**inductor**.

# What is an Inductor?

In electrical and electronics, an **inductor **is a passive
circuit component that is designed to store electrical energy in the form of a magnetic
field.

In other words, a circuit element whose terminal voltage is
directly proportional to the derivative of current with respect to time is
called an **inductor**.

In practice, all conductors of electricity have inductive
properties and may be regarded as an inductor. But to enhance the inductive
effect of the conductor, it is twisted into a coil as shown in figure-1.

An inductor is a two-terminal electric circuit element
consisting of a coil of *N* turns. It
is used to introduce inductance into an electrical circuit. Where, **inductance** is the property of a coil by
virtue of which it opposes any change in the amount of electric current through
it.

The inductance of an inductor depends upon its construction
and physical dimensions, i.e.

`\"Inductance",L=(μN^2 a)/l" "…(1)`

Where, *N* is the number of turns in the inductor coil, *l* is the mean length of the inductor, *a* is the area of cross-section, and *µ* is the permeability of the core.

The
commercially available inductors come in different values and types. Typical
practical inductors have inductance values ranging from a few micro-henry (µH)
to tens of henrys (H). Inductors are almost used in every electrical and
electronic circuit. Inductors may be classified as **fixed inductors **or **variable
inductors**. The circuit symbols of the fixed and variable inductors are
shown in figure-2.

**linear inductor**, and an inductor whose inductance varies with current is called a

**non-linear inductor**. The voltage-current relationship of a linear inductor is a straight line as shown in figure-3. The slope of the curve line gives the inductance (

*L*) of the linear inductor.

# Factors Affecting Inductance

From equation (1), we can see that the inductance
of an inductor depends upon the following four factors:

- The inductance of an inductor can be
increased by increasing the number of turns (
*N*) in the coil. - Inductance can be increased by using a
core of high permeability (
*µ*). - Inductance can be increased by increasing
the cross-sectional area (
*a*) of the wire of the coil. - Inductance can be increased by reducing
the length (
*l*) of the inductor coil.

# Current-Voltage Relationship of Inductor

If an electric current is allowed to pass
through an inductor, then it is found that the voltage across the inductor is
directly proportional to the time rate of change of the current, i.e.

`\v(t)∝(di(t))/dt`

`\⟹v(t)=L (di(t))/dt" "…(2)`

Where, *L* is the inductance of the inductor, measured in Henry (H).

Again,

`\di(t)=1/L v(t) dt`

Integrating on both sides gives,

`\i(t)=1/L ∫_(-∞)^tv(τ)dτ" "…(3)`

Or,

`\i(t)=1/L ∫_(t_0)^tv(τ)dτ+i(t_0 )" "…(4)`

Where, *i(t _{0})* is the initial current, i.e. current for

*-∞ < t < t*, and

_{0}*i(-∞) = 0*, because there must be a time in the past when there was no current in the inductor.

# Energy Stored in Inductor

The inductor is mainly designed to store
electrical energy in the form of a magnetic field. The expression of energy
stored in the inductor can be derived as follows-

The power supplied to the inductor is
given by,

Thus, the energy store is given by,

`\w(t)=∫_(-∞)^t p(τ) dτ`

`\⟹w(t)=∫_(-∞)^t v(τ)i(τ)dτ`

`\⟹w(t)=L∫_(-∞)^t (di(τ))/(dτ) i(τ)dτ`

`\⟹w(t)=L∫_(-∞)^t i(τ) di(τ)`

`\⟹w(t)=L[(i^2 (t))/2]_(-∞)^t`

`\⟹w(t)=1/2 Li^2 (t)-1/2 Li^2 (-∞)`

Since,

`\i(-∞)=0`

`\∴w(t)=1/2 Li^2 (t)" "…(5)`

From equation (5), we can see that the
total energy stored in the inductor is always positive (or zero). Therefore, an
inductor is a passive circuit component.

# Characteristics of an Ideal Inductor

The following are the important
characteristics of an ideal inductor:

- There is no voltage across an inductor if the current flowing through it remains constant with respect to time. Therefore, a pure inductor acts as short-circuit on the application of DC.
- An inductor can store a finite amount of energy even if the voltage across the inductor is zero.
- The current through an inductor can never be changed abruptly, i.e. in zero time.
- An ideal inductor never dissipates energy, but only stores it in the form of a magnetic field.

# Circuit Model for a Practical Inductor

An ideal inductor does not have any
resistance, but a practical inductor has a significant resistive component. It
is because the inductor is made of a conductive material like copper which has
some resistance. This resistance of the inductor is called the **winding resistance ( R_{w})**, and it appears in series with the inductor
coil. Due to the winding resistance, a practical inductor store as well
dissipate the energy. Also, a practical inductor has a

**winding capacitance (**which appears in parallel with the series combination of the coil and winding resistance. Although, the winding resistance and capacitance are very small, thus they can be neglected in most practical applications.

*C*)_{w}# Applications of Inductors

The inductor is one of the most
extensively used circuit components in electrical and electronic circuits. The
following are some important applications of the inductor-

- Inductors are used in tuning circuits to select the desired frequency.
- Inductors are used in different contactless sensors like proximity sensors.
- Inductors are also used to store electrical energy in the form of a magnetic field.
- Inductors are used to form windings of electrical machines like motors, generators, transformers, measuring instruments, etc.
- Inductors are used in electronic filter circuits.
- Inductors are also used in chokes for blocking the alternating current flow and passing the direct current.
- Inductors are also used in ferrite beads to reduce radio frequency interference. The ferrite beads are used in computer cables and mobile charging cables.
- Inductors are also used in electromagnetic relays.

# Summary

Now, we can conclude this article with
the following points-

- An inductor is a passive circuit component.
- The inductor is a two-terminal circuit element that opposes any change in the magnitude of current through it.
- The property of an inductor by which it opposes any change in the current is called its inductance.
- An inductor can either be fixed or variable.
- A pure inductor stores electrical energy in the form of a magnetic field, but does not dissipate.
- The current through an inductor cannot change instantaneously. Thus, an inductor opposes an abrupt change in the current through it.
- A practical or non-ideal inductor shows very small resistive and capacitive effects as well.
- In the steady state condition, the inductor acts like a short circuit.

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