Self Inductance: Definition and Explanation

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What is self inductance? Self inductance is the ratio of prompted electromotive force (EMF) over a coil to the rate of progress of current through the coil. Or Self inductance as the property of the coil due to which it opposes the change of current flowing through it. Inductance is achieved 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 connected voltage. Self-inductance does not keep the difference in current, however it defers the difference in 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

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 accompanying qualities in the above conditions as e = 1 V, and dI/dt = 1 A/s then the estimation of Inductance will be L = 1 H.

Hence, from the above derivation, an announcement 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

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 begins flowing from its zero value to a specific esteem and as for time, there will be a rate of progress in current immediately. This current produces changing flux (φ) through the coil. As current changes flux (φ) additionally changes and the rate of progress regarding the time is

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

Where, N is the quantity of turn of the coil and e is the prompted EMF over this coil. Considering Lenz’s law we can compose the above condition 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.

Self inductance, L is a geometric amount; it depends just on the elements of the solenoid, and the quantity of turns in the solenoid. Moreover, in a DC circuit when the switch is simply shut, at that point just immediately impact of self-inductance happens 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.