# Inductors and Inductance : Working, Unit, Function, Types and Uses

- Link: https://studyelectrical.com/2019/11/inductors-inductance-working-unit-function-types-uses.html
- Published: 2019-11-11T19:22:20+00:00
- Author: Tesla

**Inductors** are electrical components that oppose the flow of alternating current(
AC) by temporarily storing energy as magnetic fields. The action of an inductor 
is known as **Inductance**.

This article discusses inductors and inductance. By the end of this article, you
will learn the following.

 * What is inductor and inductance and how they work?
 * What are the different types of inductors?
 * Series and parallel inductors and their connection
 * Mutual inductance and coefficient of coupling.
 * Advantages and disadvantages of different types of inductors

Inductors often, but not always, consist of wire coils. Sometimes a length of wire,
or a pair of wires, is used as an inductor.

![Types of Inductors](https://studyelectrical.com/wp-content/uploads/2019/11/Types-
of-Inductors.jpg)

Types of Inductors

## What is Inductance?

Suppose you have a wire 1 million miles long (about 1.6 million kilometers). Imagine
that you make this wire into a huge loop, and connect its ends to the terminals 
of a battery as shown in the figure below. An electrical current will flow through
the loop of wire, but this is only part of the picture.

![the principle of inductance.](https://studyelectrical.com/wp-content/uploads/2019/
10/A-huge-imaginary-loop-of-wire-can-be-used-to-illustrate-the-principle-of-inductance..
jpg)

A huge, imaginary loop of wire can be used to illustrate the principle of inductance.

If the wire was short, the current would begin to flow immediately, and it would
attain a level limited by the resistance in the wire and in the battery.

But because the wire is extremely long, it takes a while for the electrons from 
the negative terminal to work their way around the loop to the positive terminal.
It will take a little time for the current to build up to its maximum level.

The magnetic field produced by the loop will be small during the first few moments
when current flows in only part of the loop. The magnetic field will build up as
the electrons get around the loop. Once a steady current is flowing around the entire
loop, the magnetic field will have reached its maximum quantity and will level off.

![Relative magnetic flux as a function of time](https://studyelectrical.com/wp-content/
uploads/2019/10/Relative-magnetic-flux-as-a-function-of-time.png)

Relative magnetic flux in and around a huge loop of wire connected to a current 
source, as a function of time.

A certain amount of energy is stored in this magnetic field. The amount of stored
energy depends on the inductance of the loop, which is a function of its overall
size.

Inductance, as a property or as a mathematical variable, is symbolized by an italicized,
uppercase letter **L**.

The loop constitutes an inductor, the symbol for which is an uppercase, nonitalicized
letter L.

## Practical Inductors

It is impractical to make wire loops 1 million miles in circumference. But lengths
of wire can be coiled up. When this is done, the magnetic flux is increased for 
a given length of wire compared with the flux produced by a single-turn loop.

The magnetic flux density inside a coil is multiplied when a **ferromagnetic core**
is placed within it.

The increase in flux density has the effect of increasing the inductance, too. So,
Inductance (L) is many times greater with a ferromagnetic core than with an air 
core or a nonmagnetic core such as plastic or wood.

The current that an inductor can handle depends on the diameter (gauge) of the wire.
But the value of inductance L is a function of the number of turns in the coil, 
the diameter of the coil itself, and the overall shape of the coil.

In general, the inductance of a coil is directly proportional to the number of turns
of wire.

Inductance is directly proportional to the diameter of the coil. The length of a
coil, given a certain number of turns and a certain diameter, has an effect as well.

If a coil having a certain number of turns and a certain diameter is “stretched 
out,” its inductance decreases. Conversely, if it is “squashed up,” its inductance
increases.

### The Unit of Inductance

When a battery is first connected across an inductor, the current builds up at a
rate that depends on the inductance. The greater the inductance, the slower the 
rate of current buildup for a given battery voltage.

The unit of inductance is an expression of the ratio between the rate of current
buildup and the voltage across an inductor. An inductance of 1 henry (1 H) represents
a potential difference of 1 volt (1 V) across an inductor within which the current
is changing at the rate of 1 ampere per second (1 A/s).

**Henry is a huge unit of inductance.** You won’t often see an inductor this large,
although some power-supply filter chokes have inductances up to several henrys.

Usually, inductances are expressed in millihenrys (mH), microhenrys (µH), or nanohenrys(
nH). You should know your prefix multipliers by now, but in case you’ve forgotten:

**1 mH = 0.001 H = 10^(-3) H**
 **1 µH = 0.001 mH = 10^(-6) H** **1 nH = 0.001 µH
= 10^(-9) H**

Small coils with few turns of wire produce small inductances, in which the current
changes quickly and the induced voltages are small.

Large coils with ferromagnetic cores, and having many turns of wire, have high inductances
in which the current changes slowly and the induced voltages are large.

The current from a battery, building up or dying down through a high-L coil, can
give rise to a deadly potential difference between the end terminals of the coil—
many times the voltage of the battery itself. This is how spark coils work in internal
combustion engines. Be careful around them!

### Inductors in Series

When the magnetic fields around inductors do not interact, inductances in series
add like resistances in series. The total value is the sum of the individual values.

It’s important to be sure that you are using the same size units for all the inductors
when you add their values. After that, you can convert the result to any inductance
unit you want.

**Example 1**

Suppose three 40.0-µH inductors are connected in series, and there is no interaction,
or mutual inductance, among them. What is the total inductance?

Add up the values.

Call the inductances of the individual components L1 , L2 , and L3 , and the total
inductance L.

Then **L = L1 + L2 + L3** = 40.0 + 40.0 + 40.0 = 120 µH.

**Example 2**

Imagine three inductors, with no mutual inductance, with values of 20.0 mH, 55.0
µH, and 400 nH. What is the total inductance, in millihenrys, of these components
if they are connected in series as shown in the figure?

![Inductors in Series](https://studyelectrical.com/wp-content/uploads/2019/10/Inductors-
in-Series.png)

Inductors in Series

First, convert all the inductances to the same units. Microhenrys are a good choice
because that unit makes the calculation process the least messy.

Call L1 = 20.0 mH = 20,000 µH, L2 = 55.0 µH, and L3 = 400 nH = 0.400 µH.

The total inductance is therefore L = 20,000 + 55.0 + 0.400 = 20,055.4 µH.

This is 20.1 mH after converting and rounding off.

### Inductors in Parallel

If there is no mutual inductance among two or more parallel-connected inductors,
their values add up like the values of resistors in parallel.

Suppose you have inductances L1, L2, L3,. . . , Ln all connected in parallel.

Then you can find the reciprocal of the total inductance, 1/L, using the following
formula:

**1/L = 1/L1 + 1/L2 + 1/L3 + . . . + 1/Ln**

The total inductance, L, is found by taking the reciprocal of the number you get
for 1/L.

Again, as with inductances in series, it’s important to remember that all the units
have to agree during the calculation process. Once you have completed the calculation,
you can convert the result to any inductance unit.

**Example 1**

Suppose there are three inductors, each with a value of 40 µH, connected in parallel
with no mutual inductance, as shown in the figure. What is the net inductance of
the combination?

![Inductors in Parallel](https://studyelectrical.com/wp-content/uploads/2019/10/
Inductors-in-Parallel.png)

Three Inductors in Parallel

Let’s call the inductances L 1 = 40 µH, L 2 = 40 µH, and L 3 = 40 µH.

Use the preceding formula to obtain 1/L = 1/40 + 1/40 + 1/40 = 3/40 = 0.075. Then
L = 1/0.075 = 13.333 µH.

This should be rounded off to 13 µH because the original inductances are specified
to only two significant digits.

**Example 2**

Imagine four inductors in parallel, with no mutual inductance and values of L 1 
= 75.0 mH, L 2 = 40.0 mH, L 3 = 333 µH, and L 4 = 7.00 H. What is the net inductance
of this combination?

You can use henrys, millihenrys, or microhenrys as the standard units in this problem.
Suppose you decide to use Henry.

Then L 1 = 0.0750 H, L 2 = 0.0400 H, L 3 = 0.000333 H, and L 4 = 7.00 H.

Use the preceding formula to obtain 1/L = 13.33 + 25.0 + 3003 + 0.143 = 3041.473.

The reciprocal of this is the inductance L = 0.00032879 H = 328.79 µH.

This should be rounded off to 329 µH. This is only a little less than the value 
of the 333 µH inductor alone.

_If there are several inductors in parallel, and one of them has a value that is
much smaller than the values of all the others, then the total inductance is a little
smaller than the value of the smallest inductor._

## Interaction among Inductors

In real-world circuits, there is almost always some mutual inductance between or
among solenoidal coils. The magnetic fields extend significantly outside such coils,
and mutual effects are difficult to avoid or eliminate.

The same is true between and among lengths of wire, especially at high ac frequencies.
Sometimes, mutual inductance has no detrimental effect, but in some situations, 
it is not wanted.

**Mutual inductance can be minimized by using shielded wires and toroidal inductors.**
The most common shielded wire is a coaxial cable.

Toroidal inductors are discussed later in this article.

### Coefficient of Coupling

The coefficient of coupling, symbolized k, is an expression of the extent to which
two inductors interact.

It is specified as a number ranging from 0 (no interaction) to 1 (the maximum possible
interaction).

Two coils separated by a sheet of solid iron, or by a great distance, have a coefficient
of coupling of zero (k = 0). Two coils wound on the same form, one right over the
other, have the maximum possible coefficient of coupling (k = 1).

Sometimes, the coefficient of coupling is multiplied by 100 and expressed as a percentage
from 0 to 100 percent.

### Mutual Inductance

The mutual inductance between two inductors is symbolized M, and is expressed in
the same units as inductance: henrys, millihenrys, microhenrys, or nanohenrys.

The value of M is a function of the values of the inductors, and also of the coefficient
of coupling.

In the case of two inductors having values of L1 and L2 (both expressed in the same
size units), and with a coefficient of coupling equal to k, the mutual inductance
M is found by multiplying the inductance values, taking the square root of the result,
and then multiplying by k.

Mathematically:

**M = k √(L1 L2)**

where the √ represents the square root.

The value of M thus obtained will be in the same size unit as the values of the 
inductance you input to the equation.

### Effects of Mutual Inductance

Mutual inductance can either increase or decrease the net inductance of a pair of
series-connected coils, compared with the condition of zero mutual inductance.

The magnetic fields around the coils either reinforce each other or oppose each 
other, depending on the phase relationship of the ac applied to them.

If the two ac waves (and thus the magnetic fields they produce) are in phase, the
inductance is increased compared with the condition of zero mutual inductance. If
the two waves are in the opposing phase, the net inductance is decreased relative
to the condition of zero mutual inductance.

When two inductors are connected in series and there is reinforcing mutual inductance
between them, the total inductance L is given by the following formula:

**L = L1 + L2 + 2M**

where L 1 and L 2 are the inductances, and M is the mutual inductance.

All inductances must be expressed in the same size units.

When two inductors are connected in series and the mutual inductance is opposing,
the total inductance L is given by this formula:

**L = L1 + L2 − 2M**

where, again, L 1 and L 2 are the values of the individual inductors.

It is possible for mutual inductance to increase the total series inductance of 
a pair of coils by as much as a factor of 2, if the coupling is total and if the
flux reinforces. Conversely, it is possible for the inductances of two coils to 
completely cancel each other.

If two equal-valued inductors are connected in series so their fluxes oppose (or
buck each other) and k = 1, the result is theoretically zero inductance.

**Example 1**

Suppose two coils, having inductances of 30 µH and 50 µH, are connected in series
so that their fields reinforce, as shown in the figure. Suppose that the coefficient
of coupling is 0.500. What is the total inductance of the combination?

![30 henry and 50 henry inductors in series](https://studyelectrical.com/wp-content/
uploads/2019/10/30-henry-and-50-henry-inductors-in-series.png)

First, calculate M from k.

According to the formula for this, given previously, M = 0.500(50 × 30) 1/2 = 19.4
µH.

Then figure the total inductance.

It is equal to L = L 1 + L 2 + 2M = 30 + 50 + 38.8 = 118.8 µH, rounded to 120 µH
because only two significant digits are justified.

**Example 2**

Imagine two coils with inductances of L 1 = 835 µH and L 2 = 2.44 mH. Suppose they
are connected in series so that their coefficient of coupling is 0.922, acting so
that the coils oppose each other, as shown in the figure. What is the net inductance
of the pair?

![Series inductors](https://studyelectrical.com/wp-content/uploads/2019/10/Series-
inductors.png)

First, calculate M from k.

The coil inductances are specified in different units. Let’s use microhenrys for
our calculations, so L 2 = 2440 µH.

Then M = 0.922(835 × 2440) 1/2 = 1316 µH.

Then figure the total inductance. It is L = L 1 + L 2 − 2M = 835 + 2440 − 2632 =
643 µH.

## Types of Inductors

There are different types of inductors. Depending on the type of core material used,
inductors are categorized into the following.

 1.  **Air Core Inductor**
 2.  **Iron Core Inductor**
 3.  **Ferrite Core Inductor**
 4.  **Iron Powder Inductor**
 5.  **Laminated Core inductor**
 6.  **Toroidal Inductor**
 7.  **Ceramic Inductor**
 8.  **Film Layer Inductor**
 9.  **Variable Inductor**
 10. **Coupled Inductors**

## Air-Core Inductor

The simplest inductors (besides plain, straight lengths of wire) are coils.

A coil can be wound on a hollow cylinder of plastic or other nonferromagnetic material,
forming an air-core coil. In practice, the maximum attainable inductance for such
coils is about 1 mH.

![Air core inductor coil](https://studyelectrical.com/wp-content/uploads/2019/10/
air-core-inductor-coil.png)

Air Core Inductor Coil

Air-core coils are used mostly in radio-frequency transmitters, receivers, and antenna
networks.

In general, the higher the frequency of ac, the less inductance is needed to produce
significant effects. Air-core coils can be made to have the almost unlimited current-
carrying capacity, simply by using heavy-gauge wire and making the radius of the
coil large. Air does not dissipate much energy in the form of heat. It’s efficient,
even though it has low permeability.

## Ferromagnetic Cores

Ferromagnetic substances can be crushed into dust and then bound into various shapes,
providing core materials that greatly increase the inductance of a coil having a
given number of turns.

Depending on the mixture used, the increase in flux density can range from a factor
of a few times, up through many thousands of times. A small coil can thus be made
to have a large inductance.

There are two main types of ferromagnetic material in common use as coil cores. 
These substances are known as powdered iron and ferrite.

 1. Powdered Iron Cores
 2. Ferrite Core

### Advantages and Limitations of Ferromagnetic Cores

Powdered-iron cores are common at high and very high radio frequencies.

A ferrite is a special form of powdered iron that has exceptionally high permeability,
causing a great concentration of magnetic flux lines within the coil.

![A Ferrite Core Inductor](https://studyelectrical.com/wp-content/uploads/2019/10/
ferrite-core-inductor.png)

A Ferrite Core Inductor

Ferrite is used at audio frequencies, as well as at low, medium, and high radio 
frequencies. Coils using these materials can be made much smaller, physically, than
can air-core coils having the same inductance.

The main trouble with ferromagnetic cores is that, if the coil carries more than
a certain amount of current, the core will saturate. This means that the ferromagnetic
material is holding as much flux as it possibly can.

When a core becomes saturated, any further increase in coil current will not produce
a corresponding increase in the magnetic flux in the core. The result is that the
inductance changes, decreasing with coil currents that are more than the critical
value.

In extreme cases, ferromagnetic cores can also waste considerable power as heat.
This makes a coil lossy.

### Permeability Tuning

Solenoidal coils can be made to have variable inductance by sliding ferromagnetic
cores in and out of them. The frequency of a radio circuit can be adjusted in this
way.

Because moving the core in and out of a coil changes the effective permeability 
within the coil, this method of tuning is called permeability tuning. The in/out
motion can be precisely controlled by attaching the core to a screw shaft, and anchoring
a nut at one end of the coil.

As the screw shaft is rotated clockwise, the core enters the coil, and the inductance
increases. As the screw shaft is rotated counterclockwise, the core moves out of
the coil, and the inductance decreases.

### Toroids

Inductor coils do not have to be wound on cylindrical forms, or on cylindrical ferromagnetic
cores. There’s another coil geometry, called the toroid.

![Toroidal Core inductor](https://studyelectrical.com/wp-content/uploads/2019/11/
Toroidal_Core_inductor.jpg)

Toroidal Core inductor

Toroid gets its name from the shape of the ferromagnetic core. The coil is wound
over a core having this shape which resembles a donut or bagel.

There are several **advantages** to toroidal coils over solenoidal, or cylindrical,
ones.

 1. First, fewer turns of wire are needed to get a certain inductance with a toroid
    compared to a solenoid.
 2. Second, a toroid can be physically smaller for a given inductance and current-carrying
    capacity.
 3. Third, practically all the flux is contained within the core material. This reduces
    unwanted mutual inductances with components near the toroid.

Toroidal coils have **limitations**, too.

 1. It is more difficult to permeability-tune a toroidal coil than it is to tune a 
    solenoidal one.
 2. Toroidal coils are harder to wind than solenoidal ones.
 3. Sometimes, mutual inductance between or among physically separate coils is actually
    desired; with a toroid, the coils have to be wound on the same form for this to
    be possible.

### Pot Cores

There is another way to confine the magnetic flux in a coil so that unwanted mutual
inductance does not occur: wrap ferromagnetic core material around a coil. A wraparound
core of this sort is known as a **pot core**.

![Pot Core Inductor](https://studyelectrical.com/wp-content/uploads/2019/11/Pot-
Core-Inductor.jpg)

Pot Core Inductor

A typical pot core comes in two halves, inside one of which the coil is wound. Then
the parts are assembled and held together by a bolt and nut. The entire assembly
looks like a miniature oil tank. The wires come out of the core through small holes
or slots.

Pot cores have the same **advantages** as toroids.

The core tends to prevent the magnetic flux from extending outside the physical 
assembly. Inductance is greatly increased compared to solenoidal windings having
a comparable number of turns.

In fact, pot cores are even better than toroids if the main objective is to get 
a large inductance in a small space.

The main **disadvantage** of a pot core is that tuning, or adjustment of the inductance,
is all but impossible. The only way to do it is by switching in different numbers
of turns, using taps at various points on the coil.

### Filter Chokes

The largest values of inductance that can be obtained in practice are on the order
of several henrys.

![Filter choke inductor](https://studyelectrical.com/wp-content/uploads/2019/11/
Filter-choke-inductor.jpeg)

Filter choke inductor

The primary use of a coil this large is to smooth out the pulsations in direct current
that result when ac is rectified in a power supply. This type of coil is known as
a filter choke.

### Inductors at AF

Inductors for audio frequency (AF) applications range in value from a few millihenrys
up to about 1 H. They are almost always toroidally wound, or are wound in a pot 
core, or comprise part of an audio transformer. Ferromagnetic cores are the rule.

Inductors can be used in conjunction with moderately large values of capacitance
in order to obtain AF-tuned circuits. However, in recent years, audio tuning has
been largely taken over by active components, particularly integrated circuits.

## Inductors at RF

The radiofrequency (RF) spectrum ranges from a few kilohertz to well above 100 GHz.
At the low end of this range, inductors are similar to those at AF. As the frequency
increases, cores having lower permeability are used.

Toroids are common up through about 30 MHz. Above that frequency, air-core coils
are more often used.

In RF applications, coils are routinely connected in series or in parallel with 
capacitors to obtain tuned circuits.

Other arrangements yield various characteristics of attenuation versus frequency,
serving to let signals at some frequencies pass through while rejecting signals 
at other frequencies.

### Transmission-Line Inductors

At frequencies about 100 MHz, another type of inductor becomes practical. This is
the type formed by a length of the transmission line.

A transmission line is generally used to get energy from one place to another. In
radio communications, transmission lines get energy from a transmitter to an antenna,
and from an antenna to a receiver.

Most transmission lines are found in either of two geometries,

 1. parallel-wire transmission line
 2. coaxial type transmission line

A parallel-wire transmission line consists of two wires running alongside each other
with constant spacing.

The spacing is maintained by polyethylene rods molded at regular intervals to the
wires, or by a solid web of polyethylene. The substance separating the wires is 
called the dielectric of the transmission line.

A coaxial transmission line has a wire conductor surrounded by a tubular braid or
pipe. The wire is kept at the center of this tubular shield by means of polyethylene
beads, or more often, by solid or foamed polyethylene, all along the length of the
line.

### Line Inductance

Short lengths of any type of transmission line behave as inductors, as long as the
line length is less than 90° ( 1⁄4 of a wavelength).

At 100 MHz, 90° in free space is 75 cm, or a little more than 2 ft. In general, 
if f is the frequency in megahertz, then 1⁄4 wavelength in free space, expressed
in centimeters (s cm ), is given by this formula:

**S_(cm) = 7500/f**

The length of a quarter-wavelength section of the transmission line is shortened
from the free-space quarter wavelength by the effects of the dielectric.

In practice, 1 ⁄ 4 wavelength along the line can be anywhere from about 0.66 (or
66 percent) of the free-space length for coaxial lines with solid polyethylene dielectric
to about 0.95 (or 95 percent) of the free-space length for parallel-wire line with
spacers molded at intervals of several centimeters. The factor by which the wavelength
is shortened is called the velocity factor of the line.

The shortening of the wavelength in a transmission line, compared with the wavelength
in free space, is a result of a slowing down of the speed with which the radio signals
move in the line compared with their speed in space (the speed of light).

If the velocity factor of a line is given by v, then the preceding formula for the
length of a quarter-wave line, in centimeters, becomes:

**S_(cm) = 7500v/f**

Very short lengths of line—a few electrical degrees—produce small values of inductance.
As the length approaches 1⁄4 wavelength, the inductance increases.

Transmission line inductors behave differently than coils in one important way: 
the inductance of a coil, particularly an air-core coil, is independent of the frequency.

But the inductance of a transmission-line section changes as the frequency changes.
At first, the inductance becomes larger as the frequency increases. At a certain
limiting frequency, the inductance becomes theoretically infinite.

Above that frequency, the line becomes capacitive rather than inductive. Learn more
about [capacitors and capacitance](https://studyelectrical.com/2019/10/capacitance-working-unit-types-specification.html).

## Unwanted Inductances

Any length of wire has some inductance. As with a transmission line, the inductance
of a wire increases as the frequency increases. Wire inductance is more significant
at RF than at AF.

In some cases, especially in radio communications equipment, the inductance of, 
and among, wires can become a major problem. Circuits can oscillate when they should
not. A receiver might respond to signals that it’s not designed to intercept.

A transmitter can send out signals on unauthorized and unintended frequencies. The
frequency response of any circuit can be altered, degrading the performance of the
equipment. Sometimes the effects of this stray inductance are so small that they
are not important; this might be the case in a stereo hi-fi set located at a distance
from other electronic equipment. But in some situations, stray inductance can cause
serious equipment malfunctions.

A good way to minimize stray inductance is to use coaxial cables between and among
sensitive circuits or components. The shield of the cable is connected to the common
ground of the apparatus.
 In some cases, enclosing individual circuits in metal 
boxes can prevent stray inductance from causing feedback and other problems.

### Related posts:

 [ ⌊Three wattmeter method of measuring three phase power⌉Measurement of Three Phase Power | Wattmeter Methods](https://studyelectrical.com/2019/01/three-phase-power-measurement-wattmeter-method.html)
[ ⌊Types-of-Electric-current⌉Types of Electric Current – Steady (DC), Varying & Alternating (AC) Current](https://studyelectrical.com/2019/11/types-of-electric-current-steady-dc-varying-alternating-ac-current.html)
[ ⌊How to rescue a person from electric shock⌉How to Rescue a Person from Electric Shock?](https://studyelectrical.com/2019/11/how-to-rescue-a-person-from-electric-shock.html)
[ ⌊Series Combination of Resistances⌉Combination of Resistances – (Series, Parallel and Series Parallel)](https://studyelectrical.com/2019/11/series-parallel-resistance-connection-combination.html)
[ ⌊capacitor charging and discharging⌉Charging and Discharging a Capacitor](https://studyelectrical.com/2020/02/charging-and-discharging-a-capacitor.html)
[ ⌊Electric current concept⌉Concept of Electric Charge and Current](https://studyelectrical.com/2021/12/electric-charge-and-current.html)
[ ⌊Capacitor in Parallel⌉Combination of Capacitors | Series & Parallel with Problems](https://studyelectrical.com/2024/04/combination-of-capacitors.html)
[ ⌊Kirchoffs law problem 1⌉Kirchhoff’s laws (KCL & KVL): Problems with Solution](https://studyelectrical.com/2024/06/kirchhoffs-laws-kcl-kvl-problems-with-solution.html)
[ ⌊Complete Guide on Ground Fault Circuit Interrupters⌉GFCI (Ground Fault Circuit Interrupter) – Working, Types, Installing and Troubleshooting](https://studyelectrical.com/2019/03/gfci-ground-fault-circuit-interrupter-breaker.html)
[ ⌊Underdamped, Overdamped and Critically damped Graphical Representation⌉Damping Systems – Air friction, Fluid Friction & Eddy Current Damping](https://studyelectrical.com/2019/11/damping-systems-air-friction-eddy-current-fluid-friction-and-electromagnetic.html)