java Tutorial on Inductive ReactanceNational High Magnetic Field Laboratory
{{DEFAULTSORT:Reactance
Electrical resistance and conductance
Physical quantities