Inductors

Chap 11

Magnetic fields• A magnetic field may be represented by a mathematical

description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field

• Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles

Compasses reveal the direction of the local magnetic field.

Magnetic field of an ideal cylindrical magnet with its axis of symmetry inside the image plane.

Electromagnetism

Magnetic fields

Magnetic fields

Magnetic fields

• The magnetic flux is measured in webers (Wb) and the applied symbol is the capital Greek letter phi Φ

Flux density

Example

1. For the core determine the flux density B in teslas.

2. if the flux density is 1.2 T and the area is 0.25 in^2 , determine the flux through the core.

However, converting 0.25 in.2 to metric units,

Inductors• Inductors are coils of various dimensions designed to

introduce specified amounts of inductance into a circuit.

• The inductance of a coil varies directly with the magnetic properties of the coil.

• Ferromagnetic materials, are frequently employed to increase the inductance by increasing the flux linking the coil.

• Inductance is measured in Henries (H) • 1 Henry is the inductance level that will establish a

voltage of 1 volt across the coil

Inductors

• An inductor is a passive two-terminal electrical component that stores energy in its magnetic field.

• An inductor is typically made of a wire or other conductor wound into a coil, to increase the magnetic field.

• When the current flowing through an inductor changes, creating a time-varying magnetic field inside the coil, a voltage is induced, according to Faraday's law of electromagnetic induction

• Inductors are one of the basic components used in electronics where current and voltage change with time, due to the ability of inductors to delay and reshape alternating currents.

Inductors

Inductor symbols

FARADAY’S LAW OFELECTROMAGNETIC INDUCTION

If a conductor is moved through a magnetic field so that it cuts

magnetic lines of flux, a voltage will be induced across the conductor

If a conductor is moved through a magnetic field so that it cuts

magnetic lines of flux, a voltage will be induced across the conductor

The greater the number of flux lines cut per unit Time or the stronger the magnetic field

strength, the greater will be the induced voltage across the conductor.

The greater the number of flux lines cut per unit Time or the stronger the magnetic field

strength, the greater will be the induced voltage across the conductor.

Increase the number of magnetic flux lines by increasing the speed with which the

conductor passes through the field

Increase the number of magnetic flux lines by increasing the speed with which the

conductor passes through the field

Equation for voltage induced across a coil if a coil of N turns is placed in the

region of a changing flux

Equation for voltage induced across a coil if a coil of N turns is placed in the

region of a changing flux

Faraday’s law induced voltage equation

If the flux linking the coil ceases to change

= is the instantaneous change in flux (in webers)

N = number of turns of the coil

&

Equation for inductance of the coilsN = number of turnsµ = permeability of the coreA = area of the corein square meters l = the mean length of the core in meters.

µ is not a constant butdepends on the level of B and H, since µ = B/H

µ is not a constant butdepends on the level of B and H, since µ = B/H

Substituting µ = µr µo into Equation we get

Lo is the inductance of the coil with an air core

Example 11.1

For the air-core coila)Find the inductance

Example 11.1 cont’

b) Find the inductance if a metallic core with µr = 2000 is inserted in the coil

In class exercise 1

Find the inductance of the air-core coil

Use equation for inductance of the coils

L

In class exercise 1 part2

• Repeat In class exercise 1 , but with an iron core and conditions such that µr = 2000.

Use equation

In class exercise 1 part2

• Repeat In class exercise 1 , but with an iron core and conditions such that µr = 2000.

We found in part 1 that Lo = 1.58 µH, so

Example 11.2 • If each inductor in the left column is changed to the type

appearing in the right column, find the new induced level for each change, assume that the other factors remain the same.

(a)

L =

The only change was the number of turns, but it is a square factor, resulting in

The only change was the number of turns, but it is a square factor, resulting in

The area is 3 times the original size increasing the inductance by a factor of 3. The number of turns is ½, which is reduced by

(½ )^2 = ¼ .

The area is 3 times the original size increasing the inductance by a factor of 3. The number of turns is ½, which is reduced by

(½ )^2 = ¼ .

Example 11.2 cont’

= 43.2 mH

µ and the number of turns increased have increased, the increased length reduces inductance

µ and the number of turns increased have increased, the increased length reduces inductance

Relative size of different types of inductors

Types of Inductors

• Inductors like Capacitor can be fixed or variable

Equivalent circuit for the inductor

Typical areas of application for inductive elements

HW

• Problem# 1, 3, 5 & 7