Inductors and Inductance
Electrical inductance (L) is a property of conductors and it is defined in terms of the electromotive force (emf), or voltage, generated in a conductor to oppose a given change in current (I). This is expressed as:
emf = -L ▵I/▵t.
Inductance is illustrated by the behavior of a coil resisting any change in electric current going through it. If the current inside the coil increases, then a voltage opposing that increase will be created by the magnetic field of the coil. Inductance is a consequence of Faraday's law of induction, which states that an emf is induced in a conductor when the magnetic field around it changes. Thus, inductance results in opposition to an increase or decrease in current. This is consistent with Lenz's law, which states that when an emf is generated by a change in magnetic flux following Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. This is why the induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant.
The voltage induced in a conductor is also proportional to the rate of change of the magnetic flux and the faster the magnetic field is changing, the larger the induced voltage. This represents the operating principle of electric motors and generators and also explains the behavior of magnets and conductors when one is moving relative to the other. For example, when a conductor is moving across a magnetic field, a current is produced in the conductor inducing a magnetic field that acts to stop the conductor from moving. The inductance of a coil is expressed as follows:
L = [b.mu ]N2
where is the magnetic permeability of the coil, N is the number of turns of wire in the coil, and A is the surface area of the coil.
Inductors may be coupled. When a steady current flows in one coil, a constant magnetic field will be induced in the other coil. If this magnetic field is not changing, there will be no induced voltage in the secondary coil. But if the current is altered, there will be a change in the magnetic field and a voltage will be induced causing a current flow in the secondary coil that will then try to maintain the original magnetic field. Once the current is resumed, an induced current in the opposite direction will oppose the increase in the magnetic field. This generation of voltages to oppose changes in the magnetic field represents the operating principle behind transformers. It also describes a property known as mutual inductance, where a change in the current of one coil affects the current and voltage in the second coil.
Inductance is also an important concept in the design of AC motors, which operate by rotating a coil in a magnetic field and generating a torque on it. Since the current produced is alternating, such synchronous motors run smoothly only at the frequency of the sine wave. If the frequency is disrupted, the current will slip out of sync thus disrupting the output to the motor. The most common design is provided by the small AC induction motor, in which an electric current is not directly supplied, but is induced in the closed loop low-resistance rotating coils.
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