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An online electrical engineering study site. Today, we are going to discuss about inductor, and its inductance
A current through a conductor produces a magnetic field surround it. The strength of this field depends upon the value of current passing through the conductor
The direction of the magnetic field is found by using the right hand drip rule, which shown
If you hold the current carrying conductor by your right hand, as shown, the thumb will
indicate the direction of current whereas other four fingers will indicate the direction
of magnetic flux lines. Here the flux pattern for this magnetic field would be number of concentric circle perpendicular
to the direction of current. Now if we wound the conductor in form of a coil or solenoid, it can be assumed that there
will be concentric circular flux lines for each individual turn of the coil, as shown
But it is not possible practically, as if concentric circular flux lines for each individual
turn exist, they will intersect each other. However, since lines of flux cannot intersect, the flux lines for individual turn, will distort
to form, complete flux loops around the whole coil as shown. This flux pattern of a current carrying coil is similar to a flux pattern of a bow magnet
as shown. Now, if the current through the coil is changed, the magnetic flux produced by it will also
be changed at same rate. As the flux is around the coil, this changing flux obviously links the coil
Now according to Faraday's law of electromagnetic induction, if changing flux links with a coil
there would be an induced EMF in it. Again as per, Lenz's law this induced EMF opposes every cause of producing it
Hence, the induced EMF is in opposite of the applied voltage across the coil
Hence, self-induced EMF in a coil is produced due to its own changing flux and changing
flux is caused by changing current in the coil. So, it can be concluded that self-induced EMF is ultimately due to changing current
in the coil. And self-inductance is the property of a coil or solenoid, which causes a self-induced EMF
to be produced, when the current through it, changes. Now, mathematically this can be written as minus E proportional to dI dt
Where, minus E is the induced counter EMF, dI dt is the rate of change of current through
the coil with respect to time. The above equation can also be rewritten as minus E equals L into dI dt
Say this is equation 1, where, L is the constant of proportionality and this L is defined as
the self-inductance of the coil or solenoid. This L determines how much EMF will be induced in a coil for a specific rate of change of
current through it. However, the induced EMF is basically due to the rate of change of flux linkages
Thus, the EMF, may also be calculated by Faraday's law of electromagnetic induction as follows
minus E equals N into d phi dt. Say this is equation 2, where N is the number of turns in the coil and d phi dt is the rate
of change of flux linkage with respect to time with one turn
Now, from equation 1, and 2, we get, L dI dt equals N d phi dt, or L dI equals N d phi
Integrating, both sides we get, L I equals N phi, or L equals N phi by I
Say this is equation 3. From the above expression, inductance can be also be defined as, if the current I through
an N turn coil produces a flux of phi where bar, then its self-inductance would be L
A coil, which is designed to have a specific value of self-inductance, is known as an inductor
Now, if cross-sectional area of the inductor core is, A A, and flux density in the core
is B, then total flux inside the core of inductor is, A into B
Therefore, equation 3 can be written as L equals N into, A A, into B divided by I
Now, B equals mu 0 H where, H is magnetic field strength, and mu 0 is permeability of the core
Now, H equals mmf per unit length, that means H equals N I by L
Where L is the mean length of the coil. Therefore, L equals N into A A into mu 0 into N into I divided by L I, equals mu 0 into
N square into I divided by L. This is the final expression of inductance of an inductor
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