Electrical Engineering ⇒ Topic : Self Inductance
When the current in a coil is changing, the flux linked with the coil is also changing. In this case, an e.m.f. is produced in the coil. If the permeability of the coil is assumed to be constant, the induced e.m.f. of the coil is proportional to the rate of change of current, i.e.,
In Eq. (1), L is the constant of proportionality and it is known as self inductance of the coil. According to Faraday's law of electromagnetic induction, the induced e.m.f. in a coil having N turns is given by
From Eqs. (1) and (2), it can be written as:
If (Φ) versus i graph is taken as linear, Eq. (3) can be expressed as:
where S is the reluctance of the coil and is equal to l/μA.
From Eq. (6), it can be given as:
Using Eq. (7), it can be obtained from Eq. (5) as:
Equation (8) suggests that the inductance of any coil depends on the length and the area of cross-section of the coil.
From Eq. (5), self inductance can be defined as the flux linkage of the coil per ampere current flow through it. The unit of self inductance is Henry (H).
The property of a coil that opposes any change in the amount of current flowing through it is called its self-inductance or inductance.
This property (i.e. inductance) is due to the self-induced e.m.f. in the coil itself by the changing current. If the current in the coil is increasing, the self-induced e.m.f. is set up in such a direction so as to oppose the rise of current i. e. direction of self-induced e.m.f. is opposite to that of the applied voltage. Similarly, if the current in the coil is decreasing, self-induced voltage will be such so as to oppose the decrease in current i.e. self-induced e.m.f. will be in the same direction as the applied voltage. It may be noted that self-inductance does not prevent the current from changing ; it serves only to delay the change
Two coils C1 and C2 are shown separately in Figure (a). Assume that the coil / having N1 turns carries a current of /1 amperes and links with a flux of Φ1 Wb. Similarly, let coil 2, having N2 turns carry a current of I2 amperes and link with a flux of Φ2 Wb. Then, the self-inductance of coil l(L1) will be the number of flux linkages with the same coil due to its own current of /1 amperes. Thus
Similarly, the self-inductance of coil 2 (L2) is
FIGURE (a) Self-inductance of a coil
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