[Physics Class Notes] on Inductance Pdf for Exam

On passing a changing current through a closed-current carrying conductor or an inductor, a magnetic field generates around it. 

In simple terms, this changing current produces an additional current, i.e., an induced current. 

This induced current creates an EMF that opposes the further change in the current.  This opposing ability is what we call inductance. 

When the inductance happens within the same coil, it is self-inductance. 

However, if the current flow in the primary coil shows the inductance effect in the secondary coil, we call it mutual inductance.

This page discusses in-depth the types of inductance with their uses.

Electric Induction

When a current establishes in a closed conducting loop, it generates a magnetic field. 

Further, this magnetic field generates flux (magnetic induction) in an area of the closed-loop. 

So, when the current varies with time, the flux via the loop also changes. 

Furthermore, this variation generates an induced EMF in the loop. We call this phenomenon self-induction.

Here, we note that the magnetic field at any point varies directly with the current. The magnetic flux in an enclosed area of the conductor is given as;                 

Φ  ∝ i  =>   Φ = L i

So, the more is the change in the current, the more in the flux generation. 

Therefore, removing the sign of proportionality constant, we get “L,” which is the coefficient of self-inductance or simply self-inductance of the loop.                        

The inductance in the coil (Fig.1) depends on the following parameters:

1. The number of turns, 

2. Area of cross-section, and 

3. The nature of the material of the core on which the coil is wrapped.

Inductance Definition

If i =1,  

Φ = L x i  

Or

L =    Φ

We say that the coefficient of self-inductance is numerically equal to the amount of magnetic flux associated with the coil when unit current flows through it.

From Faraday’s law of induction, any change in the magnetic field induces an emf, which is given by,

E =  –  dΦ (t) / dt  

= – L di / dt

The negative sign shows that the changing current induces a voltage in the conductor

The induced voltage produced in the same direction opposes any increase or decrease in the electric current (Lenz’s law). We also call this phenomenon the back EMF.

Types of Inductors

Induction is a magic that a closed-current loop or an ability acquires. The types of inductance are:

• Self inductance

• Mutual inductance

Self Inductance

The concept of self induction lie hereunder:

Let’s consider a circular loop in which changing current produces a magnetic field (B). 

Here, we can determine the direction of the magnetic field by curling the fingers of our right hand in the direction of B, pointing inwards. We indicate the inward direction by making cross marks, as shown in the diagram below:

                           

Furthermore, on increasing the current, the magnetic field lines also increase. 

This means B α i

Due to the increase in B, flux (ΦB) also increases. 

Here, we notice that when the flux increases, by Faraday’s law of electromagnetic induction, an EMF also induces in this induction coil.

By Lenz’s law, we can state the above principle in the following manner:

Firstly, we call this induced EMF the potential difference (push) between the two points in the coil because of which an induced current generates. 

Secondly, this induced current decreases the primary current. Its direction points outward, i.e., opposite to the direction of B.

Therefore, an induced current opposes the flux (ΦB) or the magnetic field lines because of which it was generated.

Since this is happening inside the coil itself, we call it self-inductance.

Mutual Inductance

To understand what mutual induction is, let us take two distinct coils P and S and set them side-by-side.                                                       

Connect P to the switch, and S to a galvanometer.

    

                            

Also, on supplying a varying current across P, a current induces in the coil S.

It happens because a varying current in P generates varying magnetic field lines that cross both the coils.

Hence, the increasing current in P increases the magnetic field lines in S, i.e., the flux. 

Accordingly, when ΦB increases, an induced EMF generates in the coil because of which an induced current starts flowing in it. 

      

                           

Therefore, the galvanometer (connected to S) shows a deflection.

To determine the direction of the magnetic field lines, we curl/curve our right-hand fingers around the wire in the following manner:

      

                                

Here, the direction in which the thumb points is the magnetic field’s direction.

It means that the magnetic field lines lie parallel to the direction of the current. 

Additionally, these lines change (because of the changing current), the flux in S changes because of which an induced emf and the induced current generates in it.

Uses of Inductors

Inductors have applications in various electrical transmissions. Besides this, the uses of inductors are:

1. Transformers (Step-up and Step-down transformers)

2. Tuning circuits

3. Sensors

4. Store energy in a device

5. Induction motors

6. Filters

7. Chokes

8. Ferrite beads

9. As relays