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Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the electric current, and follows any changes in the magnitude of the current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called back EMF.

Inductance is defined as the ratio of the induced voltage to the rate of change of current causing it.^[1] It is a proportionality constant that depends on the geometry of circuit conductors (e.g., cross-section area and length) and the magnetic permeability of the conductor and nearby materials.^[1] An electronic component designed to add inductance to a circuit is called an inductor. It typically consists of a coil or helix of wire.

The term inductance was coined by Oliver Heaviside in May 1884, as a convenient way to refer to "coefficient of self-induction".^[2][3] It is customary to use the symbol ${\displaystyle L}$ for inductance, in honour of the physicist Heinrich Lenz.^[4][5] 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.^[6] The unit is named for Joseph Henry, who discovered inductance independently of Faraday.^[7]

History

The history of electromagnetic induction, a facet of electromagnetism, began with observations of the ancients: electric charge or static electricity (rubbing silk on amber), electric current (lightning), and magnetic attraction (lodestone). Understanding the unity of these forces of nature, and the scientific theory of electromagnetism was initiated and achieved during the 19th century.

Electromagnetic induction was first described by Michael Faraday in 1831.^[8][9] In Faraday's experiment, he wrapped two wires around opposite sides of an iron ring. He expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. Using a galvanometer, he observed a transient current flow in the second coil of wire each time that a battery was connected or disconnected from the first coil.^[10] This current was induced by the change in magnetic flux that occurred when the battery was connected and disconnected.^[11] Faraday found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical lead ("Faraday's disk").^[12]

Source of inductance

A current ${\displaystyle i}$ flowing through a conductor generates a magnetic field around the conductor, which is described by Ampere's circuital law. The total magnetic flux ${\displaystyle \Phi }$ through a circuit is equal to the product of the perpendicular component of the magnetic flux density and the area of the surface spanning the current path. If the current varies, the magnetic flux ${\displaystyle \Phi }$ through the circuit changes. By Faraday's law of induction, any change in flux through a circuit induces an electromotive force (EMF, ${\displaystyle {\mathcal {E}}}$) in the circuit, proportional to the rate of change of flux

$${\displaystyle {\mathcal {E}}(t)=-{\frac {\text{d}}{{\text{d}}t}}\,\Phi (t)}$$

The negative sign in the equation indicates that the induced voltage is in a direction which opposes the change in current that created it; this is called Lenz's law. The potential is therefore called a back EMF. If the current is increasing, the voltage is positive at the end of the conductor through which the current enters and negative at the end through which it leaves, tending to reduce the current. If the current is decreasing, the voltage is positive at the end through which the current leaves the conductor, tending to maintain the current. Self-inductance, usually just called inductance, ${\displaystyle L}$ is the ratio between the induced voltage and the rate of change of the current

$${\displaystyle v(t)=L\,{\frac {{\text{d}}i}{{\text{d}}t}}\qquad \qquad \qquad (1)\;}$$

Thus, inductance is a property of a conductor or circuit, due to its magnetic field, which tends to oppose changes in current through the circuit. The unit of inductance in the SI system is the henry (H), named after Joseph Henry, which is the amount of inductance that generates a voltage of one volt when the current is changing at a rate of one ampere per second.

All conductors have some inductance, which may have either desirable or detrimental effects in practical electrical devices. The inductance of a circuit depends on the geometry of the current path, and on the magnetic permeability of nearby materials; ferromagnetic materials with a higher permeability like iron near a conductor tend to increase the magnetic field and inductance. Any alteration to a circuit which increases the flux (total magnetic field) through the circuit produced by a given current increases the inductance, because inductance is also equal to the ratio of magnetic flux to current^{[13][14][15][16]}

$${\displaystyle L={\Phi (i) \over i}}$$

An inductor is an electrical component consisting of a conductor shaped to increase the magnetic flux, to add inductance to a circuit. Typically it consists of a wire wound into a coil or helix. A coiled wire has a higher inductance than a straight wire of the same length, because the magnetic field lines pass through the circuit multiple times, it has multiple flux linkages. The inductance is proportional to the square of the number of turns in the coil, assuming full flux linkage.

The inductance of a coil can be increased by placing a magnetic core of ferromagnetic material in the hole in the center. The magnetic field of the coil magnetizes the material of the core, aligning its magnetic domains, and the magnetic field of the core adds to that of the coil, increasing the flux through the coil. This is called a ferromagnetic core inductor. A magnetic core can increase the inductance of a coil by thousands of times.

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. Due to Faraday's law of induction, a change in current in one circuit can cause a change in magnetic flux in another circuit and thus induce a voltage in another circuit. The concept of inductance can be generalized in this case by defining the mutual inductance ${\displaystyle M_{k,\ell }}$ of circuit ${\displaystyle k}$ and circuit ${\displaystyle \ell }$ as the ratio of voltage induced in circuit ${\displaystyle \ell }$ to the rate of change of current in circuit ${\displaystyle k}$. This is the principle behind a transformer. The property describing the effect of one conductor on itself is more precisely called self-inductance, and the properties describing the effects of one conductor with changing current on nearby conductors is called mutual inductance.^[17]

Self-inductance and magnetic energy

If the current through a conductor with inductance is increasing, a voltage ${\displaystyle v(t)}$ is induced across the conductor with a polarity that opposes the current—in addition to any voltage drop caused by the conductor's resistance. The charges flowing through the circuit lose potential energy. The energy from the external circuit required to overcome this "potential hill" is stored in the increased magnetic field around the conductor. Therefore, an inductor stores energy in its magnetic field. At any given time ${\displaystyle t}$ the power ${\displaystyle p(t)}$ flowing into the magnetic field, which is equal to the rate of change of the stored energy ${\displaystyle U}$, is the product of the current ${\displaystyle i(t)}$ and voltage ${\displaystyle v(t)}$ across the conductor^[18][19][20]

$${\displaystyle p(t)={\frac {{\text{d}}U}{{\text{d}}t}}=v(t)\,i(t)}$$

From (1) above