23 February, 2007

Inductor, Self and Mutual Inductance and Inductance Properties

Inductor :
An inductor is a passive electrical device employed in eletical circuits for its property of inductance.The term covers devices with a wide range of uses, sizes, and types, including components for electric-wave filters, tuned circuits, electrical measuring circuits, and energy storage devices.
Inductors are classified as fixed, adjustable, and variable. All are made either with or without magnetic cores. Inductors without magnetic cores are called air-core coils, although the actual core material may be a ceramic, a plastic, or some other nonmagnetic material. Inductors with magnetic cores are called iron-core coils. A wide variety of magnetic materials are used, and some of these contain very little iron.
In fixed inductors coils are wound so that the turns remain fixed in position with respect to each other. Adjustable inductors have either taps for changing the number of turns desired, or consist of several fixed inductors which may be switched into various series or parallel combinations. Variable inductors are constructed so that the effective inductance can be changed. Means for doing this include (1) changing the permeability of a magnetic core; (2) moving the magnetic core, or part of it, with respect to the coil or the remainder of the core; and (3) moving one or more coils of the inductor with respect to one or more of the other coils, thereby changing mutual inductance
The energy (measured in joules, in SI) stored by an inductor is equal to the amount of work required to establish the current flowing through the inductor, and therefore the magnetic field. This is given by:

where L is inductance and I is the current flowing through the inductor

Inductance :
Inductance (or electric inductance) is a measure of the amount of magnetic flux produced for a given electric current. The term was coined by Oliver Heaviside in February 1886 The SI unit of inductance is the henry (symbol: H), in honour of Joseph Henry.
It is also defined as the property of an electric circuit or of two neighboring circuits whereby an electromotive force is induced (by the process of electromagnetic induction) in one of the circuits by a change of current in either of them. The term inductance coil is sometimes used as a synonym for inductor, a device possessing the property of inductance.
The symbol L is used for inductance, possibly in honour of the physicist Heinrich Lenz.
The inductance has the following relationship:

L is the inductance in henrys,
i is the current in amperes,
Φ is the magnetic flux in webers .
Strictly speaking, the quantity just defined is called self-inductance, because the magnetic field is created solely by the conductor that carries the current.
When a conductor is coiled upon itself N number of times around the same axis (forming a solenoid), the current required to produce a given amount of flux is reduced by a factor of N compared to a single turn of wire. Thus, the inductance of a coil of wire of N turns is given by

where λ is the total 'flux linkage'.

For a given coil, the ratio of the electromotive force of induction to the rate of change of current in the coil is called the self-inductance of the coil. An alternative definition of self-inductance is the number of flux linkages per unit current. Flux linkage is the product of the flux and the number of turns in the coil. Self-inductance does not affect a circuit in which the current is unchanging; however, it is of great importance when there is a changing current, since there is an induced emf during the time that the change takes place. For example, in an alternating-current circuit, the current is constantly changing and the inductance is an important factor.
Inductance of a solenoid:
The self-inductance L of a solenoid can be calculated from

μ0 is the permeability of free space (4π × 10-7 henrys per metre)
μr is the relative permeability of the core (dimensionless)
N is the number of turns.
A is the cross sectional area of the coil in square metres
l is the length of the coil (NOT the wire) in metres.
Φ = BA is the flux in webers (B is the flux density, A is the area).
i is the current in amperes

Inductance of a circular loop :The inductance of a circular conductive loop made of a circular conductor can be determined using

μ0 and μr are the same as above
r is the radius of the loop
a is the radius of the conductor

The mutual inductance of two neighboring circuits is defined as the ratio of the emf induced in one circuit to the rate of change of current in the other circuit.
The mutual inductance of two circuits may also be expressed as the ratio of the flux linkages produced in a circuit by the current in a second circuit to the current in the second circuit.
Properties of inductance:

These equations together state that, for a steady applied voltage v, the current changes in a linear manner, at a rate proportional to the applied voltage, but inversely proportional to the inductance. Conversely, if the current through the inductor is changing at a constant rate, the induced voltage is constant.

For more explanation and derivations of expressions visit the following sites :

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