[Physics Class Notes] on Unit of Inductance Pdf for Exam

The attribute of a current-carrying closed-loop that causes an electromotive force to be generated or induced by a change in the current flowing via it. Such an attribute is called the inductance.

On This Page, We’ll Learn About the Following:

Inductor

An inductor is a coil of wire cloaked around a magnetic material.

Current flowing via the inductor generates a magnetic field that does not change, as it is trying to oppose the change in the flow of current which means the current flow remains constant inside the inductor. 

The inductor won’t generate any forces on the charged particles flowing via it. In such a case, the inductor just behaves like a normal wire.

The current flow is opposed by the resistance, and the time comes when there comes a 

current decay (decline). The larger the resistance, the faster the current will decline.

On the other hand, the larger the inductance of the inductor, the slower the current will decay.

What is Inductance?

The inductance is the ability of an inductor or any current-carrying conductor to oppose the change in the current flowing through it. The inductors do this by generating a self-induced emf within itself (Faraday’s law of induction) as a result of their changing magnetic field. 

S.I. Unit of the Inductor

The S.I unit of the inductor is Henry H

MKS unit is Kg m² s⁻² A⁻²

Where one Henry is equal to the one-kilogram meter squared per second squared per ampere squared.

What is Self – Inductance?

Inductance is also called self-inductance. When a current is established in a closed conducting loop, it creates a magnetic field. This magnetic field has flux produced in an area of the closed-loop. If the current varies with time, the flux via the loop also changes. Hence an EMF is induced in the loop. Such a process is called self-induction.

The magnetic field at any point due to current is proportional to the current. The magnetic flux in an enclosed area of the conductor can be represented as,

φ  ∝ i  ⇒ φ = L i

Where L is a proportionality constant and is called the coefficient of self-inductance or simply self-inductance of the loop.

The inductance in the coil (Fig.1) depends on the number of turns, area of cross-section, and nature of the material of the core on which the coil is wrapped.

If i =1,  φ = L x i  or  L = φ

Therefore, the coefficient of self-inductance is numerically equal to the amount of magnetic flux linked with the coil when unit current flows through the coil.

From Faraday’s law of induction, any variation in the magnetic field generates emf, given by,

E =  –  dφ (t) / dt  = – L di / dt

The negative sign indicates that the changing current induces a voltage in the conductor and this induced voltage is in a direction that tends to oppose the change (increase or decrease) in the electric current (Lenz’s law) is called the back EMF.

Inductance for a Long Solenoid

The inductance of a solenoid is given by,

B = μ₀ N I / L

The magnetic flux density can be obtained by multiplying the B with cross-sectional area A, we get,

φ = B xA = μ₀ N x i x A / l….(1)

Since total magnetic flux inside the coil = flux via each turn x total number of turns. 

φ = B xA = μ₀ N x N i x A / l….(2)

Where μ₀ is the magnetic constant or absolute magnetic permeability of free space/air forms the core of the solenoid.

We know that

φ  = L i….(3)

From (2) and (3) we get,

L i =  μ₀ N x N x A xi / l x N we get,

L = μ₀ N² x A/ l

μ = μ₀ . μr

When the core is of any other magnetic material μ₀ is replaced by 

μr (relative magnetic permeability).

Here, we Conclude the Following Things,

S.I. Unit of Inductance

The S.I. unit of self-inductance is weber/ ampere or volt-second/ ampere. 

It is also denoted by Henry (H), named after an American scientist named Joseph Henry. 

Where Henry is the amount of inductance that generates a change of one volt and when the current is varying at the rate of one ampere per second.

Note: All conductors have some inductance, which may have either desirable or detrimental effects in electrical circuits and it depends on the geometry of the current path and on the magnetic permeability of the materials.

The ferromagnetic material tends to have a high inductance because of the flow of large amounts of electric flux (total magnetic field) through the conductor produced by a current flowing through it increases the inductance in that conductor.

Inductor Working Principle

When ac current is applied to the inductor coil, its own current changes, causing its own magnet to change, creating an electromotive power. This condition is called self-inductance. The direction of the self-induced current is always affected. When the alternating current increases, the direction of the self-inductance current is opposite to that of the AC current. When the AC current is weak, the direction of the self-inductance current is the same as that of the alternating current, which has a blocking effect.

• Self-Induction- When the current flows into the coil, a magnetic field is produced around the coil. As the current in the coil changes, the surrounding magnetic field also changes accordingly. This change in a magnetic field can cause the coil itself to generate electromotive energy (EMF is used to represent the terminal voltage of the active power of the active components).

• Mutual Inductance- If two coils of an inductor are close together, the magnetic field conversion of one coil will affect the other, and this effect is mutually beneficial. Its size depends on the degree of interaction between self-inductance and the two coils. The components formed by this policy are called mutual inductors.

Factors affecting Inductance in a Circuit

The following factors affect inductance in a circuit

• The Number of Wires Transforming into Coil – The greater the amount of cable twist on the coil, the greater the inductance. Slight twisting of the cable to the coil results in a small inlet. Most cable coils show a large amount of magnetic field in a given number of current coils.

• Coil Location – The larger the coil area, the greater the inductance. The location of the small coil leads to the small entrance. The large coil area exhibits minimal resistance to the formation of magnetic field flux, with a given amount of field strength

• Length of the Coil – When the coil length is longer, the inductance decreases. The shorter the coil length, the greater the inductance.

Summary

With the change in the magnetic flux, induced emf is a must, but induced current will only appear only when the circuit is closed.

An Inductor is equivalent to a short circuit to DC, because once the storage phase has been completed, the current, i, that flows through is stable, no emf is induced. So the inductor behaves like a normal wire where Resistance R is zero