Inductance 

By on

When current flows within a wire, a magnetic field is created. The potion of this magnetic field perpendicular to the wire is called the magnetic flux (measured in weber, Wb). Inductance is the ratio of magnetic flux to current in a circuit. The unit of inductance is the henry, H (Wb/A) and is normally represented by the symbol L.

Self Inductance

Whenever current in a coil of wire changes,  the magnetic field]it produces will change. That will change the magnetic flux through the coil and hence produce a voltage across the coil. This is called self-inductance, and the coil is referred to as an inductor.

Example – Self Inductance of a Solenoid

Consider a coil of wire around a magnetic core, whose length is much greater than it's diameter. 

Given the permeability of free space μo , relative permeability of the magnetic core μr , number of turns N and length of solenoid l, with a current i flowing, the magnetic flux density, B within the coil is is given by:

image00

The magnetic flux, Φ is obtained by multiplying flux density by the cross sectional area A:

image01

Given that the inductance is the ratio of magnetic flux to current, we have:

image02

Note: if the solenoid is wound around a non-magnetic core, then μr = 1.

Mutual Inductance

When the magnetic field of one coil links with that of another coil, a change in current in the first coil will produce a linking magnetic field with the second coil.  The magnetic field linking with the second coil will produce a voltage within that coil.  This is called mutual inductance.

For two inductors (coils) we have:

  • L11 – self inductance of inductor 1
  • L22 – self inductance of inductor 2
  • L12 = L21 – mutual inductance between the two

Inductance Formulae

The table below lists some common formulae for calculating the theoretical inductance of several inductor constructions.

  • L = inductance (H)
  • μ0 = permeability of free space = 4 π× 10-7 (H/m)
  • μr = relative permeability of core material

Cylindrical coil:

myElectrical Equation N = number of turns
A = area of cross-section of the coil in square metres (m2)
l = length of coil in metres (m)

 

Straight wire conductor:

myElectrical Equation l = length of conductor (m)
d = diameter of conductor (m)

 

Flat spiral air-core coil:

myElectrical Equation r = mean radius of coil (m)
N = number of turns
d = depth of coil (outer radius minus inner radius) (m)

Toroidal core, circular cross-section:

myElectrical Equation N = number of turns
r = radius of coil winding (m)
D = overall diameter of toroid (m)

Application to Circuits

The quantitative measure of applying an inductance L, to a circuit defined by:

myElectrical Equation

An inductor can store energy. The power (= energy / time) being stored in an inductor is:

myElectrical Equation

This implies (by a little calculus) that the energy stored in an inductor is :

myElectrical Equation



Steven McFadyen's avatar Steven McFadyen

Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author

myElectrical Engineering

comments powered by Disqus

  1. Chris's avatar Chris says:
    7/12/2012 3:52 AM

    You list the relative permeability of non-magnetic materials as 0. Shouldn't it be 1?

    • Steven's avatar Steven says:
      7/14/2012 9:45 AM

      Thanks for spotting the error Chris. I have corrected it.


Comments are closed for this post:
  • have a question or need help, please use our Questions Section
  • spotted an error or have additional info that you think should be in this post, feel free to Contact Us



Introduction to Lighting

When looking at the design of a lighting scheme it is useful to have an understanding on the nature of light itself and some of the basic theory associated...

Variable Frequency Drive

Variable frequency drives are widely used to control the speed of ac motors.  This note looks at the mechanisms which enable drive units to control the...

Contribute to myElectrcial

Have an opinion or something to say, want to ask or answer questions, share your knowledge then use our site to do it . As a community of people interested...

DC Motor Operation

Coils of wire on the rotor carry a d.c. current which generates a magnetic field. A stator magnetic field is created using either permanent magnets or...

How to Calculate Motor Starting Time

Request to look at induction motor starting time have come up a few times on the site. Hopefully in this post, I give you guys some idea on how to calculate...

Tips for a better Low Voltage Protection Discrimination Study

Carrying out a protection system discrimination study is critical to ensure the correct functioning of  the electrical system in the event of faults. ...

Induction Motor Equivalent Circuit

Induction motors are frequently used in both industrial and domestic applications.  Within the induction motor, an electrical current in the rotor is induced...

Medium Voltage Switchgear Room Design Guide

Many medium voltage (MV) indoor switchgear rooms  exist worldwide. The complexity of these rooms varies considerably depending on location, function and...

Back to Basics - Ohm’s Law

Electrical engineering has a multitude of laws and theorems. It is fair to say the Ohm's Law is one of the more widely known; it not the most known. Developed...

UPS Sizing - Rules of Thumb

It wasn't so long ago I was telling someone that I don't use rules of thumb as most things are easily calculated anyhow.   As it turns out I last week...

Have some knowledge to share

If you have some expert knowledge or experience, why not consider sharing this with our community.  

By writing an electrical note, you will be educating our users and at the same time promoting your expertise within the engineering community.

To get started and understand our policy, you can read our How to Write an Electrical Note