## Self Induction

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# Self Induction

When a current flows in a coil, a magnetic field is set up in it. If the current through the coil is changed, the flux linked with the coil also changes. An induced emf is set up in the coil. By Lenz’s law, the direction of induced emf is set up in the coil. By Lenz’s law, the direction of induced emf is such as to oppose the change in current. When the current is increasing, the induced emf is against the current. When the current is decreasing, the induced emf is in the direction of current. The phenomenon is called self-induction. The induced emf is called back emf.When the current in a coil is switched on, self- induction opposes the growth of the current. Hence the current increases slowly and takes some time = OD to increase from zero to maximum value. During the period of growth, energy is absorbed. When the current is switched on, self-deduction opposes the decay of current. So the current does not become zero instantaneously but takes some time = DB. When the current is switched off, the stored energy is given back in the form of spark. The effect of self-induction in an electric circuit is similar to inertia in motion.

The phenomenon of the production of an induced emf. In a circuit itself due to the change in current through it is called self induction and the induced emf. is called back e.m.f.

Self Inductance. The magnetic flux φ produced in a coil is directly proportional to the current l flowing in the coil, i.e.,

Φ ∞ I

or Φ = LI … (1)

where L is a constant of proportionality, called the coefficient of self induction or self inductance of the coil.

From Eq. (1), if I = 1, then, Φ = L

Therefore, the self, inductance of a coil is the total magnetic flux linked with it when a unit current passes through it.

When the flux changes, the back e.m.f, induced in the coil is given (Faraday’s law)

ε = - dΦ / dt = - L dI / dt … (2)

if dI / dt = 1 unit, | ε | = L.

Self-inductance of a coil is numerically equal to the induced emf when current in it is changing at unit rate.

S.I. unit of self-induction is henry (H).

From Eq. (1), one henry is the z`self-inductance of a coil or circuit, if an induced emf of one volt is produces a magnetic flux of one Weber in it.

From Eq. (2), one henry is the self-inductance of a coil or circuit, if an induced emf. of one volt is produced in it due to a rate change of current of one ampere per sec.

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