CHAPTER 1 ef BY UNI DWM20032

Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Resistive-Capacitive Series Circuit Time Constant

• RC time constant of a circuit is calculated by
using the formula:

T= R Χ C

t is time in seconds
R is resistance in ohms
C is capacitance in farads

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Example:

If a circuit has a resistance of 20kΩ and a capacitor of 15µF, what is it RC time
constant

Answer:

T= R X C

T= 20 × 103 ×15 × 10-6 = 0.3 seconds

In a RC circuit, the capacitor becomes fully charged (100%) in

approximately 5RC seconds

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Circuit Discharging

A capacitor does not discharge in a linear
manner.

When a capacitor is discharged through a
RC circuit, the voltage does not immediately
fall to zero but decreases exponentially.

The voltage drops to approximately 37%
from its initial value in the same RC time
constant and reaches zero in approximately
5RC

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Series Capacitances

• When capacitors are connected in series, the
total capacitance is less than any one of the
series capacitors’ individual capacitances.

• If two or more capacitors are connected in
series, the overall effect is that of a single
(equivalent) capacitor having the sum total of 1/Ctotal = 1/C1 + 1/C2 + 1/Cn. . .
the plate spacings of the individual capacitors.

• An increase in plate spacing, with all other
factors unchanged, results in decreased
capacitance.

• Thus, the total capacitance is less than any one
of the individual capacitors’ capacitances.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

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Parallel Capacitances

• When capacitors are connected in parallel,
the total capacitance is the sum of the
individual capacitors’ capacitances.

• If two or more capacitors are connected in Ctotal = C1 +C2 +Cn. . .
parallel, the overall effect is that of a single
equivalent capacitor having the sum total of
the plate areas of the individual capacitors.

• An increase in plate area, with all other
factors unchanged, results in increased
capacitance.

• The formula for calculating the parallel total
capacitance is the same form as for
calculating series resistances

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Testing of capacitors

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Testing of capacitors

An analogue multimeter or digital multimeter
set to high resistance range can be used to
test a capacitor.

(a) Non – polarized Types – If the

resistance is less than about 1MΩ is
allowing current from the battery in the
multimeter to ‘pass’ so it is leaking and is
faulty.

Note –there may be an initial short burst of
current as the capacitor charges up.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Testing of capacitors

(b) Polarized Types – For the dielectric to form in these types a positive voltage must

be applied to the positive side of the capacitor.

In most analogue multimeters the terminal marked – (black) is the positive of the
internal battery when selected to the ohms setting.

For digital meters the manufacturer’s instructions will have to be consulted.

When the capacitor is first connected to the multimeter its resistance is low but rises as
the dielectric forms, otherwise the capacitor is faulty

Capacitor is extensively used in electronic circuit as well as high energy ignition unit and
strobe light systems.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

• An Inductor is a passive electrical component formed by a coil of
wire and which exhibits the property of inductances.

• When there is current through an inductor, an electromagnetic
field is established.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

• When the current changes, the electromagnetic field also
changes.

• An increase in current expands the field, and a decrease in
current reduces it.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

• Therefore, a changing current produces a changing electromagnetic
field around the inductor (also known as coil and in some
applications)

• In turn, the changing electromagnetic field causes an induced
voltage across the coil in a direction to oppose the change in
current.

.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

• This property is called self-inductance but is usually referred to as
simply inductance, symbolized by L.

• Inductance is a measure of a coil's ability to establish an induced
voltage as a result of a change in its current, and that induced
voltage is in a direction to oppose that change in current.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

The unit of inductance, symbolized by H.

Henry is the basic unit of inductance.

By definition, the inductance of a coil is one henry when current through the
coil, changing at the rate of one ampere per second, induces one volt across
the coil. The henry is a large unit, so in practical applications, millihenries
(mH) and microhenries (µH) are the more common units

Inductor symbol

Fixed inductor Variable inductor

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

Inductors are made in a variety of shapes and sizes. Basically, they fall into two general
categories: fixed and variable.

• Both fixed and variable inductors can be classified according to the type of core
material. Three common types are the air core, the iron core, the ferrite core. Each
has a unique symbol.

a) Air core b) Iron core c) Ferrite core

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

• Adjustable (variable) inductors usually have a screw-type adjustment that moves a
sliding core in and out, thus changing the inductance. A wide variety of inductors
exist.

• Small fixed inductors are usually encapsulated in an insulating material that
protects the fine wire in the coil. Encapsulated inductors have an appearance
similar to a small resistor.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

FACTORS AFFECTING INDUCTANCE

1) Number Of Wire Wraps, Or "Turns" In The Coil

A greater number of turns of wire in the coil results in greater inductance;
fewer turns of wire in the coil results in less inductance.
More turns of wire means that the coil will generate a greater amount of
magnetic field force (measured in amp-turns), for a given amount of coil
current.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

2) Coil Area
A greater coil area (as measured looking lengthwise through the coil, at the
cross-section of the core) results in greater inductance; less coil area results in
less inductance.
Greater coil area presents less opposition to the formation of magnetic field
flux, for a given amount of field force (amp-turns).

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

3) Coil Length
 The longer the coil's length, the less inductance; the shorter the coil's
length, the greater the inductance.
 A longer path for the magnetic field flux to take results in more
opposition to the formation of that flux for any given amount of field
force (amp-turns).

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

4) Core Material
 The greater the magnetic permeability of the core which the coil is
wrapped around, the greater the inductance; the less the permeability of
the core, the less the inductance.
 A core material with greater magnetic permeability results in greater
magnetic field flux for any given amount of field force (amp-turns).

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE
SELF INDUCTANCE
• When current through a coil changes, the changing flux induces an emf that opposes the

current flow. This emf is the result of self inductance and is called ‘back emf’. The term
‘self inductance’ is often replaced merely by inductance.
• The value of back emf is given by:

• Where L is the inductance in henries, and the rate of change of
current.

• The minus indicates back emf. FOR TRFOAIRNTINRGAIPNUINRGPOPSUEROPONSLYE ONLY
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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

SELF INDUCTANCE

• The unit of inductance is the henry and is based on the equation. If current
changing at a rate of 1 amp a second induces an emf of 1 volt then the
inductance is 1 henry.

• All circuits have inductance even a straight conductor, but if a straight piece of
wire is formed into a coil the number of flux linkages increases and so does
the inductance.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

SELF INDUCTANCE
• A further increase in inductance is achieved by increasing the flux density. This depends

on the area, the length of the coil and the permeability of material in which flux is
established.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE
MUTUAL INDUCTANCE
If the changing flux in a coil links with the turns of a second coil, the two coils are said to be
mutually coupled and mutual inductance exists between them.
The unit of mutual inductance is Henry
If the primary current, changing at a rate of 1 amp per second, induces a secondary voltage
of 1v, then the mutual inductance is 1 henry.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Series Inductors

• When inductors are connected in series, the total inductance is the sum of
the individual inductances.

• The formula for calculating the series total inductance is the same form as
for calculating series resistances:

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Parallel Inductors

• When inductors are connected in parallel, the total inductance is less than the
smallest inductance.

• The general formula states that the reciprocal of the total inductance is equal to
the sum of the reciprocals of the individual inductances.

• The formula for calculating the parallel total inductance is the same form as for
calculating parallel resistances:

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

PRINCIPLES OF INDUCTION

• In 1831 Michael Faraday discovered that an electric
current was produced by the relative movement of
a magnet and a coil.

• This phenomenon known as electromagnetic
induction.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE

PRINCIPLES OF INDUCTION

• If a magnet is moved into or out of a coil of wire and
if the coil is connected to a meter, the meter records
a flow of current as long as the magnet is moving.

• The same result is obtained if the magnet is kept
stationary and the loop is moved

• The meter in the diagram shows that there is a
current as long as there is relative
movement between the loop (coil) and
the magnet (magnetic field).

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTOR & INDUCTANCE
FARADAYS LAW

• When the magnetic flux through the coil is made to vary, an emf is induced in the coil.

• The magnitude of the induced emf is proportional to the rate of change of flux

Hence, E α dΦ where dΦ = change of flux
dt = time taken to change
dt

• The emf is also dependent on the number of turns on the coil (N), the greater the

number of turns on the coil, the greater emf.

E α N dΦ volts
dt

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

LENZ’S LAW

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011) • A conductor must cut 108 lines of flux
per second in order to induce 1 volt.
LENZ’S LAW
• That is the flux must be changing at a
• A change of flux in a closed circuit induces an rate of 108 lines per second. The
emf and sets up a current. formula should therefore be written as:

• The direction of this current is such that its E = - N dΦ x 10-8 volts
magnetic field tends to oppose the change of dt
flux.

• The direction of the induced emf as given by
Lenz’s Law may be shown in equation by
introducing a negative sign, but remember that
the negative sign is vectorial and not
arithmetic.

Hence E = - N dΦ volts
dt

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INDUCTORS IN A DC CIRCUIT

• If a circuit contained only pure resistance, then the current would rise to its
full value I = RE in zero time when the switch is closed.

• In practice, there is no such thing as ‘pure’ resistance and it is normal to
find a circuit containing resistance and inductance in series.

• Also, there is no such thing as pure inductance since any coil must have
some resistance.

• Therefore, the circuit to be considered will have inductance and resistance
in series.

• An inductance opposes any change in current by producing a back emf.
The back emf tries to prevent current flow when the circuit is switched ‘ON’
and tries to maintain current flow when the circuit is switched ‘OFF’.

• Current can therefore not rise instantly to a maximum, or fall instantly to
zero.

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

INDUCTORS IN A DC CIRCUIT
WHEN DC CURRENT IS APPLIED
• On moving the switch to position A in the diagram below, the current circuit will start to rise. All times Kirchhoff’s

second law applies

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

ELECTRICAL FUNDAMENTALS & ELECTRON THEORY

INDUCTORS IN A DC CIRCUIT
WHEN DC CURRENT IS APPLIED

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

ELECTRICAL FUNDAMENTALS & ELECTRON THEORY

WHEN DC CURRENT IS APPLIED

• If E, L and R are constant, therefore as I increases, (the slope of the graph
at any point) must decrease.

• The current therefore follows a curve whose gradient is
continually decreasing which is called an ‘exponential curve’

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Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

TIME CONSTANT

It is impossible to decide exactly when the maximum point is reached on an exponential curve, or when the curve has
fallen to exactly zero.

To enable calculations to be performed a time constant is used.

The time constant gives an indication of the time taken for the current to rise to its maximum value or
fall to zero. The time constant is defined as either:

• The time taken for a current to reach its maximum value if the initial rate of increase were maintained.
• The time taken for the current to reach 0.632 of its maximum value (or 63.2%).

The latter definition arises since it is found that after one time constant, the current has always built up to 63.2% of its
maximum value. The time constant for a series LR circuit is given by:

Time Constant = L seconds
R

Therefore, although it is not possible to say exactly when the current reaches its maximum value, for all practical
purpose it can be considered a maximum after 5 time constants:

Maximum Current flows after

5L
R

DIPLOMA ENGINEERING IN AIRCRAFT MAINTENANCE FOR TRFOAIRNTINRGAIPNUINRGPOPSUEROPONSLYE ONLY
DWM 2032: ELECTRICAL FUNDAMENTALS DAM/TDPW-0M3-20013/R2/ETVP0001//1RMEVA0R0C/H2270N1O8V2017

Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

WHEN DC CURRENT IS REMOVED

• A similar situation occurs when the switch is moved from
position A to position B.

• The current does not immediately fall to zero because
the inductor opposes any change and tries to maintain
the current flow.

• Instead the current decays exponentially to zero over a Switch is moved from position A to position B.
period of 5 times constant.

• In the circuit shown, the resistor is kept in circuit,
therefore the time constant calculated will be the same
as when the switch was moved to position A.

• If a different value of resistance is present then the time
constant will be different.

• It should be noted that in trying to keep the current
flowing in the same direction around the circuit, the
polarity of the voltage across the inductor must be the
reverse of what it was when the switch was moved to
position A. ie +ve at the bottom of the coil and –ve at the
top.

•

DIPLOMA ENGINEERING IN AIRCRAFT MAINTENANCE FOR TRFOAIRNTINRGAIPNUINRGPOPSUEROPONSLYE ONLY
DWM 2032: ELECTRICAL FUNDAMENTALS DAM/TDPW-0M3-20013/R2/ETVP0001//1RMEVA0R0C/H2270N1O8V2017

Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

Energy Stored in an Inductive Circuit

• An inductor stores energy in the magnetic field created by the current. The
energy stored is expressed as
W=1/2 LI2

• As you can see, the energy stored is proportional to the inductance and the
square of the current. When current (I) is in amperes and inductance (L) is in
henries, the energy (W) is in joules.

DIPLOMA ENGINEERING IN AIRCRAFT MAINTENANCE FOR TRFOAIRNTINRGAIPNUINRGPOPSUEROPONSLYE ONLY
DWM 2032: ELECTRICAL FUNDAMENTALS DAM/TDPW-0M3-20013/R2/ETVP0001//1RMEVA0R0C/H2270N1O8V2017

Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

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pprriinncciippllee ooff eelleeccttrroommaaggnneettiicc
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Moving Coil Microphone & Speaker.

DIPLOMA ENGINEERING IN AIRCRAFT MAINTENANCE FOR TRFOAIRNTINRGAIPNUINRGPOPSUEROPONSLYE ONLY
DWM 2032: ELECTRICAL FUNDAMENTALS DAM/TDPW-0M3-20013/R2/ETVP0001//1RMEVA0R0C/H2270N1O8V2017

Topic contents refer as in AN1101/Appendix 1/Issues 1 (01 January 2011)

QUESTION????

DIPLOMA ENGINEERING IN AIRCRAFT MAINTENANCE FOR TRFOAIRNTINRGAIPNUINRGPOPSUEROPONSLYE ONLY
DWM 2032: ELECTRICAL FUNDAMENTALS DAM/TDPW-0M3-20013/R2/ETVP0001//1RMEVA0R0C/H2270N1O8V2017