EducationWhat is an inductor - Inductor definition, Inductor formulas

What is an inductor – Inductor definition, Inductor formulas

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Inductor definition

Inductor (also named coil or reactor) is a passive electronic component, which manufacturing process is based on winding a given number of conductor windings on a particular surface e.g. a ring (which creates a toroidal inductors, a roller (solenoids) or a plane (spiral, flat inductors). In addition, on the outside/inside of the inductors there can be created a core made of a magnetic, diamagnetic or ferromagnetic material. 

Inductor symbol

inductor symbol

In the matter of the fact, that inductor is the inertial element, it stores energy in the generated magnetic field. Applying an inductor with the capacitor in one circuit results in the resonant circuit (which is one of elementary electronic circuits). inductor that is powered by direct current is commonly called electromagnet, which is used to generate magnetic field or its compensation (balancing e.g. during demagnetization). In the circuit of alternating current, the inductor induces a current, thus it causes a delay of its voltage in relation to the phase voltage and the total resistance increase. Inductor placed in electrical systems has a number of properties, for example except generating a magnetic field, it can induce a current as well as affect on the current and voltage phase. The inductor symbol is denoted by the letter L – as its inductance. 

How does an inductor work

Inductor in the direct current circuits plays the role of the resistive component (resistance depends on the material from which it was made). However, when the frequency has a value greater than 0 (ω > 0), the resistance of the inductor is called electrical reactance (usually denoted with the letter X).

Reactance of an inductor

inductor reactance

ω – angular frequency

Inductor impedance

When we deal with an ideal inductor, the impedance is equal to the product of its reactance and the imaginary unit:

inductor impedance

Inductor inductance

Inductance is a fundamental electrical parameter that describes a inductor, marked with the “L” letter. It is defined as the current (magnetic induction vector stream) flowing through the inductor. The unit of inductance is Henr [H]. Formula is presented below:

inductor inductance

– a magnetic induction flux,

i – the current intensity flowing through the inductor.

The shape of the inductor, thickness of the wire used in the component and the number of turns of this wire has direct influence at k factor. The inductance of the inductor is also dependent of the magnetic properties of the core. 

Induction flux of the magnetic field flowing through the inductor is described by the formula:

Induction flux of the magnetic field

L – inductance of the inductor,
i – the current flowing through the inductor.

The current flowing through the conductor of a given intensity generates magnetic field at the same time. The energy of this field is numerically equal to the work needed to produce it, which is: 

current flowing through the conductor

L – inductance of the inductor,
I – the current flowing through the inductor,
B – magnetic induction,
V – the volume of the inductor (the focus of the B induction).

The electromotive force (EMF) that is inducing in the inductor is described by the formula:

electromotive force

If we assume that the inductance of the inductor is constant (as it’s true for most electrical circuits), the above formula can be written as:

electromotive force

Inductor constant

Inductor constant for the DC current corresponds to the inductance:

inductor constant

H – the intensity of the magnetic field,
I – current intensity.

Inductor current

The immediate current of the inductor is determined from the equation for the instantaneous voltage of the inductor. An ideal makeover of the claimed equation lead to a differential equation with split variables, where one variable is the inductor current and the other is the inductor voltage.

inductor current

Power of inductor

A inductor has the capability to save power in a magnetic field. The formula for inductor power originated from the general energy/work formula. Work is the integral of instant power p at time t.→ W=∫p·dt, Thinking about the truth that instantaneous power is the item of instant voltage as well as instantaneous current → p=u-i and thinking about the formulas derived earlier, the outcome is the formula for the energy saved in the inductor. Note that the power saved in the inductor is symmetrical to the current in the 2nd power.

Power of inductor

Resistance of inductor

For a inductor without a ferromagnetic core (air inductor), its inductance is constant. For a inductor with a ferromagnetic core, its inductance varies and depends from type of ferromagnet, magnetic induction in the core along with the application of the magnetic circuit magnetic circuit (core with air space). Inductance of a inductor can be determined directly or figured out utilizing indirect techniques. For direct measurement an RLC meter with digital readout is utilized. Of the indirect approaches, the most typically utilized is the technological method to determine the inductor reactance XL as well as therefore its very own inductance L.

For this objective, the inductor is provided from an AC resource of well-known frequency f as well as the voltage U on the inductor, the current I flowing with the inductor and the active power P drawn by the inductor are determined.

Resistance of inductor

For an air inductor, the resistance resulting from the relationship:

Resistance of inductor

is practically the resistance of the inductor winding wire.

Time constant for inductor

The time dependence of the current in the circuit when it is separated from the resource of electromotive force is stood for by the list below equation.

Time constant for inductor

The result shows that the current in the circuit will certainly decay according to an exponential relationship, as well as the rate of degeneration is established by the proportion of resistance to inductance of the circuit. The inverse of this ratio is the time constant of the circuit RL, which we have signified by τ.

Time constant for inductor

Inductor Series and parallel connections

Inductors can be combined like resistors and capacitors in series and parallel configurations and used in e.g. input voltage LC filtering systems in digital circuits (“before” microcontrollers).

In the series connection, the same curent value flows through every component. However, it is worth noting that each of them can have different voltage. Total inductance of such system is given by:

series connection coils formula
Series connection coils
Series connection coils

Inductors connected by parallel connection can be replaced by one with a total inductance given by formula: 

parallel connection coil formula
Parallel connection coils
Parallel connection

Properties shown above apply only when the magnetic field of each of the inductors does not affect each other.

Inductor circuits

Coupling inductor

With combining inductor 2 cables are wrapped around a magnetic core. In this diagram, note that both wires are wrapped around the core in opposite directions and also generate the very same polarity of voltage. This is due to Lenz’s law. A differing magnetic field, produced by the current, will induce a current in the opposite instructions on the coupled inductor. Heinrich Lenz included the negative indication to Faraday’s law of induction.

Coupling inductor

Here ɸB, is the change in magnetic flux and is the electromotive force.

The flux within the magnetic core of the coupled inductors depends upon the product of the
core, the number of turns of the wire around the core, and the current.

Coupling inductor

The voltage throughout the inductor is associated with the flux by the number of turns of the inductor.

Coupling inductor

The magnetic flux will certainly be the same (as induced by the first inductor), as well as we acquire as well as formula for the shared inductance.

Coupling inductor

The variable M is the mutual inductance of the system, in henrys. This depends on the geometrical properties of the inductors, such as the number of turns and radii of the turns of each inductor.

Coupling inductor

A dot convention is made use of to define the direction of the windings around the core. Dots on the very same ends of the inductor, mean that the inductors are wrapped clockwise-counterclockwise per other. If the dots get on the opposite sides, then the inductors are wrapped parallel (clockwise-clockwise or counterclockwise-counterclockwise).

Coupling inductor schematic

It’s crucial to keep in mind that the dot convention adheres to passive convention. Over figure displays the voltages as the very same polarity, one of the voltages will certainly be negative. The dot convention states: If the current enters the dotted terminal of one inductor, the voltage will be positive at the dot on the 2nd inductor.

Coupling inductor schematic

This voltage is the voltage induced by the coupled current. A transformer can have current getting in from both the initial and also 2nd inductors. The voltage across each inductor will certainly be dependant on the current via this inductor as well as the induced voltage from the other inductor. Suppose the dots are on the very same end, and also both currents go into at the dots. The voltages will be.

 voltage induced by the coupled current

If the dots are on the contrary sides of each other, then the voltages will certainly be.

voltage induced by the coupled current.

Since the induction relies on an altering current, coupled inductors have to be utilized with alternating current. This means that we can evaluate coupled inductors in the frequency domain as phasors.

coupled inductors have to be utilized with alternating current

Variable inductor

Variable inductor, is a component of induction heater, which identifies the efficiency as well as effectiveness of warming the fee. The range of our inductors is large; from basic spirals containing a number of copper inductors encompassing a mandrel, to exactly machine made shapes constructed from solid copper items, consequently welded together with high melting solder.

The exciter is made use of to transfer the energy of an alternating electromagnetic field from an induction generator to the fee. The electromagnetic field generates a current in the charge that shows the current flowing in the inductor. If the current circulations through the resistance of the charge, it generates warm in the form of losses according to the formula I2R.

The 2nd factor for home heating is associated with the hysteresis phenomenon, which applies to magnetic materials such as carbon steel. Energy is produced in the charge because of the alternating electromagnetic field causing the charge to transform polarity (remagnetize). Hysteresis heating happens in (magnetic) charges just approximately the Curie temperature level (750oC for steel) at which the magnetic permeability goes down to 1.

Variable inductor

Current flowing through a conductor creates an electromagnetic field. The alternating current generates an alternating electromagnetic field, which generates an alternating current in the additional conductor (charge). The current in the charge is proportional to the field strength.

There is a transformer impact since the current flow induced in the charge is symmetrical to the number of turns of the inductor as well as is like a reflected image of the inductor.

The shape of the inductor is the basis for the performance and also performance of the induction home heating process. We develop inductors primarily to suggest the location of home heating. Warmth needs to be produced in such a location as well as in such a way to accomplish the desired technical result.
Inductors are water cooled copper conductors, made of copper tubes or profiles, which can be quickly formed for the needed induction home heating procedure. Inductors are cooled down and also do not warm up, since water flows with them.

Matching the inductor to the generator output circuit is necessary for process performance. This is quickly accomplished for various inductors as a result of the ability to use several taps on the outcome transformer to which the inductors are attached.

Choke inductor

Induction chokes have a vast array of applications, especially in the electronics and also electrical sector. They are frequently made use of in drive systems, where they cooperate with inverters, i.e. devices altering direct current into alternating current with flexible voltage as well as frequency. Induction chokes are additionally utilized in power electronic devices, where their task is to decrease the quantity of electro-magnetic interference happening throughout procedure. Furthermore, these aspects are made use of in rectifiers supplied from the electro-magnetic network. In this situation, they are created to suppress ripple. In AC circuits, inductive chokes are used to decrease short-circuit currents.

Chokes are excellent anti-interference protection for AC circuits of generally used devices. It is likewise worth understanding that the inductive choke will discover application in the case of pulse stabilizers running at high frequencies, i.e. incorporated circuits that power a provided receiver. These stabilizers are responsible for generating steady outcome voltage based upon the phenomenon of self-induction. An equally common application of an inductive choke is to utilize it to interrupt the current regulating transistors in converters improved thyristors. This indicates that the choke is among one of the most functional electric gadgets as well as its relevance in a given circuit needs to not be underestimated.

Capacitor vs inductor

  • Some differences arise from the construction of the private elements themselves. A capacitor contains 2 covers constructed from conductive product, however between them is a layer of non-conductive dielectric. The conclusion? A capacitor does not conduct direct current, it is just a break in the circuit. For alternating current, on the other hand, the situation is various – the capacitor conducts. For high frequencies it is a short circuit – as if it really did not exist, i.e. there would be simply an item of wire or a path on the PCB … How does it associate with the inductor? A inductor is generally a correctly formed item of cable. In the easiest terms. It conducts direct current. The situation is completely different for alternating current. It conducts, yet the higher the frequency, the even worse. Theoretically, for very high frequencies it constitutes … a break in the circuit.
  • Referring to the first point. A capacitor constitutes a short circuit for high frequencies, as well as an inductor makes up a circuit break. This belongs to their reactance (you know, that resistance for AC current). The capacitive reactance (capacitor) lowers as the frequency boosts. The opposite holds true for an inductor. Inductance reactance boosts as frequency increases.
  • The inductor resists changes in current by inducing a voltage within itself. What does a capacitor do? It does the total reverse, in a manner of speaking. It opposes adjustments in voltage entirely. It replies to a rapid modification in voltage with a similarly quick modification in current.
  • You can locate both inductors and also capacitors in power circuits, such as increase converters.
  • Both the inductor and the capacitor can be built with your own hands. You only need an item of cable o build a inductor. Building a capacitor is a bit more advanced, however once again, all you need is aluminum foil and food cover. As well as scissors.
  • The inductor and the capacitor (and also the resistor, remember) are easy aspects. They don’t create electricity, they trigger power loss.
  • A capacitor shops energy in an electric field, a inductor subsequently in an electromagnetic field.
  • The fundamental physical quantity explaining a capacitor is the electric capacitance – shared in farads. For a inductor, it is the inductance – shared in henries.


Michal Pukala
Electronics and Telecommunications engineer with Electro-energetics Master degree graduation. Lightning designer experienced engineer. Currently working in IT industry.