# Is inductor linear or non-linear

## What is an inductor and how does it work (facts to never forget)

### Inductor, what is it?

We have all heard the term inductor many times, but what is it? Well, it's a passive element To store energy in its magnetic field. Inductors have numerous uses in electronic systems and power systems. They are used in power supplies, transformers, radios, televisions, radars and electric motors.

What is an Inductor and How Does It Work - Facts You Should NEVER Forget (Photo credit: Tamara Kwan via Flickr)

Every electrical current conductor has inductive properties and can be viewed as an inductor.

In order to enhance the inductive effect, a practical inductor is usually formed into a cylindrical coil with many turns of conductive wire, as shown in FIG.

An inductor consists of a Conductive wire coil.

Figure 1 - Typical shape of an inductor

When the current flows through the inductor, it is determined that the voltage across the inductor is directly proportional to the rate of change of the current over time. Use the passive sign convention in the following Equation (1):

where from L. is the constant of proportionality known as the inductance of the inductance. The unit of inductance is Henry (H), named after the American inventor Joseph Henry (1797-1878). It is clear from the above equation that 1 henry equals 1 volt-second per ampere.

With regard to the above equation, an inductor must have a voltage at its terminals, the current of which must vary over time. Therefore v = 0 for a constant current through the inductance.

Inductance is the property where an inductor resists the change in current flowing through it, measured in henries (H).

The inductance of an inductance depends on its inductance physical dimension and construction. Formulas for calculating the inductance of inductors of different shapes are derived from electromagnetic theory and can be found in commercially available electrical engineering manuals.

For example for the Inductor (magnet) shown in Figure 1,

where from:

• N is the number of revolutions,
• l is the length
• A is the cross-sectional area and
• m is the permeability of the core.

We can see this equation above the equation can be increased by increasing the number of coil turns, using higher permeability material as the core, increasing the cross-sectional area, or reducing the length of the coil.

Figure 2 - Different types of inductors: (a) magnetically wound inductors, (b) toroidal coils, (c) chip inductors

Commercially available inductors, like capacitors, come in different values ​​and types. Typical practical inductors have inductance values ​​of a some microhenrys (mH)as in communication systems Dozen of Henrys (H) like in energy systems. Inductors can be fixed or variable. The core can be made of iron, steel, plastic or air.

The terms Kitchen sink and choke are also used for inductors.

Common inductors are shown in Figure 2 above. The circuit symbols for inductors are shown in Figure 3 and follow the passive convention.

Figure 3 - Circuit symbols for inductors: (a) air core, (b) iron core, (c) variable iron core

Equation (1) is the Voltage-current relationship for an inductance. 4 shows this relationship graphically for an inductance whose inductance is current-independent. Such an inductance is known as a linear inductance.

For a nonlinear inductor, the graph of equation (1) is not a straight line because its inductance varies with the current.

In this technical article we assume linear inductors.

Figure 4 - Voltage-current ratio of an inductor

The current-voltage relationship is obtained from equation (1) as:

Integrating gives:

or

where from it0) is the total current for −∞ O and i (−∞) = 0. To make the idea i (−∞) is practical and useful because there was a time in the past when there was no current in the inductor.

The inductor is designed to store energy in its magnetic field. The stored energy can be obtained from equation (1). The power delivered to the inductor is:

The stored energy is:

Since i (−∞) = 0,

### Remarks //

We should note the following important properties of an inductor:

NOTE 1 //

Notice from Equation 1 that the voltage across an inductor is zero when the current is constant.

So an inductor acts like a Short circuit to DC.

NOTE 2 //

An important property of the inductor is the rejection of the current change flowing through it. The current through an inductor cannot change immediately.

According to Equation (1)A discontinuous change in the current through an inductor requires an infinite voltage, which is physically not possible. An inductance thus counteracts an abrupt change in the current.

For example, the current through an inductance can take the form shown in FIG Figure 5 (a)However, the inductor current cannot take the form shown in FIG 5 (b) in real situations due to the discontinuities. However, the voltage across an inductor can change abruptly.

Figure 5 - Current through an inductor: (a) allowed, (b) not allowed; an abrupt change is not possible

NOTE 3 //

Like the ideal capacitor The ideal inductor does not consume any energy. The energy stored in it can be called up at a later point in time. The inductor draws energy from the circuit when it is storing energy and supplies power to the circuit when returning previously stored energy.

NOTE 4 //

A practical, non-ideal inductor has a resistance component as shown in FIG. This is due to the fact that the inductor is made of a conductive material such as copper, which has some resistance.

Since an inductor often consists of a highly conductive wire, it has very little resistance.

Figure 6.26 - Circuit model for a practical inductor

This resistance is called Winding resistance Rw, and it appears in series with the inductance of the inductor. The presence of Rw makes it both an energy storage and an energy dissipation device. Since Rw is usually very small and is ignored in most cases. The non-ideal inductor has one too Winding capacitance Cw due to the capacitive coupling between the conductive coils.

C.w is very small and can be ignored in most cases except for high frequencies. In this article we only assume ideal inductors.

### Who Was Joseph Henry?

Joseph Henry (1797–1878), an American physicist, discovered inductance and built an electric motor. Henry was born in Albany, New York and studied at Princeton University from 1832 to 1846.

The American physicist Joseph Henry (1797–1878) discovered inductance and constructed an electric motor

He was the first secretary of the SmithsonianInstitution. He conducted several experiments on electromagnetism and developed powerful electromagnets that could lift objects weighing thousands of pounds. Interestingly, Joseph Henry discovered electromagnetic induction before Faraday, but was unable to publish his results.

The unit of inductance, the henrywas named after him.

Reference // Basics of electrical circuits by Charles K. Alexander and Matthew N.O. Sadiku (buy hardcopy from Amazon)