A coil has an inductance of 0.03 h rate at which energy is being stored in the coil when current is 10 ampere and rate of change of current is hundred ampere per second is
Answers
The basic unit of measurement for inductance is called the Henry, ( H ) after Joseph Henry, but it also has the units of Webers per Ampere ( 1 H = 1 Wb/A ).
Lenz’s Law tells us that an induced emf generates a current in a direction which opposes the change in flux which caused the emf in the first place, the principal of action and reaction. Then we can accurately define Inductance as being: “a coil will have an inductance value of one Henry when an emf of one volt is induced in the coil were the current flowing through the said coil changes at a rate of one ampere/second”.
In other words, a coil has an inductance, ( L ) of one Henry, ( 1H ) when the current flowing through the coil changes at a rate of one ampere/second, ( A/s ). This change induces a voltage of one volt, ( VL ) in it. Thus the mathematical representation of the rate of change of current through a wound coil per unit time is given as:
current through a coil
So by increasing the number of loops or turns within a coil, increases the coils inductance. Then the relationship between self-inductance, ( L ) and the number of turns, ( N ) and for a simple single layered coil can be given as:
Self Inductance of a Coil
self inductance of a coil
Where:
L is in Henries
N is the Number of Turns
Φ is the Magnetic Flux
Ι is in Amperes
This expression can also be defined as the magnetic flux linkage, ( NΦ ) divided by the current, as effectively the same value of current flows through each turn of the coil. Note that this equation only applies to linear magnetic materials.
Inductance Example No1
A hollow air cored inductor coil consists of 500 turns of copper wire which produces a magnetic flux of 10mWb when passing a DC current of 10 amps. Calculate the self-inductance of the coil in milli-Henries.
inductance coil example
inductance of the coil
Inductance Example No2
Calculate the value of the self-induced emf produced in the same coil after a time of 10mS.
self induced emf of a coil
The self-inductance of a coil or to be more precise, the coefficient of self-inductance also depends upon the characteristics of its construction. For example, size, length, number of turns etc. It is therefore possible to have inductors with very high coefficients of self induction by using cores of a high permeability and a large number of coil turns. Then for a coil, the magnetic flux that is produced in its inner core is equal to:
magnetic flux of a coil
Where: Φ is the magnetic flux, B is the flux density, and A is the area.
If the inner core of a long solenoid coil with N number of turns per metre length is hollow, “air cored”, then the magnetic induction within its core will be given as:
magnetic induction of a hollow coil
Then by substituting these expressions in the first equation above for Inductance will give us:
inductance of a hollow coil
By cancelling out and grouping together like terms, then the final equation for the coefficient of self-inductance for an air cored coil (solenoid) is given as:
coefficient of self inductance
Where:
L is in Henries
μο is the Permeability of Free Space (4.π.10-7)
N is the Number of turns
A is the Inner Core Area (πr 2) in m2
l is the length of the Coil in metres
As the inductance of a coil is due to the magnetic flux around it, the stronger the magnetic flux for a given value of current the greater will be the inductance. So a coil of many turns will have a higher inductance value than one of only a few turns and therefore, the equation above will give inductance L as being proportional to the number of turns squared N2.
EEWeb have a free online Coil Inductance Calculator for calculating the inductance of a coil for different configurations of wire size and positioning.
As well as increasing the number of coil turns, we can also increase inductance by increasing the coils diameter or making the core longer. In both cases more wire is required to construct the coil and therefore, more lines of force exists to produce the required back emf.
The inductance of a coil can be increased further still if the coil is wound onto a ferromagnetic core, that is one made of a soft iron material, than one wound onto a non-ferromagnetic or hollow air core.
ferrite core
Ferrite Core
If the inner core is made of some ferromagnetic material such as soft iron, cobalt or nickel, the inductance of the coil would greatly increase because for the same amount of current flow the magnetic flux generated would be much stronger. This is because the material concentrates the lines of force more strongly through the the softer ferromagnetic core material as we saw in the Electromagnets tutorial.
So for example, if the core material has a relative permeability 1000 times greater than free space, 1000μο such as soft iron or steel, then the inductance of the coil would be 1000 times greater so we can say that the inductance of a coil increases proportionally as the permeability of the core increases.