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Mutual Inductance | Self Inductance

The electrical element which stores energy in the magnetic field in association with a flow of current is called an inductor.

The inductor can be classified according to the type of core and whether the inductor is fixed or variable. Some type of inductors is shown in the following Fig.

It should be noted that any inductor is made of wire which, in turn, possesses resistance. This resistance is distributed throughout the coil and is essentially in series with the ideal inductance of the coil. When the coil resistance is negligible, the coil behaves as a pure inductor, whereas when the resistance is appreciable, the coil is replaced by the practical inductor shown in the following figure.

Practical inductors are made up of many turns of fine wire wound in a coil to enhance the magnetic effect. Often, the wire is wound on a magnetic material, which is capable of storing more energy per ampere than is air. Because of their shapes, inductors are called coils and because of energy required to establish a current in them, they are called chokes.

Inductance

Inductance is the property of an element to store energy in a magnetic field.

The SI unit of inductance is Henry.

A coil has an inductance of one henry when a current change of one ampere per second induces a counter emf of one volt. Thus;

$e=-L\frac{di}{dt}$

L is the symbol of inductance in henry. The negative sign indicates that induced voltage is a counter emf and is in opposition to the applied voltage. The inductance of a coil mainly depends upon the number of turns and the reluctance of the core of the coil

$L=\frac{{{N}^{2}}}{\Re }$

N shows a number of turns and is the reluctance of a core.

Self-Inductance

The phenomenon in which a changing current in a coil induces an emf in itself is called self-induction.

Let’s consider the case in which a single coil is connected in series with a battery and rheostat as shown in Fig.

When current is passed through the coil, it produces a magnetic field which passes through the coil itself. As long as constant current is passing through the coil, no change in flux takes place and no induced energy is established but if we change the current by changing the resistance in the circuit, the magnetic flux passing through the coil also changes. This change in magnetic flux induces an emf in the coil itself. Such an emf is called self-induced emf and this phenomenon is called self-induction.

Mutual Inductance

Mutual induction is the phenomenon in which a changing current in the coil induces emf in another coil.

Let’s consider the case of following figure in which two coils placed side by side close to each other.

The coil containing a battery and rheostat is the primary coil while another coil containing a galvanometer is called the secondary coil. When current is passed through the primary coil, a magnetic flux is produced due to the current in the coil. Some portion of this flux passes through the secondary coil as well. Since there is no change in flux because of constant current no induced current is produced in the secondary coil. But when current changes in a primary, flux through secondary coil also changes. According to Faraday’s law, an emf is induced in the secondary coil due to flux change. This phenomenon of producing emf in the secondary coil by changing magnetic flux is called mutual induction.

Mutual induction depends upon the following factors:

• Number of turns in the coil
• Cross section area of coils
• Distance between two coils
• Nature of core material upon which two coils are wound

Applications of an inductor

• In filter and resonant circuits
• Avoids inrush current and high voltage spikes
• Can be used as current limiter in numerous electronic circuit