Transcript Chapter 11: Inductors

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
Electromagnetism
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.
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 OF
ELECTROMAGNETIC 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
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.
Equation for voltage induced across a
coil if a coil of N turns is placed in the
region of a changing flux
Increase the number of magnetic flux lines
by increasing the speed with which the
conductor passes through the field
Faraday’s law induced voltage equation
N = number of turns of the coil
= is the instantaneous change in flux (in webers)
If the flux linking the coil ceases to change
&
Equation for inductance of the coils
N = number of turns
µ is not a constant but
µ = permeability of the core
depends on the level of B
A = area of the core
and H, since µ = B/H
in square meters
l = the mean length of the core in meters.
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 coil
a) 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
Use equation for
inductance of the coils
Find the inductance of the air-core coil
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 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
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