- 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).

- 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

Φ_{tot}=NΦ

where Φ is the flux through single turn of the coil .So we have,

Φ_{tot}=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

V_{ab}=LdI/dt

- 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,

- 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.

Class 12 Maths Class 12 Physics

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