1
Electrical Engineering
Fundamentals
2013 – 2014 (Lecture-1)
Introduction
The international system of Units (SI)
The SI units are based on seven defined quantities:
2
TABLE of SI Prefix
The Electric Current
The force of attraction or repulsion between two charged bodies Q1 and Q2 can be determined by
Coulomb’s law:
where F is in Newtons, k is a constant = 9.0× 109 N.m2/C2, Q1 and Q2 are the charges in
coulombs, and r is the distance in meters between the two charges.
3
the free electron is the charge carrier in a copper wire or any other solid conductor of
electricity.
Random motion of free electrons in
an atomic structure.
Random motion of electrons in
a copper wire with no external
“pressure” (voltage) applied
With no external forces applied, the net flow of charge in a conductor in any one
direction is zero.
Suppose that in a conductor, the number of free electrons available per m3 of the
conductor material is n and let their axial drift velocity be v metres/second. In time dt,
distance travelled would be vdt. If A.is area of cross-section of the conductor, then the
volume is Avdt and the number of electrons contained in this volume is nAvdt. Obviously,
all these electrons will cross the conductor cross-section in time dt. If e is the charge of
each electron, then total charge which crosses the section in time dt is:
Since current is the rate of flow of charge, it is given as :
:. i=enAv (A)
If 6.242 × 1018 electrons drift at uniform velocity through the imaginary circular cross
section of Figure. in 1 second, the flow of charge, or current, is said to be 1 ampere (A),
where a coulomb (C) of charge was defined as the total charge associated with
6.242×1018electrons.
Charge/electron
The current in amperes can now be calculated using the
following equation:
4
Example 1/. A conductor material has a free-electron density of 1024 electrons per m3.
When a voltage is applied, a constant drift velocity of 1.5 × 10-2 metre/second is attained
by the electrons. If the cross-sectional area of the material is 1 cm2,calculate the
magnitude of the current. Electronic charge is 1.6 x 10-19coulomb.
Solution
n=1024 e/m3; v=1.5 × 10-2 metre/second; A=1×10-4m2; e=1.6 x 10-19coulomb
i=enAv (A) i=0.24A
Example 2/ The charge flowing through the imaginary surface of Figure. is 0.16 C every
64 ms. Determine the current in amperes.
Solution
Example 3/ Determine the time required for 4 × 1016 electrons to pass through the
imaginary surface of upper Figure if the current is 5 mA.
Solution: Determine Q:
Voltage (The Idea of Electric Potential)
The flow of charge described in the previous section is established by an external
“pressure” derived from the energy that a mass has by virtue of its position: potential
energy.
Energy, by definition, is the capacity to do work. If a mass (m) is raised to some height
(h) above a reference plane, it has a measure of potential energy expressed in joules (J)
that is determined by
,where g is the gravitational acceleration (9.754 m/s2).
A potential difference of 1 volt (V) exists between two points if 1 joule (J) of energy is
exchanged in moving 1 coulomb (C) of charge between the two points.
5
In general, the potential difference between two points is determined by
Example 4./ Find the potential difference between two points in an electrical system if 60
J of energy are expended by a charge of 20 C between these two points.
Solution
Potential difference: The algebraic difference in potential (or voltage) between two
points of a network.
Voltage: When isolated, like potential, the voltage at a point with respect to some
reference such as ground (0 V).
Voltage difference: The algebraic difference in voltage (or potential) between two points
of the system. A voltage drop or rise is as the terminology would suggest.
Electromotive force (emf): The force that establishes the flow of charge (or current) in a
system due to the application of a difference in potential.
Fixed (dc) Supplies
The terminology dc employed in the heading of this section is an abbreviation for direct
current, which encompasses the various electrical systems in which there is a
unidirectional (“one direction”) flow of charge.
DC Voltage Sources
Since the dc voltage source is the more familiar of the two types of supplies, it will be
examined first. The symbol used for all dc voltage supplies in this text appears in the
figure.
6
The relative lengths of the bars indicate the terminals they represent DC voltage sources
can be divided into three broad categories:
(1) batteries (chemical action), (2) generators (electromechanical), and (3) power supplies
(rectification).
Ampere-Hour Rating
Batteries have a capacity rating given in ampere-hours (Ah) or milliampere-hours (mAh).
Some of these ratings are included in the above figures. A battery with an ampere-hour
rating of 100 will theoretically provide a steady current of 1 A for 100 h, 2 A for 50 h, 10
A for 10 h, and so on, as determined by the following equation:
the capacity of a dc battery decreases with an increase in the current demand
and
the capacity of a dc battery decreases at relatively (compared to room temperature) low
and high temperatures
BH 500 characteristics:
(a) capacity versus discharge
current;
(b) capacity versus temperature
EXAMPLE
a. Determine the capacity in mill-ampere-hours and life in
minutes for the 0.9-V BH 500 cell of Fig. (a) if the discharge
current is 600 mA.
b. At what temperature will the mAh rating of the cell of
Fig. (b) be 90% of its maximum value if the discharge
current is 50 mA?
Solutions:
a. From Fig.(a), the capacity at 600 mA is about 450 mAh.
Thus, from Eq. ,
7
dc laboratory supply: (a) available terminals; (b) positive voltage
with respect to (w.r.t.) ground; (c) negative voltage w.r.t. ground; (d)
floating supply.
a dc voltage source will provide
ideally a fixed terminal voltage,
even though the current demand
from the electrical/electronic
system may vary,
8
the current source will supply,
ideally, a fixed current to an
electrical/electronic system, even
though there may be variations in
the terminal voltage as determined
by the system,
Conductors and Insulators
conductors are those materials that permit a generous flow of electrons with very little
external force (voltage) applied.
In addition,
good conductors typically have only one electron in the valence (most distant from the
nucleus) ring.
Insulators are those materials that have very few free electrons and require a large
applied potential (voltage) to establish a measurable current level.
9
SEMICONDUCTORS
Semiconductors are a specific group of elements that exhibit characteristics between
those of insulators and conductors.
The prefix semi, included in the terminology, has the dictionary definition of half, partial,
or between, as defined by its use. The entire electronics industry is dependent on this
class of materials since electronic devices and integrated circuits (ICs) are constructed of
semiconductor materials. Although silicon (Si) is the most extensively employed
material, germanium (Ge) and gallium arsenide (GaAs) are also used in many important
devices.
Problems 1- to – 39 pages (56-57)  Reference
(Boylestad)
10
Resistance
The flow of charge through any material encounters an opposing force similar in many
respects to mechanical friction. This opposition, due to the collisions between electrons
and between electrons and other atoms in the material, which converts electrical energy
into another form of energy such as heat, is called the resistance of the material. The unit
of measurement of resistance is the ohm, for which the symbol is Ω , the capital Greek
letter omega.
The resistance of any material with a uniform cross-sectional area is determined by the
following four factors:
1. Material
2. Length
3. Cross-sectional area
4. Temperature
At a fixed temperature of 20°C (room temperature), the resistance is related to the other
three factors by
where rho (Greek letter rho) is a characteristic of the material called the resistivity, l is
the length of the sample, and A is the cross-sectional area of the sample.
RESISTANCE: CIRCULAR WIRES
Note that the area of the conductor is measured in circular mils (CM) or square
millimeter (mm2) and not in squaremeters, inches, and so on, as determined by the
equation
The mil is a unit of measurement for length and is related to the inch by
11
By definition,
a wire with a diameter of 1 mil has an area of 1 circular mil (CM), as shown in Figure
One square mil was superimposed on the 1-CM area of Fig. 3.4 to clearly show that the
square mil has a larger surface area than the circular mil.
Applying the above definition to a wire having a diameter of 1 mil,
and applying above Equation, we have
Therefore
12
WIRE TABLES
1- American Wire Gage (AWG)
This wire table was designed primarily to standardize the size of wire produced
by manufacturers throughout the United States.
2345- Other Tables such as BS-Standard Table
13
14
2- RESISTANCE: METRIC UNITSMetric Wire Tables
15
RESISTANCE: METRIC UNITS
The design of resistive elements for various areas of application, including thin-film
resistors and integrated circuits, uses metric units for the quantities of R-Eq. In SI units,
the resistivity would be measured in ohm-meters, the area in square meters, and the
length in meters. However, the meter is generally too large a unit of measure for most
applications, and so the centimeter is usually employed. The resulting dimensions for its
Equation are therefore
16
TEMPERATURE EFFECTS
Figure reveals that for copper (and most other metallic conductors), the resistance
increases almost linearly (in a straight-line relationship) with an increase in temperature.
17
Inferred Absolute Temperature
It is important that we have some method of determining the resistance at any
temperature within operating limits. An equation for this purpose can be obtained by
approximating the curve of Fig. 3.14 by the straight dashed line that intersects the
temperature scale at _234.5°C. Although the actual curve extends to absolute zero
(_273.15°C, or 0 K), the straight-line approximation is quite accurate for the normal
operating temperature range.
The temperature of _234.5°C is called the inferred absolute temperature of copper. For
different conducting materials, the intersection of the straight-line approximation will
occur at different temperatures. A few typical values are listed in Table 3.5.
18
Temperature Coefficient of Resistance
There is a second popular equation for calculating the resistance of a conductor at
different temperatures. Defining
as the temperature coefficient of resistance at a temperature of 20°C, and R20 as the
resistance of the sample at 20°C, the resistance R1 at a temperature T1 is determined by
the higher the temperature coefficient of
resistance for a material, the more sensitive
the resistance level to changes in temperature.
TYPES OF RESISTORS, Fixed and variable
COLOR CODING ANDSTANDARD RESISTOR VALUES, Thermostats,
APPLICATIONS,
Measurement
All these things are taken as Laboratory subjects
PROBLEMS Page 92  Reference - Boylestad
19
LAB Tables