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6. Self induction

Self induction is induction of emf in a coil due to its own current change. Total flux N Self-Inductance | Physics Class 12 - NEETpassing through a coil due to its own current is proportional to the current and is given as N Self-Inductance | Physics Class 12 - NEET = L i where L is called coefficient of self induction or inductance. The inductance L is purely a geometrical property i.e., we can tell the inductance value even if a coil is not connected in a circuit. Inductance depends on the shape and size of the loop and the number of turns it has.

If current in the coil changes by ΔI in a time interval Δt, the average emf induced in the coil is given as

ε = Self-Inductance | Physics Class 12 - NEET = Self-Inductance | Physics Class 12 - NEET

The instantaneous emf is given as

ε = -Self-Inductance | Physics Class 12 - NEET = - Self-Inductance | Physics Class 12 - NEET

S.I unit of inductance is wb/amp or Henry (H)

L - self inductance is +ve Quantity.

L depends on : (1) Geometry of loop

(2) Medium in which it is kept. L does not depend upon current. L is a scalar Quantity.

Brain Teaser

If a circuit has large self-inductance, what inference can you draw about the circuit.

6.1 Self Inductance of solenoid

Self-Inductance | Physics Class 12 - NEET
Let the volume of the solenoid be V, the number of turns per unit length be n. Let a current I be flowing in the solenoid. Magnetic field in the solenoid is given as B = μ0 nl. The magnetic flux through one turn of solenoid f = μ0 n l A.

The total magnetic flux through the solenoid = N Self-Inductance | Physics Class 12 - NEET

= N μ0 n l A

= μ0 n2 l A l

Therefore, L = μ0 n2 l A = μ0 n2 V

Self-Inductance | Physics Class 12 - NEET= μ0 n i pr2 (n l)

L = Self-Inductance | Physics Class 12 - NEET = μ0 n2 πr2 l

Inductance per unit volume = μ0 n2

Ex.38 The current in a coil of self-inductance L = 2H is increasing according to the law i = 2 sin t2. Find the amount of energy spent during the period when the current changes from 0 to 2 ampere.

Sol. Let the current be 2 amp at t = τ

Then 2 = 2 sin τ2 ⇒ τ = Self-Inductance | Physics Class 12 - NEET

When the instantaneous current is i, the self induced emf is L Self-Inductance | Physics Class 12 - NEET. If the amount of charge that is displaced in time dt is dθ, then the elementary work done

Self-Inductance | Physics Class 12 - NEET

W = Self-Inductance | Physics Class 12 - NEET = Self-Inductance | Physics Class 12 - NEET

W = Self-Inductance | Physics Class 12 - NEET = Self-Inductance | Physics Class 12 - NEET

Let θ = 2t2

Differentiating dθ = 4t dt

Therefore, W = Self-Inductance | Physics Class 12 - NEET

= L (- cosθ) = - L cos 2t2

W = Self-Inductance | Physics Class 12 - NEET

= 2 L = 2 × 2 = 4 joule

7. Inductor

It is represent by

Self-Inductance | Physics Class 12 - NEET

electrical equivalence of loop

Self-Inductance | Physics Class 12 - NEET ⇒ Self-Inductance | Physics Class 12 - NEET

Self-Inductance | Physics Class 12 - NEET

If current i through the inductor is increasing the induced emf will oppose the increase in current and hence will be opposite to the current. If current i through the inductor is decreasing the induced emf will oppose the decrease in current and hence will be in the direction of the current.

Self-Inductance | Physics Class 12 - NEET

Over all result

Self-Inductance | Physics Class 12 - NEET

VA - L Self-Inductance | Physics Class 12 - NEET = VB

Note

Self-Inductance | Physics Class 12 - NEET If there is a resistance in the inductor (resistance of the coil of inductor) then :

Self-Inductance | Physics Class 12 - NEET Self-Inductance | Physics Class 12 - NEET

Ex.39 A B is a part of circuit. Find the potential difference vA - vB if

Self-Inductance | Physics Class 12 - NEET

(i) current i = 2A and is constant

(ii) current i = 2A and is increasing at the rate of 1 amp/sec.

(iii) current i = 2A and is decreasing at the rate 1 amp/sec.

Sol. Self-Inductance | Physics Class 12 - NEET

Self-Inductance | Physics Class 12 - NEET = Self-Inductance | Physics Class 12 - NEET

writing KVL from A to B

VA - 1Self-Inductance | Physics Class 12 - NEET - 5 - 2 i = VB

(i) Put i = 2, Self-Inductance | Physics Class 12 - NEET = 0

VA - 5 - 4 = VB    Therefore, VA - VB = 9 volt

(ii) Put i = 2, Self-Inductance | Physics Class 12 - NEET = 1 ;

VA - 1 - 5 - 4 = VB or VA - VB = 10 V0

(iii) Put i = 2, Self-Inductance | Physics Class 12 - NEET = - 1

VA + 1 - 5 - 2 × 2 = VB

VA = 8 volt

Ex.40 Find current i, i1 and i2 in the following circuit.

Self-Inductance | Physics Class 12 - NEET

Sol. at t = 0

ii2Self-Inductance | Physics Class 12 - NEET and i1 = 0

at t = ∞

Self-Inductance | Physics Class 12 - NEET

⇒ i1 = i2Self-Inductance | Physics Class 12 - NEET = Self-Inductance | Physics Class 12 - NEET

7.1 Energy stored in an inductor :

If current in an inductor at an instant is i and is increasing at the rate di/dt, the induced emf will oppose the current. Its behaviour is shown in the figure.

Self-Inductance | Physics Class 12 - NEET

Power consumed by the inductor = i L Self-Inductance | Physics Class 12 - NEET

Energy consumed in dt time = i L Self-Inductance | Physics Class 12 - NEET dt

Therefore, total energy consumed as the current increases from 0 to I = Self-Inductance | Physics Class 12 - NEET

Self-Inductance | Physics Class 12 - NEET ⇒ U = Self-Inductance | Physics Class 12 - NEET

Note :

Self-Inductance | Physics Class 12 - NEET This energy is stored in the magnetic field with energy density

Self-Inductance | Physics Class 12 - NEET

Total energy U = Self-Inductance | Physics Class 12 - NEET

Ex.41 Find out the energy per unit length ratio inside the solid long wire having current density J.

Self-Inductance | Physics Class 12 - NEET

Sol. Take a ring of radius r and thickness dr as an element inside the wire

Self-Inductance | Physics Class 12 - NEET = Self-Inductance | Physics Class 12 - NEET        

using B = Self-Inductance | Physics Class 12 - NEET    Self-Inductance | Physics Class 12 - NEET

Self-Inductance | Physics Class 12 - NEET ⇒ Self-Inductance | Physics Class 12 - NEET ⇒ Self-Inductance | Physics Class 12 - NEET

The document Self-Inductance | Physics Class 12 - NEET is a part of the NEET Course Physics Class 12.
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FAQs on Self-Inductance - Physics Class 12 - NEET

1. What is self-inductance?
Ans. Self-inductance refers to the property of a circuit or a coil to generate an electromotive force (EMF) in itself when the current flowing through it changes. It is caused by the magnetic field produced by the changing current.
2. How is self-inductance measured?
Ans. Self-inductance is measured using a device called an inductance meter or an LCR meter. This meter applies an AC voltage to the coil and measures the resulting current. By analyzing this current, the self-inductance value can be determined.
3. What factors affect the self-inductance of a coil?
Ans. The self-inductance of a coil depends on several factors, including the number of turns in the coil, the area of the coil, the shape of the coil, and the permeability of the material inside the coil. Increasing the number of turns and the area of the coil increases its self-inductance.
4. How does self-inductance affect the behavior of a circuit?
Ans. Self-inductance can cause a circuit to oppose changes in the current flowing through it. When the current changes, the self-induced EMF creates a back EMF that opposes the change. This behavior is responsible for phenomena such as the delay in the rise of current in an inductive circuit and the creation of a magnetic field around the coil.
5. Can self-inductance be used in practical applications?
Ans. Yes, self-inductance finds applications in various devices. It is used in transformers to transfer electrical energy between circuits, in inductors to store energy in magnetic fields, and in electronic components like solenoids and relays to control electrical signals. Understanding self-inductance is crucial for designing efficient and reliable electrical systems.
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