Reactance
Encyclopedia
Reactance is the opposition of a circuit element to a change of electric current
or voltage
, due to that element's capacitance
or inductance
. A built-up electric field
resists the change of voltage on the element, while a magnetic field
resists the change of current. Notion of reactance is similar to electrical resistance
, but it differs from it in several aspects.
Capacitance and inductance are inherent properties of an element, just like resistance, but their reactive effects are not exhibited under constant direct current
, but only when the conditions in the circuit change. Thus, the reactance differs with the rate of change, and is a constant only for circuits under alternating current
of constant frequency. In vector analysis of electric circuits, resistance is the real part of complex impedance, while reactance is the imaginary part. Both share the same SI unit
, the ohm
.
An ideal resistor
has zero reactance, while ideal inductor
s and capacitor
s consist entirely of reactance.
analysis, reactance is used to compute amplitude and phase changes of sinusoidal
alternating current
going through the circuit element. It is denoted by the symbol
.
Both reactance
and resistance
are required to calculate the impedance
. In some circuits one of these may dominate, but an approximate knowledge of the minor component is useful to determine if it may be neglected.
Both the magnitude
and the phase
of the impedance depend on both the resistance and the reactance.
where 
is the complex conjugate of 
The magnitude is the ratio of the voltage
and current
amplitude
s, while the phase is the voltage–current phase difference.
The reciprocal of reactance (that is,
) is susceptance
.
is inversely proportional to the signal frequency
and the capacitance
.
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 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, a capacitor will only accumulate a limited amount of charge before the potential difference changes polarity and the charge dissipates. The higher the frequency, the less charge will accumulate and the smaller the opposition to the current.
is proportional
to the signal frequency
and the inductance
.
An inductor consists of a coiled conductor. Faraday's law
of electromagnetic induction gives the counter-emf
(voltage opposing current) due to a rate-of-change of magnetic flux density 
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
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.
radians for a capacitive reactance and leads the current by 
radians for an inductive reactance. Note that 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.
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
or voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
, due to that element's capacitance
Capacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
or inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
. A built-up electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
resists the change of voltage on the element, while a magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
resists the change of current. Notion of reactance is similar to electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, but it differs from it in several aspects.
Capacitance and inductance are inherent properties of an element, just like resistance, but their reactive effects are not exhibited under constant direct current
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
, but only when the conditions in the circuit change. Thus, the reactance differs with the rate of change, and is a constant only for circuits under alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
of constant frequency. In vector analysis of electric circuits, resistance is the real part of complex impedance, while reactance is the imaginary part. Both share the same SI unit
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
, the ohm
Ohm
The ohm is the SI unit of electrical resistance, named after German physicist Georg Simon Ohm.- Definition :The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere,...
.
An ideal resistor
Resistor
A linear resistor is a linear, passive two-terminal electrical component that implements electrical resistance as a circuit element.The current through a resistor is in direct proportion to the voltage across the resistor's terminals. Thus, the ratio of the voltage applied across a resistor's...
has zero reactance, while ideal inductor
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
s and capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
s consist entirely of reactance.
Analysis
In phasorPhasor
Phasor is a phase vector representing a sine wave.Phasor may also be:* Phasor , a stereo music, sound and speech synthesizer for the Apple II computer* Phasor measurement unit, a device that measures phasors on an electricity grid...
analysis, reactance is used to compute amplitude and phase changes of sinusoidal
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...
alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
going through the circuit element. It is denoted by the symbol
.Both reactance
and resistanceElectrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
are required to calculate the impedanceElectrical impedance
Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...
. In some circuits one of these may dominate, but an approximate knowledge of the minor component is useful to determine if it may be neglected.- where
is the impedanceElectrical impedanceElectrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...
, measured in ohms.
is the resistanceElectrical resistanceThe electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, measured in ohms.
is the reactance, measured in ohms.
Both the magnitude
Magnitude (mathematics)
The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
and the phasePhase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
of the impedance depend on both the resistance and the reactance. where is the complex conjugate of The magnitude is the ratio of the voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
and current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...
s, while the phase is the voltage–current phase difference.
- If
, the reactance is said to be inductiveInductanceIn electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit... - If
, then the impedance is purely resistiveElectrical resistanceThe electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical... - If
, the reactance is said to be capacitiveCapacitanceIn electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
The reciprocal of reactance (that is,
) is susceptanceSusceptance
In electrical engineering, susceptance is the imaginary part of admittance. The inverse of admittance is impedance and the real part of admittance is conductance. In SI units, susceptance is measured in siemens...
.
Capacitive reactance
Capacitive reactance is inversely proportional to the signal frequencyFrequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
and the capacitanceCapacitance
In electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...
.A capacitor consists of two conductors separated by an insulator
Electrical insulation
thumb|250px|[[Coaxial Cable]] with dielectric insulator supporting a central coreThis article refers to electrical insulation. For insulation of heat, see Thermal insulation...
, also known as a dielectric
Dielectric
A dielectric is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material, as in a conductor, but only slightly shift from their average equilibrium positions causing dielectric...
.
At low frequencies a capacitor is open circuit
Open circuit
The term 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...
, as no current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
flows in the dielectric. A DC
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
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
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
due to the accumulated charge is the source of the opposition to the current. When the potential
Potential
*In linguistics, the potential mood*The mathematical study of potentials is known as potential theory; it is the study of harmonic functions on manifolds...
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 polarity 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 is proportionalProportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...
to the signal frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
and the inductanceInductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
.An inductor consists of a coiled conductor. Faraday's law
Faraday's law of induction
Faraday's law of induction dates from the 1830s, and is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators...
of electromagnetic induction gives the counter-emf
Electromotive force
In physics, electromotive force, emf , or electromotance refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.It is important to note that the electromotive "force" is not a...
(voltage opposing current) due to a rate-of-change of magnetic flux density 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
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
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
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
). An alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
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 radians for a capacitive reactance and leads the current by radians for an inductive reactance. Note that 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.External links
- Interactive Java Tutorial on Inductive Reactance National High Magnetic Field Laboratory
- Inductive Reactance: Endless Examples & Exercises