# Inductance

**mutual inductanceinductivemutual inductioncoupling coefficientself-inductanceelectrical inductanceelectromagnetic self-inductionCoupled inductorsself inductanceSelf-induction**

In electromagnetism and electronics, inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it.wikipedia

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### Inductor

**inductorscoilinductive**

An electronic component designed to add inductance to a circuit is called an inductor.

An inductor is characterized by its inductance, which is the ratio of the voltage to the rate of change of current.

### Henry (unit)

**henryhenriesH**

In the SI system, the unit of inductance is the henry (H), which is the amount of inductance that causes a voltage of one volt, when the current is changing at a rate of one ampere per second.

The henry (symbol: H) is the SI derived unit of electrical inductance.

### Joseph Henry

**Henry, JosephHenryJoseph Henry Papers Project**

It is named for Joseph Henry, who discovered inductance independently of Faraday.

While building electromagnets, Henry discovered the electromagnetic phenomenon of self-inductance.

### Electromagnetic coil

**coilwindingcoils**

It typically consists of a coil or helix of wire.

### Oliver Heaviside

**HeavisideHeaviside, OliverHeaviside|Heaviside's operators**

The term inductance was coined by Oliver Heaviside in 1886.

Heaviside showed mathematically that uniformly distributed inductance in a telegraph line would diminish both attenuation and distortion, and that, if the inductance were great enough and the insulation resistance not too high, the circuit would be distortionless in that currents of all frequencies would have equal speeds of propagation.

### Michael Faraday

**FaradayFaraday, MichaelM. Faraday**

Electromagnetic induction was first described by Michael Faraday in 1831.

This phenomenon is now known as mutual induction.

### Lenz's law

**his important lawlawLenz effect**

This induced voltage is in a direction which tends to oppose the change in current (as stated by Lenz's law), so it is called a back EMF.

This back-and-forth component of momentum contributes to magnetic inductance.

### Electromotive force

**EMFelectromotive force (EMF)ℰ**

From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors; this is known as electromagnetic induction.

The effect on the circuit itself, of changing the current, is known as self-induction; the effect on another circuit is known as mutual induction.

### Inductive coupling

**inductiveinductively coupledmagnetically coupled**

If multiple electric circuits are located close to each other, the magnetic field of one can pass through the other; in this case the circuits are said to be inductively coupled.

The amount of inductive coupling between two conductors is measured by their mutual inductance.

### Linear circuit

**linearnonlinearlinear circuits**

If ferromagnetic materials are located near the conductor, such as in an inductor with a magnetic core, the constant inductance equation above is only valid for linear regions of the magnetic flux, at currents below the level at which the ferromagnetic material saturates, where the inductance is approximately constant.

Informally, a linear circuit is one in which the electronic components' values (such as resistance, capacitance, inductance, gain, etc.) do not change with the level of voltage or current in the circuit.

### Electrical reactance

**reactancereactivecapacitive reactance**

Inductive reactance is the opposition of an inductor to an alternating current.

In electric and electronic systems, reactance is the opposition of a circuit element to a change in current or voltage, due to that element's inductance or capacitance.

### International System of Units

**SISI unitsSI unit**

In the SI system, the unit of inductance is the henry (H), which is the amount of inductance that causes a voltage of one volt, when the current is changing at a rate of one ampere per second.

### Electromagnetic induction

**inductionmagnetic inductioninduced**

From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors; this is known as electromagnetic induction.

### Transformer

**power transformerelectrical transformerprimary winding**

The concept of inductance can be generalized in this case by defining the mutual inductance M_{k,\ell} of circuit k and circuit \ell as the ratio of voltage induced in circuit \ell to the rate of change of current in circuit k. This is the principle behind a transformer.

Some radio-frequency transformers also have movable cores (sometimes called 'slugs') which allow adjustment of the coupling coefficient (and bandwidth) of tuned radio-frequency circuits.

### Magnetic core

**core lossiron coresoft iron**

If ferromagnetic materials are located near the conductor, such as in an inductor with a magnetic core, the constant inductance equation above is only valid for linear regions of the magnetic flux, at currents below the level at which the ferromagnetic material saturates, where the inductance is approximately constant. The inductance of a coil can be increased by placing a magnetic core of ferromagnetic material in the hole in the center.

Air core coils generally have a much lower inductance than similarly sized ferromagnetic core coils, but are used in radio frequency circuits to prevent energy losses called core losses that occur in magnetic cores.

### Electrical network

**circuitelectrical circuitelectric circuit**

If multiple electric circuits are located close to each other, the magnetic field of one can pass through the other; in this case the circuits are said to be inductively coupled.

An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances).

### Leakage inductance

**leakage fluxleakage reactanceleakage**

Equivalent circuit elements L_\text{s}, L_\text{p} have physical meaning, modelling respectively magnetic reluctances of coupling paths and magnetic reluctances of leakage paths.

Leakage inductance derives from the electrical property of an imperfectly-coupled transformer whereby each winding behaves as a self-inductance in series with the winding's respective ohmic resistance constant.

### Double-tuned amplifier

**double tuned transformertuned transformers in the intermediate-frequency amplifiers**

When a capacitor is connected across each winding, it is called a double tuned transformer.

A double-tuned amplifier is a tuned amplifier with transformer coupling between the amplifier stages in which the inductances of both the primary and secondary windings are tuned separately with a capacitor across each.

### Permeability (electromagnetism)

**permeabilitymagnetic permeabilityrelative permeability**

Let the inner conductor have radius r_i and permeability \mu_i, let the dielectric between the inner and outer conductor have permeability \mu_d, and let the outer conductor have inner radius r_{o1}, outer radius r_{o2}, and permeability \mu_0.

Permeability is the inductance per unit length.

### Impedance analogy

**mechanical analogy**

A mechanical analogy in the K = 1 case with magnetic field energy (1/2)Li 2 is a body with mass M, velocity u and kinetic energy (1/2)Mu 2.

Mechanical analogies are required for the three passive electrical elements, namely, resistance, inductance and capacitance.

### Skin effect

**skin depthconductor skin effectscurrents tend to flow on the surface of conductors**

Where high frequency currents are considered, with skin effect, the surface current densities and magnetic field may be obtained by solving the Laplace equation.

This impedance is a complex quantity corresponding to a resistance (real) in series with the reactance (imaginary) due to the wire's internal self-inductance, per unit length.

### Transformer types

**resonant transformerpulse transformeroutput transformer**

These resonant transformers can store oscillating electrical energy similar to a resonant circuit and thus function as a bandpass filter, allowing frequencies near their resonant frequency to pass from the primary to secondary winding, but blocking other frequencies.

The transformer windings have either air or ferrite cores and the bandwidth can be adjusted by varying the coupling (mutual inductance).

### Kinetic inductance

Kinetic inductance is the manifestation of the inertial mass of mobile charge carriers in alternating electric fields as an equivalent series inductance.

### Solenoid

**solenoidselectromechanical solenoidmagnetizing current loop**

A solenoid is a long, thin coil; i.e., a coil whose length is much greater than its diameter.

Combining this with the definition of inductance

### Angular frequency

**angular rateangular speedangular frequencies**

where is the amplitude (peak value) of the sinusoidal current in amperes, is the angular frequency of the alternating current, with f being its [frequency]] in hertz, and L is the inductance.

The resonant angular frequency in a series LC circuit equals the square root of the reciprocal of the product of the capacitance (C measured in farads) and the inductance of the circuit (L, with SI unit henry):