The phenomenon in which a changing current in a coil produces an induced emf in the same coil is called self-induction.
A coil, battery, and rheostat are connected in series through a switch S to form a circuit of self-induction.
When the current in the coil is changed by varying the rheostat quickly, the magnetic flux through the coil changes which causes an induced emf in the same coil such an emf is called as self-induced emf.
Expression for Self-Inductance:
Let the flux passes through one loop of the coil. Then the total flux passing through the coil N turns will be N. Thus the flux is proportional to the magnetic field and is proportional to the current I. Then
N∅ ∝ I
N∅ = LI → eq1
Where L = N∅/I is the constant of proportionality and is called the self inductance of the coil.
Self-inductance depends upon,
i)The number of turns of the coil.
ii)Aera of the cross-section of the coil.
iii)The nature of core material.
iv)Rate of change of current in the coil itself.
According to Faraday’s law, the induced emf in the coil is given by the rate of change of flux through the coil itself.
εɩ = -N ∆∅/∆t = – ∆(N∅/∆t → eq2
From eq1 N∅=LI putting in the eq2
εɩ = – Δ ( LI ) / Δt
εɩ = -L ΔI/Δt → eq3
shows that the emf induced in the coil is proportional to the time rate of change of current in the coil itself and ve sing shows that the induced emf opposes the which is according to Lenz’s law.
L = – εɩ / ΔI/Δt → eq 4
The rate of induced emf in the coil to the rate of change of current in the coil is called self-inductance.
L= εɩ / ΔI / Δt = V/A/S
L = VSA ¯¹ = Henry
The self-inductance of the coil is one Henry if current changes at the rate of one ampere per sec and in the coil cause an induced emf of one volt in the same coil.