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An inductor, also called a coil, choke, or reactor, is a
passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive * Passive language, a language from which an interpreter works * Passivity (behavior), the condition of submitting to the influence of o ...
two-terminal
electrical component An electronic component is any basic discrete device or physical entity in an electronic system used to affect electrons or their associated fields. Electronic components are mostly industrial products, available in a singular form and are n ...
that stores energy in a
magnetic field 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 ...
when
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The movi ...
flows through it. An inductor typically consists of an insulated wire wound into a coil. When the current flowing through the coil changes, the time-varying magnetic field induces an
electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical '' tran ...
(''emf'') (
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 ...
) in the conductor, described by
Faraday's law of induction Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic in ...
. According to
Lenz's law Lenz's law states that the direction of the electric current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in the initial magnetic field. It is named after p ...
, the induced voltage has a polarity (direction) which opposes the change in current that created it. As a result, inductors oppose any changes in current through them. An inductor is characterized by its
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of th ...
, which is the ratio of the voltage to the rate of change of current. In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(SI), the unit of inductance is the henry (H) named for 19th century American scientist
Joseph Henry Joseph Henry (December 17, 1797– May 13, 1878) was an American scientist who served as the first Secretary of the Smithsonian Institution. He was the secretary for the National Institute for the Promotion of Science, a precursor of the Smit ...
. In the measurement of magnetic circuits, it is equivalent to . Inductors have values that typically range from 1µH (10−6H) to 20H. Many inductors have a
magnetic core A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, generators, ...
made of iron or ferrite inside the coil, which serves to increase the magnetic field and thus the inductance. Along with
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 and
resistor A resistor is a passive two-terminal electrical 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 ...
s, inductors are one of the three passive
linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...
circuit element Electrical elements are conceptual abstractions representing idealized electrical components, such as resistors, capacitors, and inductors, used in the analysis of electrical networks. All electrical networks can be analyzed as multiple electri ...
s that make up electronic circuits. Inductors are widely used in
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 ...
(AC) electronic equipment, particularly in
radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30  hertz (Hz) and 300  gigahertz (GHz). They are generated by an electronic device called a tr ...
equipment. They are used to block AC while allowing DC to pass; inductors designed for this purpose are called chokes. They are also used in
electronic filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
s to separate signals of different
frequencies 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 e ...
, and in combination with capacitors to make
tuned circuit An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can a ...
s, used to tune radio and TV receivers. The term inductor seems to come from Heinrich Daniel Ruhmkorff, who called the famous
induction coil An induction coil or "spark coil" ( archaically known as an inductorium or Ruhmkorff coil after Heinrich Rühmkorff) is a type of electrical transformer used to produce high-voltage pulses from a low-voltage direct current (DC) supply. p.98 ...
he invented in 1851 an inductorium.


Description

An electric current flowing through a conductor generates a magnetic field surrounding it. The magnetic flux linkage \Phi_\mathbf generated by a given current I depends on the geometric shape of the circuit. Their ratio defines the inductance L. Thus :L := \frac. The inductance of a circuit depends on the geometry of the current path as well as the
magnetic permeability In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by Willi ...
of nearby materials. An inductor is a
component Circuit Component may refer to: •Are devices that perform functions when they are connected in a circuit.   In engineering, science, and technology Generic systems * System components, an entity with discrete structure, such as an assem ...
consisting of a wire or other conductor shaped to increase the magnetic flux through the circuit, usually in the shape of a coil or
helix A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helic ...
, with two terminals. Winding the wire into a coil increases the number of times the
magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ...
lines link the circuit, increasing the field and thus the inductance. The more turns, the higher the inductance. The inductance also depends on the shape of the coil, separation of the turns, and many other factors. By adding a "magnetic core" made of a
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
material like iron inside the coil, the magnetizing field from the coil will induce
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or D ...
in the material, increasing the magnetic flux. The high permeability of a ferromagnetic core can increase the inductance of a coil by a factor of several thousand over what it would be without it.


Constitutive equation

Any change in the current through an inductor creates a changing flux, inducing a voltage across the inductor. By
Faraday's law of induction Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic in ...
, the voltage \mathcal induced by any change in magnetic flux through the circuit is given by :\mathcal = -\frac. Reformulating the definition of above, we obtain : \Phi_\mathbf = LI. It follows that :\mathcal = -\frac = -\frac(LI) = -L\frac. for independent of time, current and magnetic flux linkage. So inductance is also a measure of the amount of
electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical '' tran ...
(voltage) generated for a given rate of change of current. For example, an inductor with an inductance of 1 henry produces an EMF of 1 volt when the current through the inductor changes at the rate of 1 ampere per second. This is usually taken to be the
constitutive relation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and app ...
(defining equation) of the inductor. The dual of the inductor is the
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 ...
, which stores energy in an electric field rather than a magnetic field. Its current–voltage relation is obtained by exchanging current and voltage in the inductor equations and replacing ''L'' with the capacitance ''C''.


Lenz's law

The polarity (direction) of the induced voltage is given by
Lenz's law Lenz's law states that the direction of the electric current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in the initial magnetic field. It is named after p ...
, which states that the induced voltage will be such as to oppose the change in current. For example, if the current through an inductor is increasing, the induced voltage will be positive at the current's entrance point and negative at the exit point, tending to oppose the additional current. The energy from the external circuit necessary to overcome this potential "hill" is being stored in the magnetic field of the inductor. If the current is decreasing, the induced voltage will be negative at the current's entrance point and positive at the exit point, tending to maintain the current. In this case energy from the magnetic field is being returned to the circuit.


Energy stored in an inductor

One intuitive explanation as to why a potential difference is induced on a change of current in an inductor goes as follows: When there is a change in current through an inductor there is a change in the strength of the magnetic field. For example, if the current is increased, the magnetic field increases. This, however, does not come without a price. The magnetic field contains
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potenti ...
, and increasing the field strength requires more energy to be stored in the field. This energy comes from the electric current through the inductor. The increase in the magnetic potential energy of the field is provided by a corresponding drop in the electric potential energy of the charges flowing through the windings. This appears as a voltage drop across the windings as long as the current increases. Once the current is no longer increased and is held constant, the energy in the magnetic field is constant and no additional energy must be supplied, so the voltage drop across the windings disappears. Similarly, if the current through the inductor decreases, the magnetic field strength decreases, and the energy in the magnetic field decreases. This energy is returned to the circuit in the form of an increase in the electrical potential energy of the moving charges, causing a voltage rise across the windings.


Derivation

The
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal t ...
done per unit charge on the charges passing the inductor is -\mathcal. The negative sign indicates that the work is done ''against'' the emf, and is not done ''by'' the emf. The current I is the charge per unit time passing through the inductor. Therefore the rate of work W done by the charges against the emf, that is the rate of change of energy of the current, is given by :\frac = -\mathcalI From the constitutive equation for the inductor, -\mathcal = L\frac so :\frac= L\frac \cdot I = LI \cdot \frac :dW = L I \cdot dI In a ferromagnetic core inductor, when the magnetic field approaches the level at which the core saturates, the inductance will begin to change, it will be a function of the current L(I). Neglecting losses, the
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
W stored by an inductor with a current I_0 passing through it is equal to the amount of work required to establish the current through the inductor. This is given by: W = \int_0^ L_d(I) \, I \, dI, where L_d(I) is the so-called "differential inductance" and is defined as: L_d = \frac. In an air core inductor or a ferromagnetic core inductor below saturation, the inductance is constant (and equal to the differential inductance), so the stored energy is :\begin W &= L\int_0^ I \, dI \\ W &= \fracL ^2 \end For inductors with magnetic cores, the above equation is only valid for
linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...
regions of the magnetic flux, at currents below the
saturation Saturation, saturated, unsaturation or unsaturated may refer to: Chemistry * Saturation, a property of organic compounds referring to carbon-carbon bonds **Saturated and unsaturated compounds ** Degree of unsaturation **Saturated fat or fatty aci ...
level of the inductor, where the inductance is approximately constant. Where this is not the case, the integral form must be used with L_d variable.


Voltage step response - short and long term limit

When a voltage step is applied to an inductor, its short and long-term response are easy to calculate: * In the short-time limit, since the current cannot change discontinuously, the initial current is zero. The short-time equivalence of an inductor is 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 ...
. * In the long-time limit, the transient response of the inductor will die out, the magnetic flux through the inductor will become constant, so no voltage would be induced between the terminals of the inductor. Therefore, the long-time equivalence of an inductor is a wire (''i.e''., 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 circu ...
). * To give a mathematical analysis, we should note that any practical inductor is associated with a small resistance ''R''. Then, if the inductor ''L'' is connected to a battery of voltage ''V'' at time ''t = 0'', the circuit equation for ''t > 0'' is V = L \dot I + I R , whose solution is I(t>0) = (V / R) (1 - e^), with limits at ''t = 0'' and \infty as described in the bullets above.


Ideal and real inductors

The
constitutive equation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and ap ...
describes the behavior of an ''ideal inductor'' with inductance L, and without resistance,
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 are ...
, or energy dissipation. In practice, inductors do not follow this theoretical model; ''real inductors'' have a measurable resistance due to the resistance of the wire and energy losses in the core, and
parasitic capacitance Parasitic capacitance is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other. When two electrical conductors at different voltages ...
due to electric potentials between turns of the wire. A real inductor's
capacitive reactance In electrical circuits, reactance is the opposition presented to alternating current by inductance or capacitance. Greater reactance gives smaller current for the same applied voltage. Reactance is similar to resistance in this respect, but does ...
rises with frequency, and at a certain frequency, the inductor will behave as a resonant circuit. Above this
self-resonant frequency Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscilla ...
, the capacitive reactance is the dominant part of the inductor's impedance. At higher frequencies, resistive losses in the windings increase due to the
skin effect Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
and
proximity effect Proximity effect may refer to: * Proximity effect (atomic physics) * Proximity effect (audio), an increase in bass or low frequency response when a sound source is close to a microphone * ''Proximity Effect'' (comics), a comic book series written by ...
. Inductors with ferromagnetic cores experience additional energy losses due to
hysteresis Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
and
eddy current Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnet ...
s in the core, which increase with frequency. At high currents, magnetic core inductors also show sudden departure from ideal behavior due to nonlinearity caused by magnetic saturation of the core. Inductors radiate electromagnetic energy into surrounding space and may absorb electromagnetic emissions from other circuits, resulting in potential
electromagnetic interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electrost ...
. An early solid-state electrical switching and amplifying device called a saturable reactor exploits saturation of the core as a means of stopping the inductive transfer of current via the core.


''Q'' factor

The winding resistance appears as a resistance in series with the inductor; it is referred to as DCR (DC resistance). This resistance dissipates some of the reactive energy. The
quality factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy ...
(or ''Q'') of an inductor is the ratio of its inductive reactance to its resistance at a given frequency, and is a measure of its efficiency. The higher the Q factor of the inductor, the closer it approaches the behavior of an ideal inductor. High Q inductors are used with capacitors to make resonant circuits in radio transmitters and receivers. The higher the Q is, the narrower the
bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...
of the resonant circuit. The Q factor of an inductor is defined as :Q = \frac where L is the inductance, R is the DC resistance, and the product \omega L is the inductive reactance ''Q'' increases linearly with frequency if ''L'' and ''R'' are constant. Although they are constant at low frequencies, the parameters vary with frequency. For example, skin effect,
proximity effect Proximity effect may refer to: * Proximity effect (atomic physics) * Proximity effect (audio), an increase in bass or low frequency response when a sound source is close to a microphone * ''Proximity Effect'' (comics), a comic book series written by ...
, and core losses increase ''R'' with frequency; winding capacitance and variations in permeability with frequency affect ''L''. At low frequencies and within limits, increasing the number of turns ''N'' improves ''Q'' because ''L'' varies as ''N''2 while ''R'' varies linearly with ''N''. Similarly increasing the radius ''r'' of an inductor improves (or increases) ''Q'' because ''L'' varies with ''r''2 while ''R'' varies linearly with ''r''. So high ''Q'' air core inductors often have large diameters and many turns. Both of those examples assume the diameter of the wire stays the same, so both examples use proportionally more wire. If the total mass of wire is held constant, then there would be no advantage to increasing the number of turns or the radius of the turns because the wire would have to be proportionally thinner. Using a high permeability
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
core can greatly increase the inductance for the same amount of copper, so the core can also increase the Q. Cores however also introduce losses that increase with frequency. The core material is chosen for best results for the frequency band. High Q inductors must avoid saturation; one way is by using a (physically larger) air core inductor. At
VHF Very high frequency (VHF) is the ITU designation for the range of radio frequency electromagnetic waves (radio waves) from 30 to 300 megahertz (MHz), with corresponding wavelengths of ten meters to one meter. Frequencies immediately below VHF ...
or higher frequencies an air core is likely to be used. A well designed air core inductor may have a Q of several hundred.


Applications

Inductors are used extensively in
analog circuit Analogue electronics ( en-US, analog electronics) are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relat ...
s and signal processing. Applications range from the use of large inductors in power supplies, which in conjunction with filter
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 remove ripple which is a multiple of the mains frequency (or the switching frequency for switched-mode power supplies) from the direct current output, to the small inductance of the ferrite bead or
torus In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does n ...
installed around a cable to prevent
radio frequency interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electrost ...
from being transmitted down the wire. Inductors are used as the energy storage device in many
switched-mode power supplies A switched-mode power supply (switching-mode power supply, switch-mode power supply, switched power supply, SMPS, or switcher) is an electronic power supply that incorporates a switching regulator to convert electrical power efficiently. Like ...
to produce DC current. The inductor supplies energy to the circuit to keep current flowing during the "off" switching periods and enables topographies where the output voltage is higher than the input voltage. A
tuned circuit An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can a ...
, consisting of an inductor connected to a
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 ...
, acts as a
resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
for oscillating current. Tuned circuits are widely used in
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
equipment such as radio transmitters and receivers, as narrow
bandpass filter A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects ( attenuates) frequencies outside that range. Description In electronics and signal processing, a filter is usually a two-p ...
s to select a single frequency from a composite signal, and in
electronic oscillator An electronic oscillator is an electronic circuit that produces a periodic, oscillating electronic signal, often a sine wave or a square wave or a triangle wave. Oscillators convert direct current (DC) from a power supply to an alternating ...
s to generate sinusoidal signals. Two (or more) inductors in proximity that have coupled magnetic flux ( mutual inductance) form a
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
, which is a fundamental component of every electric
utility As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosophe ...
power grid. The efficiency of a transformer may decrease as the frequency increases due to eddy currents in the core material and skin effect on the windings. The size of the core can be decreased at higher frequencies. For this reason, aircraft use 400 hertz alternating current rather than the usual 50 or 60 hertz, allowing a great saving in weight from the use of smaller transformers. Transformers enable switched-mode power supplies that isolate the output from the input. Inductors are also employed in electrical transmission systems, where they are used to limit switching currents and
fault current In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in which a live wire touches a neutral or ground wire. An open-circuit fault occurs if a circuit is interrupted by a fa ...
s. In this field, they are more commonly referred to as reactors. Inductors have parasitic effects which cause them to depart from ideal behavior. They create and suffer from
electromagnetic interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electrost ...
(EMI). Their physical size prevents them from being integrated on semiconductor chips. So the use of inductors is declining in modern electronic devices, particularly compact portable devices. Real inductors are increasingly being replaced by active circuits such as the
gyrator A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conv ...
which can synthesize inductance using capacitors.


Inductor construction

An inductor usually consists of a coil of conducting material, typically insulated
copper wire Copper has been used in electrical wiring since the invention of the electromagnet and the telegraph in the 1820s. The invention of the telephone in 1876 created further demand for copper wire as an electrical conductor. Copper is the electri ...
, wrapped around a
core Core or cores may refer to: Science and technology * Core (anatomy), everything except the appendages * Core (manufacturing), used in casting and molding * Core (optical fiber), the signal-carrying portion of an optical fiber * Core, the centra ...
either of plastic (to create an air-core inductor) or of a
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
(or
ferrimagnetic A ferrimagnetic material is a material that has populations of atoms with opposing magnetic moments, as in antiferromagnetism, but these moments are unequal in magnitude so a spontaneous magnetization remains. This can for example occur when ...
) material; the latter is called an "iron core" inductor. The high permeability of the ferromagnetic core increases the magnetic field and confines it closely to the inductor, thereby increasing the inductance. Low frequency inductors are constructed like transformers, with cores of
electrical steel Electrical steel (E-steel, lamination steel, silicon electrical steel, silicon steel, relay steel, transformer steel) is an iron alloy tailored to produce specific magnetic properties: small hysteresis area resulting in low power loss per cycle ...
laminate Lamination is the technique/process of manufacturing a material in multiple layers, so that the composite material achieves improved strength, stability, sound insulation, appearance, or other properties from the use of the differing materia ...
d to prevent
eddy current Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnet ...
s. 'Soft' ferrites are widely used for cores above
audio frequencies An audio frequency or audible frequency (AF) is a periodic function, periodic vibration whose frequency is human hearing range, audible to the average human. The International System of Units, SI unit of frequency is the hertz (Hz). It is the pr ...
, since they do not cause the large energy losses at high frequencies that ordinary iron alloys do. Inductors come in many shapes. Some inductors have an adjustable core, which enables changing of the inductance. Inductors used to block very high frequencies are sometimes made by stringing a ferrite bead on a wire. Small inductors can be etched directly onto a
printed circuit board A printed circuit board (PCB; also printed wiring board or PWB) is a medium used in electrical and electronic engineering to connect electronic components to one another in a controlled manner. It takes the form of a laminated sandwich str ...
by laying out the trace in a
spiral In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:planar core. Small value inductors can also be built on
integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...
s using the same processes that are used to make interconnects.
Aluminium interconnect In integrated circuits (ICs), interconnects are structures that connect two or more circuit elements (such as transistors) together electrically. The design and layout of interconnects on an IC is vital to its proper function, performance, power ef ...
is typically used, laid out in a spiral coil pattern. However, the small dimensions limit the inductance, and it is far more common to use a circuit called a ''
gyrator A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conv ...
'' that uses a
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 ...
and active components to behave similarly to an inductor. Regardless of the design, because of the low inductances and low power dissipation on-die inductors allow, they are currently only commercially used for high frequency RF circuits.


Shielded inductors

Inductors used in power regulation systems, lighting, and other systems that require low-noise operating conditions, are often partially or fully shielded. In
telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
circuits employing induction coils and repeating transformers shielding of inductors in close proximity reduces circuit cross-talk.


Types


Air-core inductor

The term ''air core coil'' describes an inductor that does not use a
magnetic core A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, generators, ...
made of a ferromagnetic material. The term refers to coils wound on plastic, ceramic, or other nonmagnetic forms, as well as those that have only air inside the windings. Air core coils have lower inductance than ferromagnetic core coils, but are often used at high frequencies because they are free from energy losses called
core loss A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, generators, in ...
es that occur in ferromagnetic cores, which increase with frequency. A side effect that can occur in air core coils in which the winding is not rigidly supported on a form is 'microphony': mechanical vibration of the windings can cause variations in the inductance.


Radio-frequency inductor

At high frequencies, particularly radio frequencies (RF), inductors have higher resistance and other losses. In addition to causing power loss, in resonant circuits this can reduce the
Q factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy ...
of the circuit, broadening the
bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...
. In RF inductors, which are mostly air core types, specialized construction techniques are used to minimize these losses. The losses are due to these effects: *Skin effect: The resistance of a wire to
high frequency High frequency (HF) is the ITU designation for the range of radio frequency electromagnetic waves (radio waves) between 3 and 30 megahertz (MHz). It is also known as the decameter band or decameter wave as its wavelengths range from one to ten ...
current is higher than its resistance to
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 ev ...
because of
skin effect Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
. Due to induced
eddy current Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnet ...
s, radio frequency alternating current does not penetrate far into the body of a conductor but travels along its surface. For example, at 6 MHz the skin depth of copper wire is about 0.001 inches (25 µm); most of the current is within this depth of the surface. Therefore, in a solid wire, the interior portion of the wire may carry little current, effectively increasing its resistance. *Proximity effect: Another similar effect that also increases the resistance of the wire at high frequencies is proximity effect, which occurs in parallel wires that lie close to each other. The individual magnetic field of adjacent turns induces
eddy current Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnet ...
s in the wire of the coil, which causes the current in the conductor to be concentrated in a thin strip on the side near the adjacent wire. Like skin effect, this reduces the effective cross-sectional area of the wire conducting current, increasing its resistance. *Dielectric losses: The high frequency electric field near the conductors in a
tank A tank is an armoured fighting vehicle intended as a primary offensive weapon in front-line ground combat. Tank designs are a balance of heavy firepower, strong armour, and good battlefield mobility provided by tracks and a powerful ...
coil can cause the motion of polar molecules in nearby insulating materials, dissipating energy as heat. So coils used for tuned circuits are often not wound on coil forms but are suspended in air, supported by narrow plastic or ceramic strips. *Parasitic capacitance: The capacitance between individual wire turns of the coil, called
parasitic capacitance Parasitic capacitance is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other. When two electrical conductors at different voltages ...
, does not cause energy losses but can change the behavior of the coil. Each turn of the coil is at a slightly different potential, so the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
between neighboring turns stores charge on the wire, so the coil acts as if it has a capacitor in parallel with it. At a high enough frequency this capacitance can resonate with the inductance of the coil forming a
tuned circuit An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can a ...
, causing the coil to become self-resonant. To reduce parasitic capacitance and proximity effect, high Q RF coils are constructed to avoid having many turns lying close together, parallel to one another. The windings of RF coils are often limited to a single layer, and the turns are spaced apart. To reduce resistance due to skin effect, in high-power inductors such as those used in transmitters the windings are sometimes made of a metal strip or tubing which has a larger surface area, and the surface is silver-plated. ; Basket-weave coils: To reduce proximity effect and parasitic capacitance, multilayer RF coils are wound in patterns in which successive turns are not parallel but criss-crossed at an angle; these are often called ''honeycomb'' or '' basket-weave'' coils. These are occasionally wound on a vertical insulating supports with dowels or slots, with the wire weaving in and out through the slots. ; Spiderweb coils: Another construction technique with similar advantages is flat spiral coils. These are often wound on a flat insulating support with radial spokes or slots, with the wire weaving in and out through the slots; these are called ''spiderweb'' coils. The form has an odd number of slots, so successive turns of the spiral lie on opposite sides of the form, increasing separation. ; Litz wire: To reduce skin effect losses, some coils are wound with a special type of radio frequency wire called
litz wire Litz wire is a particular type of multistrand wire or cable used in electronics to carry alternating current (AC) at radio frequencies. The wire is designed to reduce the skin effect and proximity effect losses in conductors used at frequencie ...
. Instead of a single solid conductor, litz wire consists of a number of smaller wire strands that carry the current. Unlike ordinary
stranded wire Overhead power cabling. The conductor consists of seven strands of steel (centre, high tensile strength), surrounded by four outer layers of aluminium (high conductivity). Sample diameter 40 mm A wire is a flexible strand of metal. Wire is co ...
, the strands are insulated from each other, to prevent skin effect from forcing the current to the surface, and are twisted or braided together. The twist pattern ensures that each wire strand spends the same amount of its length on the outside of the wire bundle, so skin effect distributes the current equally between the strands, resulting in a larger cross-sectional conduction area than an equivalent single wire. ; Axial Inductor Small inductors for low current and low power are made in molded cases resembling resistors. These may be either plain (phenolic) core or ferrite core. An ohmmeter readily distinguishes them from similar-sized resistors by showing the low resistance of the inductor.


Ferromagnetic-core inductor

Ferromagnetic-core or iron-core inductors use a magnetic core made of a
ferromagnetic Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials ...
or
ferrimagnetic A ferrimagnetic material is a material that has populations of atoms with opposing magnetic moments, as in antiferromagnetism, but these moments are unequal in magnitude so a spontaneous magnetization remains. This can for example occur when ...
material such as iron or ferrite to increase the inductance. A magnetic core can increase the inductance of a coil by a factor of several thousand, by increasing the magnetic field due to its higher
magnetic permeability In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by Willi ...
. However the magnetic properties of the core material cause several side effects which alter the behavior of the inductor and require special construction:


Laminated-core inductor

Low-frequency inductors are often made with
laminated core A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, generators, i ...
s to prevent eddy currents, using construction similar to
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
s. The core is made of stacks of thin steel sheets or
lamination Lamination is the technique/process of manufacturing a material in multiple layers, so that the composite material achieves improved strength, stability, sound insulation, appearance, or other properties from the use of the differing materia ...
s oriented parallel to the field, with an insulating coating on the surface. The insulation prevents eddy currents between the sheets, so any remaining currents must be within the cross sectional area of the individual laminations, reducing the area of the loop and thus reducing the energy losses greatly. The laminations are made of low-conductivity silicon steel to further reduce eddy current losses.


Ferrite-core inductor

For higher frequencies, inductors are made with cores of ferrite. Ferrite is a ceramic ferrimagnetic material that is nonconductive, so eddy currents cannot flow within it. The formulation of ferrite is xxFe2O4 where xx represents various metals. For inductor cores
soft ferrite A ferrite is a ceramic material made by mixing and firing large proportions of iron(III) oxide (Fe2O3, rust) blended with small proportions of one or more additional metallic elements, such as strontium, barium, manganese, nickel, and zinc. ...
s are used, which have low coercivity and thus low hysteresis losses.


Powdered-iron-core inductor

Another material is powdered iron cemented with a binder.
Medium frequency Medium frequency (MF) is the ITU designation for radio frequencies (RF) in the range of 300  kilohertz (kHz) to 3  megahertz (MHz). Part of this band is the medium wave (MW) AM broadcast band. The MF band is also known as the h ...
equipment almost exclusively uses powdered iron cores, and inductors and transformers built for the lower
shortwave Shortwave radio is radio transmission using shortwave (SW) radio frequencies. There is no official definition of the band, but the range always includes all of the high frequency band (HF), which extends from 3 to 30 MHz (100 to 10 me ...
s are made using either cemented powdered iron or ferrites.


Toroidal-core inductor

In an inductor wound on a straight rod-shaped core, the
magnetic field lines 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 ...
emerging from one end of the core must pass through the air to re-enter the core at the other end. This reduces the field, because much of the magnetic field path is in air rather than the higher permeability core material and is a source of
electromagnetic interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electrost ...
. A higher magnetic field and inductance can be achieved by forming the core in a closed
magnetic circuit A magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials lik ...
. The magnetic field lines form closed loops within the core without leaving the core material. The shape often used is a
toroid In mathematics, a toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its ...
al or doughnut-shaped ferrite core. Because of their symmetry, toroidal cores allow a minimum of the magnetic flux to escape outside the core (called '' leakage flux''), so they radiate less electromagnetic interference than other shapes. Toroidal core coils are manufactured of various materials, primarily ferrite, powdered iron and laminated cores.


Variable inductor

Probably the most common type of variable inductor today is one with a moveable ferrite magnetic core, which can be slid or screwed in or out of the coil. Moving the core farther into the coil increases the permeability, increasing the magnetic field and the inductance. Many inductors used in radio applications (usually less than 100 MHz) use adjustable cores in order to tune such inductors to their desired value, since manufacturing processes have certain tolerances (inaccuracy). Sometimes such cores for frequencies above 100 MHz are made from highly conductive non-magnetic material such as aluminum. They decrease the inductance because the magnetic field must bypass them. Air core inductors can use sliding contacts or multiple taps to increase or decrease the number of turns included in the circuit, to change the inductance. A type much used in the past but mostly obsolete today has a spring contact that can slide along the bare surface of the windings. The disadvantage of this type is that the contact usually short-circuits one or more turns. These turns act like a single-turn short-circuited transformer secondary winding; the large currents induced in them cause power losses. A type of continuously variable air core inductor is the ''variometer''. This consists of two coils with the same number of turns connected in series, one inside the other. The inner coil is mounted on a shaft so its axis can be turned with respect to the outer coil. When the two coils' axes are collinear, with the magnetic fields pointing in the same direction, the fields add and the inductance is maximum. When the inner coil is turned so its axis is at an angle with the outer, the mutual inductance between them is smaller so the total inductance is less. When the inner coil is turned 180° so the coils are collinear with their magnetic fields opposing, the two fields cancel each other and the inductance is very small. This type has the advantage that it is continuously variable over a wide range. It is used in
antenna tuner An antenna tuner (and any of the names in the list below) is a device that is inserted between a radio transmitter and its antenna; when placed close by the antenna and properly adjusted (tuned) it optimizes power transfer by matching the im ...
s and matching circuits to match low frequency transmitters to their antennas. Another method to control the inductance without any moving parts requires an additional DC current bias winding which controls the permeability of an easily saturable core material. ''See'' Magnetic amplifier.


Choke

A choke is an inductor designed specifically for blocking high-frequency alternating current (AC) in an electrical circuit, while allowing DC or low-frequency signals to pass. Because the inductor resistricts or "chokes" the changes in current, this type of inductor is called a choke. It usually consists of a coil of insulated wire wound on a magnetic core, although some consist of a donut-shaped "bead" of ferrite material strung on a wire. Like other inductors, chokes resist changes in current passing through them increasingly with frequency. The difference between chokes and other inductors is that chokes do not require the high
Q factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy ...
construction techniques that are used to reduce the resistance in inductors used in tuned circuits.


Circuit analysis

The effect of an inductor in a circuit is to oppose changes in current through it by developing a voltage across it proportional to the rate of change of the current. An ideal inductor would offer no resistance to 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 ev ...
; however, only
superconducting Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
inductors have truly zero
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallel ...
. The relationship between the time-varying voltage ''v''(''t'') across an inductor with inductance ''L'' and the time-varying current ''i''(''t'') passing through it is described by the
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, ...
: :v(t) = L \frac When there is a
sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often i ...
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 ...
(AC) through an inductor, a sinusoidal voltage is induced. The amplitude of the voltage is proportional to the product of the amplitude (I_P) of the current and the angular frequency (\omega) of the current. :\begin i(t) &= I_\mathrm P \sin(\omega t) \\ \frac &= I_\mathrm P \omega \cos(\omega t) \\ v(t) &= L I_\mathrm P \omega \cos(\omega t) \end In this situation, the phase of the current lags that of the voltage by π/2 (90°). For sinusoids, as the voltage across the inductor goes to its maximum value, the current goes to zero, and as the voltage across the inductor goes to zero, the current through it goes to its maximum value. If an inductor is connected to a direct current source with value ''I'' via a resistance ''R'' (at least the DCR of the inductor), and then the current source is short-circuited, the differential relationship above shows that the current through the inductor will discharge with an
exponential decay A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and (lambda) is a positive rate ...
: :i(t) = I e^


Reactance

The ratio of the peak voltage to the peak current in an inductor energised from an AC source is called the reactance and is denoted ''X''L. :X_\mathrm L = \frac = \frac Thus, :X_\mathrm L = \omega L where ''ω'' is the
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 ti ...
. Reactance is measured in ohms but referred to as ''impedance'' rather than resistance; energy is stored in the magnetic field as current rises and discharged as current falls. Inductive reactance is proportional to frequency. At low frequency the reactance falls; at DC, the inductor behaves as a short circuit. As frequency increases the reactance increases and at a sufficiently high frequency the reactance approaches that of an open circuit.


Corner frequency

In filtering applications, with respect to a particular load impedance, an inductor has a
corner frequency In physics and electrical engineering, a cutoff frequency, corner frequency, or break frequency is a boundary in a system's frequency response at which energy flowing through the system begins to be reduced ( attenuated or reflected) rather tha ...
defined as: :f_\mathrm = \frac


Laplace circuit analysis (s-domain)

When using the
Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the '' time domain'') to a function of a complex variable s (in the ...
in circuit analysis, the impedance of an ideal inductor with no initial current is represented in the ''s'' domain by: :Z(s) = Ls\, where : ''L'' is the inductance, and : ''s'' is the complex frequency. If the inductor does have initial current, it can be represented by:


Inductor networks

Inductors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent inductance (''L''eq): : : \frac = \frac + \frac + \cdots + \frac The current through inductors in series stays the same, but the voltage across each inductor can be different. The sum of the potential differences (voltage) is equal to the total voltage. To find their total inductance: : : L_\mathrm = L_1 + L_2 + \cdots + L_n \,\! These simple relationships hold true only when there is no mutual coupling of magnetic fields between individual inductors.


Mutual inductance

Mutual inductance occurs when the magnetic field of an inductor induces a magnetic field in an adjacent inductor. Mutual induction is the basis of transformer construction. : M = \sqrt where M is the maximum mutual inductance possible between 2 inductors and L1 and L2 are the two inductors. In general : M \leq \sqrt as only a fraction of self flux is linked with the other. This fraction is called "Coefficient of flux linkage (K)" or "Coefficient of coupling". : M = K\sqrt


Inductance formulas

The table below lists some common simplified formulas for calculating the approximate inductance of several inductor constructions.


See also

*
Bellini–Tosi direction finder A Bellini–Tosi direction finder (B–T or BTDF) is a type of radio direction finder (RDF), which determines the direction to, or ''bearing'' of, a radio transmitter. Earlier RDF systems used very large rotating loop antennas, which the B–T sy ...
(radio goniometer) * Hanna curve *
Induction coil An induction coil or "spark coil" ( archaically known as an inductorium or Ruhmkorff coil after Heinrich Rühmkorff) is a type of electrical transformer used to produce high-voltage pulses from a low-voltage direct current (DC) supply. p.98 ...
*
Induction cooking Induction cooking is performed using direct induction heating of cooking vessels, rather than relying on indirect radiation, convection, or thermal conduction. Induction cooking allows high power and very rapid increases in temperature to be achi ...
*
Induction loop An induction or inductive loop is an electromagnetic communication or detection system which uses a moving magnet or an alternating current to induce an electric current in a nearby wire. Induction loops are used for transmission and reception of ...
*
LC circuit An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can a ...
*
RLC circuit An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent compon ...
* Saturable reactor – a type of adjustable inductor *
Solenoid upright=1.20, An illustration of a solenoid upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whose ...
*
Accumulator (energy) An accumulator is an energy storage device: a device which accepts energy, stores energy, and releases energy as needed. Some accumulators accept energy at a low rate (low power) over a long time interval and deliver the energy at a high rate (high ...


Notes


References

;Source *


External links

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