# Bobinin Endüktansı / Inductance of a Coil

The Coil's Inductive is the name given to the property of a component that opposes the change of current passing through it, and even a flat piece of wire has some inductensity.

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Inductors do this by creating a self-induced impetus as a result of their changing magnetic field. In an electrical circuit, when the emk is induced in the same circuit in which the current changes, this effect is called Self-induction, ( L ), but sometimes called back emf because its polarity is in the opposite direction.

When the emk is induced into an adjacent component within the same magnetic field, it is said that the emk is induced by Mutual induction (M), and mutual induction is the basic principle of operation of transformers, motors, relays, etc. The self-induced is a special case of mutual inducing, and since it is produced in a single ins isolated circuit, we often call the inducing simply Induced.

The basic unit of measurement for inductence is called Henry (H) after JosephHenry, but it also has Weber units per amperage (1 H = 1 Wb/A).

The Lenz Act tells us that an induced EMK produces a current in a direction that opposes the change in flux that causes the emk, the principle of influence and response, in the first place. Then we can define the Inducta with an accurate sentence as follows: "When an emk of one volt is induced in the coil, the inductax value of a coil will be a Henry, the current passing through the coil in question varies at the speed of an amperage/second".

In other words, when the current flowing from the coil changes at an amperage/second speed, the inductee of a coil ( L ) is a Henry ( 1H ), ( A/s ). This change induces a voltage of one volt (V_{L)}in it. Thus, the mathematical representation of the rate of change of the current per unit of time along a bandaged coil is given as follows:

Where: di, the change in amps in the current, and dt, is the time it takes for this current to change in seconds. Then, as a result of this change in current, the voltage (V_{L)} induced in an L Henry induced coil is expressed as follows:

Note that the negative sign indicates that the induced voltage is against the change in the current passing through the coil at the unit time (di/dt). From the equation above, the inducing of a coil can be presented as follows:

Where: L is induced in Henry, V_{L} is the voltage on the coil and di/dt is the rate at which the current changes in amps/sec,

Inductace, L is actually a measure of an inductor's "resistance" to the change of the current that passes through the circuit, and the greater its value in Henry, the lower the current change rate.

From the previous tutorial on the inductor, we know that inductors are devices that can store their energy in the form of magnetic fields. Inductors are made from individual wire loops that are combined to form a coil, and if the number of cycles inside the coil increases, the magnetic flux for the same amount of current passing through the coil also increases.

Thus, we can increase the coil inducing by increasing the number of cycles or turns inside a coil. Then we can equation a simple single-layer coil by establishing the relationship between the self-induced, ( L ) and the number of rotations (N) as follows.

Here: L, Henry. N, Number of Returns. Φ Magnetic Flux. Ι Amperage

This expression can also be defined as magnetic flux connection (NΦ), which is divided into current, since the same current value flows effectively from each rotation of the coil. Note that this equation applies only to linear magnetic materials.

## Coil Inducing Question Example 1

A hollow (air) inductor coil consists of 500 rounds of copper wire, which produces a magnetic flux of 10 mWb as a 10-amp DC current passes. Calculate the self-inductive inducation of the coil in milli-Henry.

## Coil Inducing Question Example 2

After a period of 10mS, calculate the value of the self-induced emk produced in the same coil.

The coefficient of the self-inductace of a coil also depends on the characteristics of its structure. For example, size, length, number of turns, etc. Therefore, it is possible to have inductor with very high self-induction coefficients using high permeability cores and a large number of coil rotations. Then for a coil, the magnetic flux produced in its inner core is equal to:

Where: Φ is magnetic flux, B flux density and area A.

If a long solenoid coil with a meter-long N-number of rotations does not have an inner core, that is, "air", the magnetic induction inside its nucleus is calculated as follows:

Then, when we change these expressions for Inducktans in the first equation above, it will give us:

By simplifying and combining similar expressions, the final equation of the coefficient of self-induced coefficient for an air-core coil (solenoid) is given as follows:

Where:

L is henry μ

_{ο} The permeability of the free space (4.π.10^{-7})

is the number of N

Rotations, the inner core area in A, m^{2} ^{(πr 2})

l the length of the coil in meters

Since the inducing of a coil is caused by magnetic flux around it, the stronger the magnetic flux for a particular current value, the larger the inductace. Therefore, a multi-turn coil will have an inductens value higher than just one of the few turns, and therefore, the equation above will give L inductee in proportion to the square number of rotations N2.

In addition to increasing the number of coil rotations, we can also increase inducing by increasing the diameter of the coil or extending the core. In both cases, more wire is required to form the coil.

The inducing of the coil is that if the core of the coil is made of a ferromagetic material, it is more induced than the non-ferromagnetic or hollow air core.

If the inner core is made of a ferromagetic material such as cobalt or nickel, the inducing of the coil will greatly increase because the magnetic flux produced for the same amount of current flow will be much stronger. This is due to the fact that the material intensifies the force lines more strongly along the softer ferromagnetic core material, as we have seen in the training of electromagnets.

For example, if the core material has a relative permeability 1000 times larger than the empty space, such as 1000μ_{ο} ferromomanetic iron or steel, then the coil's inductance is 1000 times larger, so that we can say that the inductance of a coil increases proportionally.

If the coil is wrapped in a ferromary nucleus, a larger inductanx will appear, since the core permeability will change with the flux density. However, depending on the type of ferromagetic material, the inner core magnetic flux can quickly reach saturation by producing a nonlinear inductance value. The flux density around a wire coil, rather than the current passing through it, rather than the inducing, L also has a function of this current flow,

In the next tutorial on inductors, we will see that the magnetic field produced by a coil can cause a current to flow in a second coil placed next to it. This effect is called Mutual Inducing and is the basic principle of operation of transformers,engines and generators.