Home Forums Blogs Articles Photos Videos Contact FAQ

Inductance - Properties of inductance

Inductance - Properties of inductance: Encyclopedia II - Inductance - Properties of inductance

The above equation can be rearranged as follows: Taking the time derivative of both sides of the equation yields: In most physical cases, the inductance is constant with time and so By Faraday's Law of Induction we have: where is the Electromotive force (emf) and v is the induced voltage. Note that the emf is opposite to the induced voltage. Th ...

Inductance: Encyclopedia II - Inductance - Properties of inductance

Inductance - Properties of inductance

The above equation can be rearranged as follows:

Taking the time derivative of both sides of the equation yields:

In most physical cases, the inductance is constant with time and so

By Faraday's Law of Induction we have:

where is the Electromotive force (emf) and v is the induced voltage. Note that the emf is opposite to the induced voltage. Thus:

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 proportionally to the inductance. Conversely, if the current through the inductor is changing at a constant rate, the induced voltage is constant.

The effect of inductance can be understood using a single loop of wire as an example. If a voltage is suddenly applied between the ends of the loop of wire, the current must change from zero to non-zero. However, a non-zero current induces a magnetic field by Ampere's law. This change in the magnetic field induces an emf that is in the opposite direction of the change in current. The strength of this emf is proportional to the change in current and the inductance. When these opposing forces are in balance, the result is a current that increases linearly with time where the rate of this change is determined by the applied voltage and the inductance.

Inductance - Permeability

The amount of magnetic flux produced by a current depends on a physical characteristic of the medium surrounding the current that is known as the permeability, μ. The greater the permeability, the greater the magnetic flux generated by a given current. Certain materials have much higher permeability than air. If a conductor (wire) is wound around such a material, the magnetic flux is generally much greater so the inductance is much greater than the inductance of the wound wire in the air. The self-inductance L of such a solenoid (an idealization of a coil) can be calculated from

where

μ₀ is the permeability of free space (4π × 10^-7 henries per metre) μ_r 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 in metres. Φ = BA is the flux in webers (B is the flux density, A is the area). i is the current in amperes

This, and the inductance of more complicated shapes, can be derived from Maxwell's equations.

Other related archives

1886, Ampere's law, Eddy current, Electromagnetic induction, Electromotive force, Faraday's law of induction, Heinrich Lenz, Inductor, LC circuit, Leakage inductance, Maxwell's equations, Neumann, Oliver Heaviside, RL circuit, RLC circuit, SI, SI electromagnetism units, Stokes' theorem, alternating current, amperes, capacitance, electrical circuit, electricity, gyrator, henries, henry, induced emf, magnetic field, magnetic flux, metre, metres, permeability, solenoid, square metres, transformer, transformers, vector potential, webers

Adapted from the Wikipedia article "Properties of inductance", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki

More material related to Inductance can be found here:

Main Page
for
Inductance Index of Articles
related to
Inductance