Self inductance is the ration between the induced Electro Motive Force (EMF) across a coil to the rate of change of current through this coil. Self inductance is related term to self induction phenomenon. Because of self induction self inductance generates. Self-inductance or Co-efficient of Self-induction is denoted as L.
Its unit is Henry (H).
First we have to know what self induction is.
Self induction is the phenomenon by which in a coil a change in electric current produces an induced Electro Motive Force across this coil itself.
This induced Electro Motive Force (ε) across this coil is proportional to the current changing rate. The higher the rate of change in current, the higher the value of EMF.
We can write that,
But the actual equation is
The question is that why there is Minus (-) sign?
This Induced EMF across this coil is always opposite to the direction of the rate of change of current as per Lenz’s Law.
When current (I) flows through a coil some electric flux produces inside the coil in the direction of the current flowing. At that moment of self induction phenomenon, the induced EMF generates to oppose this rate of change of current in that coil. So their values are same but sign differs.
Look at the figure below.
Take a closer look at a coil that is carrying current. The magnetic field forms concentric loops that surround the wire and join to form larger loops that surround the coil.
When the current increases in one loop the expanding magnetic field will cut across some or all of the neighboring loops of wire, inducing a voltage in these loops.
Video Presentation of Self Inductance
For the DC source, when the switch is ON, i.e. just at t = 0+, a current will flow from its zero value to a certain value and with respect to time there will be a rate of change in current momentarily. This current produces magnetic flux lines (φ) through this coil. As current changes its value to zero to a certain value that’s why magnetic flux (φ) get rate of change with respect to the time, i.e.
Now apply Faraday's Law in this coil,
Where, N is the number of turn of the coil and e is the induced EMF across this coil.
Lenz's law states that an induced current due to induced EMF has a direction such that its magnetic field opposes the change in magnetic field that induced the current.
As per Lenz’s law we can write down this equation of induced voltage across the coil,
Now, we can modify this equation to calculate the value of inductance of a coil.
[B is the flux density i.e. B =φ/A, A is area of the coil],
[N. φ or L.I is called magnetic flux Linkage and it is denoted by Ѱ]
Again, H.l = N.I, where H is the magnetizing force due to which magnetic flux lines flow from south to north pole inside the coil, l is the effective length of the coil and
r is the radius of the coil cross-sectional area.
L is a geometric quantity; it depends only on the dimensions of the solenoid, and the number of turns in the solenoid.
Furthermore, in a DC circuit when the switch is just closed, then only momentarily effect of self-inductance occurs in the coil. After then no effect of self inductance is in a coil. It is because of steady flow of unidirectional current through this coil after closing the operating switch after t = 0+.
But in AC circuit, alternating effect of current always causes the self-induction in the coil and a certain value of this self-inductance gives the inductive reactance depending on the value of supply frequency.
Generally in the electrical circuit the coils those are used are known as inductor having values of L1, L2, L3 etc. when they are series combination then equivalent inductance of them is calculated as
When they are in parallel, then