Self-inductance and its Coefficient

Self-inductance and Coefficient of Self-induction

Self-inductance :

Imagine a coil of wire similar to the one shown in Figure given below connected to a battery through a rheostat. It is found that whenever an effort is made to increase current (and hence flux) through it, it is always opposed by the instantaneous production of counter e.m.f. of self-induction. Energy required to overcome this opposition is supplied by the battery. As will be fully explained later on, this energy is stored in the additional flux produced.

If, now an effort is made to decrease the current (and hence the flux), then again it is delayed due to the production of self-induced e.m.f., this time in the opposite direction. This property of the coil due to which it opposes any increase or decrease or current of flux through it, is known as self-inductance.

It is quantitatively measured in terms of coefficient of self induction L. This property is analogous to inertia in a material body. We know by experience that initially it is difficult to set a heavy body into motion, but once in motion, it is equally difficult to stop it. Similarly, in a coil having large self-induction, it is initially difficult to establish a current through it, but once established, it is equally difficult to withdraw it. Hence, self-induction is sometimes analogously called electrical inertia or electromagnetic inertia.

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Coefficient of Self-induction :

It may be defined in any one of the three ways given below :

(i) First Method for L

The coefficient of self-induction of a coil is defined as the weber-turns per ampere in the coil By ‘weber-turns’ is meant the product of flux in webers and the number of turns with which the flux is linked. In other words, it is the flux-linkages of the coil. Consider a solenoid having N turns and carrying a current of I amperes. If the flux produced is Φ webers, the weber-turns are NΦ. Hence, weber-turns per ampere are N Φ/I.

By definition, The unit of self-induction is henry.

If in the above relation,

NΦ = 1 Wb-turn,

I = 1 ampere,

then L = 1 henry (H)

Hence a coil is said to have a self-inductance of one henry if a current of 1 ampere when flowing through it produced flux-linkages of 1 Wb-turn in it.

Therefore, the above relation becomes Henry.