From http://www.electronicshub.org/inductor-basics/
From https://en.wikipedia.org/wiki/Henry_(unit)
Introduction
Inductor consists of wire wound around a core of ferrite material that includes an air gap. Inductor stores the energy in the form of the magnetic field. Inductor has many electrical properties when subjected to a magnetic field. One of the important property of this inductor is whenever the current flows through the wire it creates the magnetic field around it.
If we coil the wire , the magnetic field is stronger. When the electric current flows through the coil, the magnetic flux will increase exponentially and stabilize at particular point, then stores the electric energy in the form of magnetic energy. When electric supply stops then the magnetic energy will decrease exponentially and turns back into electrical energy. By this we can say that it will temporally store the energy. The faster the change in the magnetic field the induced emf or voltage will be greater. To know about current and magnetic flux relation let us learn about Lenz’s Law.
Lenz’s Law
Before going to Lenz’s Law first we have to know about Faraday’s Law of induction. It states that the magnitude of emf induced in the coil is equal to the rate of change of flux that links with the coil. For a tightly wound coil of wire, composed of N identical turns, each with the same ΦB, Faraday's law of induction states that
ԑ = -N (∂Φ_B / ∂t)
where N is the number of turns of wire and Φ_ B is the magnetic flux through a single loop.
Whereas the product of number of turns in the coil and flux related with the coil gives us the flux linkage.
Lenz’s Law states that an emf is generated by change in magnetic flux as stated in faraday’s law. The polarity of this induced emf is such that it produces a current such that magnetic field opposes the change which produces it. Lenz's law is shown by the negative sign in Faraday's law of induction:
ԑ = -N (∂Φ_B / ∂t)
Where ∂Φ_B = change in the magnetic flux
ԑ = induced emf
N = no. of turns
Working of inductor
When the electric current is flowing in the coil, the coil will build up the magnetic field around it. At the time of building the field , the coil inhabits the flow of current and once if the field is built up, current can flow normally through the wire. Due to this reason there will be exponential increase in the magnetic flow before reaching the steady state. When the electric current is turned off then the magnetic field around the coil will keep the current flow in the coil until the field collapses. This makes the electric current decrease exponentially before it reaches its actual state.
When the wire is coiled as a series of continuous loops , it is called as solenoid. In this type , the magnetic field strength will increase or decrease with the increasing and decreasing currents respectively. It is similar to effect of bar magnet but with the variable field strength.
magnetic field of coil and bar magnet
Inductor Symbols
The symbol of Air core
The symbol for Iron core
The symbol for Ferrite core
The symbol for Variable core
Inductance of Inductor
Inductance is the property of an Inductor .The current generated in the inductor due to magnetic field is proportional to the rate of change of magnetic field is called the inductance. The higher the inductance value, more the inductor will resists from the sudden changes in the current.
Inductance is given by L = µN2A / l
Where
L – Inductance of the coil.
µ – Permeability of the core.
N-Number of tuns in the coil
A-Area of the coil.
l -Length of the inductor.
Self-inductance
A change in the current causes change in the voltage in that circuit due to the magnetic flux generated by the current flow. Simply inductance within the coil gives us self-inductance. Chokes are best example for self-inductance effect.
Mutual-inductance
A change in the current in one circuit causes the change in voltage of next circuit .The linkage of magnetic field between both circuits leads to mutual inductance. Transformers are best example for mutual inductance effect.
Inductors in series
When ‘n’ number of inductors are connected in series the total inductance value is the sum of all the individual inductances.
Ltotal = L1+L2+… +Ln
Inductors in parallel
When ‘n’ numbers of inductors are connected in parallel the total inductance value is equated as follows
Ltotal = 1/ ((1/L1) + (1/L2) +..+ (1/Ln))
If we observe these two equations are very similar to the resistors connected in series and parallel.
Inductance Units
The SI unit of inductance is Henry. It is named after the American physicist Joseph Henry. This is denoted by ‘H’.
The inductance of an electric circuit is one henry when an electric current that is changing at one ampere per second results in an electromotive force of one volt across the inductor. This is equated as
H= (V.s)/A = Wb/A.
Where V = Volts, s = second, Wb = Weber, and A = Ampere.
Factors influencing inductance
1.Material of the core
One of the important factor that affects the inductance value is permeability. If the magnetic permeability of the core is more the inductance is more and if this permeability of the core is less, the inductance is also less. Because a core with higher permeability will generate greater amount of magnetic flux for any given amount of field force.
2.Number of turns of the inductor
If the number of turns of the inductor increases, inductance also increases. Because for any given amount of current , the amount of generated magnetic flux is always greater , if the inductor consists of more number of turns.
3.Length of the coil
If the coil length increases the inductance decreases. If the length is decreased, inductance is increased.
4.Area of the coil
By taking the cross-sectional area of the coil, if the area increases the inductance increases and if the area decreases, value of the inductance will comparatively decreases. As the area increases more flux is induced and inductance is more.
The inductance value can also be affected by the external effects caused by the other wires and components which are near by the inductor, once it is assembled in the circuit. For accurate inductance value the approximated inductance value has to be calculated.
Let us consider a solenoid wound with a single layer of turns with some diameter of the wire and the turns are placed evenly, then the typical formula for approximating the inductance value is given as follows.
L = (d2n2)/(l + 0.45d)
Where
d = diameter of the coil in meters.
n = no. of turns in the coil.
L = inductance in henry.
l = length of the wire in meters.
Current, Voltage and power calculation
The work done by the source in order to remain the current flowing through the coil against the induce emf is power. It is given as
P = d/dt (½ (L x I2)).
The magnetic field density B (t) which is measured in tesla is equal to the magnetic field strength H (t), multiplied by the magnetic core permeability ‘μ’ .
This is given as
B (t) = μ x H (t).
The magnetic flux which is measured in webers, is equal to the magnetic flux density B (t), multiplied by the cross-sectional area of the core ‘Ac’.
This is given as
Φ(t) = Ac x B (t).
The energy stored in an inductor is equal to the amount of work done to establish the current flow through the inductor and to generate magnetic flux.
This given as
E = ½ (L x I2)
Where
L = Inductance,
I = current flow through the inductor and
E = Energy stored.
Quality Factor
Since the inductors are formed by the electrically conductive metal wire , they will have a series resistance. This series resistance will generate heat by converting the electric current flowing through the coil. Due to this heat the sensitivity of the inductor decreases. Thus the quality factor is nothing but the ratio of the inductance to the resistance. This is given as
Q = ω L/R
Where
Q = quality factor
ω = angular frequency (Hz)
L = inductance (H)
R = resistance (Ω)
Back EMF generated in an inductor: The EMF produced in the inductor will depends on the source currents that is either the current is AC or DC.
The self-induced emf VL = – L di/dt is applicable only for the AC current because there will be rate of change of current that is di/dt is not equal to zero. If the flow of the inductor current is constant , that is at DC current the di/dt is zero. At this stage the inductor acts like a piece of wire.
Time constant of an inductor: Let us consider the circuit as shown below with an inductor and an open switch.
Since the switch is open there will be no flow of current in the circuit. Thus the rate of change of current di/dt is zero at this condition. We know that when di/dt is zero there is no self-induced emf in the circuit.
When we close the switch the current will flow through the circuit and slowly rise to its maximum value at the rate determined by the inductance of the inductor.
This rate of current flowing through the inductor multiplied by the inductors inductance in Henry’s, results in some fixed value self-induced emf being produced across the coil as determined by Faraday’s equation above, VL = Ldi/dt.
This self-induced emf across the inductors coil, ( VL ) fights against the applied voltage until the current reaches its maximum value and a steady state condition is reached. The current which now flows through the coil is determined only by the DC or “pure” resistance of the coils windings as the reactance value of the coil has decreased to zero because the rate of change of current (di/dt) is zero in steady state. In other words, only the coils DC resistance now exists to oppose the flow of current.
Likewise, if switch, (S1) is opened, the current flowing through the coil will start to fall but the inductor will again fight against this change and try to keep the current flowing at its previous value by inducing a voltage in the other direction. The slope of the fall will be negative and related to the inductance of the coil as shown below.
Inductor Applications
- Inductor with inductances in the nano-henry range , will only filter out very high frequencies i.e., above 100 MHz so these are mainly used in radio frequency circuits like old boom box in 1980s.
- Inductors in micro-henry range will filter out the frequencies about 50 KHz to few MHz. These are typically used in D.C. power supplies to smooth out the voltage.
- Inductors in milli-henry range are very effective and these are used in audio crossover circuits to separate low and high frequency sounds.
- Inductor ideally acts like a low pass filter since the impedance of an inductor increases as the frequency of a signal increases.
- Since inductor will sense the magnetic fields from a distance these are used in inductive sensors. These inductive sensors are used in traffic signalling to detect the amount of traffic.
- By combining two inductors which have a shared magnetic field will acts like a transformer. These inductive based transformers are applicable only at lower frequencies.
- In fixed speed applications inductive motors are used.
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