Inductance Formula

What Is Inductance? 

Inductance is a property of an electrical component that expresses its ability to store energy in a magnetic field when an electric current flows through it. The units of inductance are called Henrys. Henry (H), is named after Joseph Henry, the American physicist considered the father of electromagnetism.

Formula for Inductance

Inductance L of an indicators is given by the formula,

Where,

• N is the number of turns in the coil

• μ is the permeability of core material, which comprises the permeability of free space ​μ0 and relative permeability​ μr ​.

• A is the cross-section area of the coil. 

• l is the length of the coil.

The voltage induced in a coil with inductance L is given by,

The voltage induced in a coil with inductance L is given by Faraday's Law of Electromagnetic Induction. Thus, the voltage V, induced in a coil by means of the changing current, depends upon:

where,

• V represents the induced voltage or (electromotive force - EMF)

• L represents the inductance of a coil, which is measured in Henrys (H).

• ​dI/dt is the rate of change of current through the coil  (in Amperes per second).

Explanation 

• Inductance (L): This expresses the coil's ability to resist changes in current. The magnitude depends upon the physical dimensions of the coil and upon the core material.

• Rate of Change of Current (dI/dt): This is the term that describes the rate of change of the current through the coil. The greater the rate of change of current, the greater the voltage induced.

• Negative Sign: The minus sign is because of Lenz's Law, which says the direction of the induced EMF will always be such as to oppose the change in current that it caused. 

The reactance of an inductor, often referred to as inductive reactance, quantifies the opposition an inductor presents to alternating current (AC). It is given by the formula:

where,

• XL = inductive reactance in Ohms, Ω.

• ω  = angular frequency of the AC signal in radians per second.

• L  = inductance of the coil in Henrys, H.

Explanation

•  Angular Frequency (ω): This is related to the frequency of the AC signal. It is given by:
     
  where f is the frequency of the AC signal (in Hertz, Hz).

• Inductance (L): This is the property of the coil that opposes changes in current.

Formula Derivation of Angular Frequency

• Relationship with Frequency: Since the angular frequency ω is related to the frequency f of the AC signal, therefore:

  L = L 1 + L 2 + L 3 + … . + L n

• Inductive Reactance: Substituting the value of ω in the inductive reactance formula yields:

        1 L = 1 L 1 + 1 L 2 + 1 L 3 + … . + 1 L n

Conclusion

The formula of inductance gives the most important understanding of inductors and how they relate electronically. Keeping in mind some of the physical features of the inductor, an engineer could make a new but effective way of producing electronic components and devices by understanding how inductors react to differing frequencies of supply current. Be it energy storage, filtering of signals, or transformation of voltages, principles of inductance will be an integral part of modern technologies of electrical and electronic devices.