What is Self Inductance? Definition and Explanation

What is Self Inductance? Definition and Explanation

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What is self inductance? Self inductance definition: Self inductance is the ratio of induced electromotive force (EMF) across a coil to the rate of change of current through the coil. Or Self inductance definition: as the property of the coil due to which it opposes the change of current flowing through it. Inductance is attained by a coil due to the self-induced emf produced in the coil itself by changing the current flowing through it.

If the current in the coil is increasing, the self-induced emf produced in the coil will oppose the rise of current, that means the direction of the induced emf is opposite to the applied voltage.

What is Self Inductance? Definition and Explanation

If the current in the coil is decreasing, the emf induced in the coil is in such a direction as to oppose the fall of current; this means that the direction of the self-induced emf is same as that of the applied voltage. Self-inductance does not prevent the change of current, but it delays the change of current flowing through it.

Self Inductance Explanation

This property of the coil only opposes the changing current (alternating current) and does not affect the steady current that is (direct current) when flows through it. The unit of inductance is Henry (H).

We denote self inductance or coefficient of with English letter L. Its unit is Henry (H). Since, the induced emf (E) is proportional to the current changing rate, we can write,

But the actual equation is

Expression For Self Inductance

You can determine the self-inductance of a coil by the following expression

self-induction-eq-1

The above expression is used when the magnitude of self-induced emf (e) in the coil and the rate of change of current (dI/dt) is known.

Putting the following values in the above equations as e = 1 V, and dI/dt = 1 A/s then the value of Inductance will be L = 1 H.

Hence, from the above derivation, a statement can be given that a coil is said to have an inductance of 1 Henry if an emf of 1 volts is induced in it when the current flowing through it changes at the rate of 1 Ampere/second.

The expression for Self Inductance can also be given as

self-induction-eq2

where:

N – number of turns in the coil
Φ – magnetic flux
I – current flowing through the coil

Derivation of Inductance

For the DC source, when the switch is ON, i.e. just at t = 0+, a current starts flowing 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 changing flux (φ) through the coil. As current changes flux (φ) also changes and the rate of change with respect to the time is

self inductance

Now by apply Faraday’s Law of Electromagnetic Induction, we get,

Where, N is the number of turn of the coil and e is the induced EMF across this coil. Considering Lenz’s law we can write the above equation as,

Now, we can modify this equation to calculate the value of inductance.

So,

[B is the flux density i.e. B =φ/A, A is area of the coil], [Nφ or Li is called magnetic flux Linkage and it is denoted by Ѱ]

Where H is the magnetizing force due to which magnetic flux lines flow from south to north pole inside the coil, l (small L) is the effective length of the coil and

r is the radius of the coil cross-sectional area.

inductor

Self inductance, 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 some time, no effect of self inductance remains in the coil because after certain time the current becomes steady.

Self Inductance Conclusion

After going through the above portion of self inductance explanation we can now establish a Self inductance definition. I hope you enjoy when reading this article, thank you.