 # Inductance

## (1) Introduction

• Before defining inductance first of all, we will define an inductor.
• Like capacitor, inductor is another component commonly in electronic circuits.
• An inductor consists of a coil wound on a core or former of a suitable material like solid or laminated iron. core or ferrites which are highly ferromagnetic substances.
• when a current through an inductor changes am emf is induced in it which opposes this change of current in the inductor.
• This property of inductor or coil due to which it opposes change of current through it called the inductance denoted by letter L.
• Unit of inductance is henry(H).

## (2) Self Inductance

• Consider the figure given below • When we establish a current through an inductor or coil, it generates a magnetic field and this result in a magnetic flux passing through the coil as shown in figure 1(a).
• If we vary the amount of current flowing in the coil with time, the magnetic flux associated with the coil also changes and an emf ξ is induced in the coil.
• According to the Lenz�s law, the direction of induced emf is such that it opposes its cause i.e. it opposes the change in current or magnetic flux.
• This phenomenon of production of opposing induced emf in inductor or coil itself due to time varying current in the coil is known as self induction.
• If I is the amount of current flowing in the coil at any instant then emf induced in the coil is directly proportional to the change in current i.e. where L is a constant known as coefficient of self induction.
• If (-dI/dt)=1 then ξ=L
Hence the coefficient of self induction of a inductor or coil is numerically equal to the emf induced in the coil when rate of change of current in the coil is unity.
• Now from the faraday's and Lenz�s laws induced emf is comparing equation 1 and 2 we have, or Φ=LI
• Again for I=1, Φ=L
hence the coefficient of self induction of coil is also numerically equal to the magnetic flux linked with the inductor carrying a current of one ampere
• If the coil has N number of turn�s then total flux through the coil is
Φtot=NΦ
where Φ is the flux through single turn of the coil .So we have,
Φtot=LI
or L=NΦ/I
for a coil of N turns
• In the figure given below consider the inductor to be the part of a circuit and current flowing in the inductor from left to right • Now when a inductor is used in a circuit, we can use Kirchhoff�s loop rule and this emf(Self induced emf) can be treated as if it is a potential drop with point A at higher potential and B at lower potential when current flows from a to b as shown in the figure
• We thus have
Vab=LdI/dt

## (3) Self induction of a long solenoid

• Consider a long solenoid of length l, area of cross-section A and having N closely wound turns.
• If I is the amount of current flowing through the solenoid them magnetic field B inside the solenoid is given by, • Magnetic flux through each turn of the solenoid is, ## (4) Energy in an inductor

• Changing current in an inductor gives rise to self induced emf which opposes changes in the current flowing through the inductor.
• This self inductance thus plays the role the inertia and it is electromagnetic analogue of mass in mechanics.
• So a certain amount of work is required to be done against this self induced emf for establishing the current in the circuit.
• In order to do so, the source supplying current in a circuit must maintain Potential difference between its terminals which is done by supplying energy to the inductor.
• Power supplied to the inductor is given by relation
P=ξI                      ---(4)
where L is Self inductance and
dI/dt is rate of change of current I in the circuit.
• Energy dW supplied in time dt would be
dW=Pdt
=LI(dI/dt) dt
=LIdI
and total energy supplied while current I increases from o to a final value I is • Once the current reaches its final value and becomes steady ,the power input becomes zero.
• The energy so far supplied to the inductor is stored in it as a form of potential energy as long as current is maintained.
• When current in circuit becomes zero, the energy is returned to the circuit which supplies it.

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