INDUCTORS
AND
INDUCTANCE
GROUP 10
INDUCTANCE AND INDUCTOR VOLTAGE
MAGNETIC
INDUCTOR AND CURRENT
FLUX
CONSTRUCTION RELATION
SINGLE-INDUCTOR
TOTAL ENERGY
DC EXCITED
INDUCTANCE STORAGE
CIRCUITS
MAGNETIC
FLUX
MAGNETIC FLUX
number of magnetic field lines passing
through a given closed surface.
MAGNETIC FLUX
CURRENT FLOW THROUGH COILED
WIRE
COIL STRUCTURE AND COIL
MATERIAL
INDUCTANCE AND MAGNETIC
ENERGY STORAGE
MAGNETIC FLUX DENSITY
Force acting per unit length on a wire
placed at right angles to the magnetic field.
Formula:
B= μ*N*I
where:
B= magnetic field measured in Tesla (T)
μ= magnetic permeability of material
N= number of turns
I= current
INDUCTANCE AND
INDUCTOR
CONSTRUCTION
INDUCTORS INDUCTANCE
a passive element It is the property whereby
used to store energy the inductance opposition
in its magnetic field. to the change of current
it consists of a coil of flowing through it.
conducting wire. It describes the ability of a
Its inductance level coil or conductor to
determines the induce an electromotive
strength of the force (EMF) or voltage
magnetic field when the magnetic field
around the coil due around it changes. It is a
to an applied property that opposes any
current. change in the flow of
electric current.
TYPICAL FORM OF AN INDUCTOR
TYPES OF CORE MATERIALS
AIR CORE FERRITE CORE
VARIABLE
IRON CORE
CORE
TYPES OF CORE MATERIALS
Think of the core in an inductor like the conductor's
"helper" for handling magnetic fields.
INDUCTOR CONSTRUCTION
DERIVIATON OF FORMULA:
EXAMPLE # 1
SOLUTION
EXAMPLE # 2
SOLUTION
a.)
b.)
c.)
INTEGRAL VOLTAGE-
CURRENT
RELATIONSHIPS
The instantaneous voltage drop across an inductor is directly
proportional to the rate of change of the current passing
through the inductor. Inductors do not have a stable
“resistance” as conductors dour topic or idea
FORMULA
Where:
v = instantaneous voltage across the inductor
L = inductance in henries (H)
di/dt = instantaneous rate of current change
in amperes per second (A/s)
VOLTAGE DROP ACROSS AN INDUCTOR
WITH A CONSTANT CURRENT
Like a capacitor, an inductor’s behavior is rooted in the variable of time.
Aside from any resistance intrinsic to an inductor’s wire coil (which we
will assume is zero for the sake of this section), the voltage dropped
across the terminals of an inductor is purely related to how quickly its
current changes over time.
Formula:
DERIVATION OF MAIN FORMULA
VOLTAGE DROP ACROSS AN INDUCTOR
WITH A CONSTANTLY INCREASING
CURRENT
If we move the potentiometer wiper slowly in the “up” direction,
its resistance from end to end will slowly decrease.
Figure 3 Figure 4
Decreasing the A constantly increasing
potentiometer inductor current
resistance increases results in a fixed,
the inductor current. positive inductor
voltage.
VOLTAGE DROP ACROSS AN INDUCTOR
WITH A VARIABLE, INCREASING
CURRENT
Changing the rate of current
increase through the inductor
by moving the potentiometer
wiper “up” at different speeds
Figure 5
results in different amounts of
voltage being dropped across A changing, increasing
inductor current
the inductor, all with the same results in a variable,
positive inductor
polarity (opposing the increase voltage
in current).
VOLTAGE DROP ACROSS AN INDUCTOR
WITH A DECREASING CURRENTROP ACROSS
AN INDUCTOR WITH A VARIABLE,
INCREASING CURRENT
Reversing the direction
of the wiper motion on
the potentiometer
(going “down” rather
than “up”) will result in
its end-to-end Figure 6
resistance increasing. Increasing the
potentiometer
resistance decreases
the inductor current
VOLTAGE DROP ACROSS AN
INDUCTOR WITH RAPID CURRENT
CHANGES
High voltages will be produced if the current through an
inductor is forced to change rapidly. Consider the following
circuit.
When the switch is closed, the inductor
will briefly oppose the change in current
from zero to some magnitude but will
drop only a small amount of voltage.
Figure 7 Figure 8
Inductor circuit with a Closing the switch
neon lamp and an open allows current to flow
switch. in the circuit.
When the switch is opened, however, it
suddenly introduces an extremely high
resistance into the circuit (the resistance
of the air gap between the contacts).
Figure 9
Opening the circuit
results in a rapid
decrease in the current
and a high voltage
across the inductor
that lights the neon
lamp.
EXAMPLE # 1
Let's be specific and say V = 3V and L = 10mH
SOLUTION
EXAMPLE # 2
BEFORE the switch is pressed, the circuit has a voltage
source in series with our 10 Mh inductor, plus a push-
button switch (pb). The top terminal of the inductor is at
a constant 3V above ground. The name of the voltage
across the inductor is vL.
EXAMPLE # 2
AFTER the switch is pressed, the vpb goes to 0 V. +3 from
the source is now connected across the inductor, and
current begins to flow.
SOLUTION
EXAMPLE # 3
Let's consider an inductor in an electronic circuit with an
inductance of 2 henries and a flowing current of 3
amperes.
SOLUTION
TOTAL
INDUCTANCE
SERIES
AND
PARALLEL
INDUCTORS
INDUCTORS
IN SERIES
When inductors are
connected in series, the
total inductance is the sum
of the individual inductors’
inductances.
FORMULAS:
EXAMPLE :
INDUCTORS
IN PARALLEL
The equivalent inductance
of parallel inductors is the
reciprocal of the sum of
the reciprocals of the
individual inductances
FORMULAS:
FOR THE SPECIAL CASE OF TWO
INDUCTORS IN PARALLEL:
EXAMPLE :
INDUCTORS IN
SERIES AND
PARALLEL
EXAMPLE # 1
SOLUTION #1
EXAMPLE # 2
Calculate the equivalent inductance of the following inductive circuit.
SOLUTION # 2
ENERGY
STORAGE
ENERGY STORAGE
THE AMOUNT OF ENERGY STORED DEPENDS
ON HOW MUCH CURRENT IS FLOWING
THROUGH THE INDUCTOR AND THE
CHARACTERISTICS OF THE INDUCTOR
ITSELF, SPECIFICALLY ITS INDUCTANCE.
DERIVIATON OF FORMULA:
FORMULA:
ENERGY STORED IN AN INDUCTOR
WHERE:
W= ENERGY STORED IN THE
INDUCTOR (IN JOULES)
L= INDUCTANCE (IN HENRYS)
I= CURRENT
EXAMPLE 1
DETERMINE THE AMOUNT OF POTENTIAL ENERGY
STORED IN THE INDUCTOR
SOLUTION
DETERMINE THE AMOUNT OF POTENTIAL ENERGY
STORED IN THE INDUCTOR
EXAMPLE 2
FIND THE ENERGY STORED IN THE INDUCTOR
SOLUTION
FIND ENERGY STORED IN
THE INDUCTOR
DC EXCITATION
The DC excitation mentioned here includes a constant
magnetic field using a permanent magnet and a constant
magnetic field excited by a DC current.
The presence of DC voltage, as shown in Figure
3-4, will cause the positive ions of the
electrolyte liquid in the measuring tube to
move to the negative electrode, and the
negative ions to move to the positive
electrode.
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