ELECTRICITY & MAGNETISM (Fall 2011)
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Transcript of ELECTRICITY & MAGNETISM (Fall 2011)
ELECTRICITY & MAGNETISM (Fall 2011)
LECTURE # 1
BY
MOEEN GHIYAS
TODAY’S LESSON
ENGINEERING DEFINITIONS &
CHAPTER 1 – Introductory Circuit Analysis by Boylested
Today’s Lesson Contents
• A Brief History & Definitions
• Units of Measurement & System of Units
• Conversion Within and Between System of Units
• Problem # 38 Solving – Ch 1
• Significant Figures, Accuracy and Rounding off
• Fixed-point, Floating-point, Scientific & Engineering
Notation and Prefixes
• Powers of Ten
• Conversion Between Levels of Powers of Ten
A Brief History of Electrical Engg
• The spectacle of lightening is as old as the age of earth
and the phenomenon of static electricity has been toyed
with since antiquity (400 BC – Frog eg).
• The Greeks so often used to demonstrate the effects of
static electricity elektron, but no extensive study was
made of the subject until 1600s.
• In the early stages, the contributors were not engineers
but instead physicists, chemists, mathematicians, or
even philosophers.
A Brief History of Electrical Engg
• However, the first electrical engineer is considered to be
William Gilbert (a physicist), with his 1600 publication of De
Magnete, who was the originator of the term "electricity“.
• In later years, Otto von Guericke, developed the first
machine to generate large amounts of charge, and
Stephen Gray, was able to transmit electrical charge
over long distances on silk threads.
• Charles DuFay demonstrated that charges either attract
or repel each other, leading him to believe that there
were two types of charges (+ve and –ve charges).
A Brief History of Electrical Engg
• In 1784, Charles Coulomb demonstrated in Paris that
the force between charges is inversely related to the
square of the distance between the charges.
• Hans Christian Oersted, a Swedish professor of
physics, announced in 1820 a relationship between
magnetism and electricity that serves as the foundation
for the theory of electromagnetism as we know it today.
A Brief History of Electrical Engg
• In the same year 1820, a French physicist, André
Ampère, demonstrated that there are magnetic effects
around every current-carrying conductor and that
current-carrying conductors can attract and repel each
other just like magnets.
• In 1831, an English physicist, Michael Faraday,
demonstrated his theory of electromagnetic induction,
whereby a changing current in one coil can induce a
changing current in another coil, even though the two
coils are not directly connected.
A Brief History of Electrical Engg
• Professor Faraday also did extensive work on a
storage device he called the condenser, which we
refer to today as a capacitor.
• The first voltaic cell, with its ability to produce
electricity through the chemical action of a metal
dissolving in an acid, was developed by another
Italian, Alessandro Volta, in 1799.
A Brief History of Electrical Engg
• Thus in modern era, electrical engineering can trace
its origins in the experiments of André Ampère and
Alessandro Volta in the 1800s, the experiments of
Michael Faraday, Georg Ohm and others and the
invention of the electric motor in 1872.
• The work of James Maxwell and Heinrich Hertz in the
late 19th century gave rise to the field of Electronics.
A Brief History of Electrical Engg
• The later inventions of the vacuum tube and the
transistor further accelerated the development of
electronics to such an extent that electrical and
electronics engineers currently outnumber their
colleagues of any other Engineering specialty.
• Note that many of the units of measurement bear the
name of major contributors in those areas — e.g.
– Volt after Count Alessandro Volta, (Italian Physicist)
– Ampereafter André Ampère, (Italian Physicist)
– Ohm after Georg Ohm. (German Physicist)
Definitions
• Who is an Engineer?
– An engineer is one who analysis complex
problems of world, solves the problems by
simplification methods and presents a practical
solution.
Definitions
• Electricity (from the New Latin ēlectricus,
meaning "amber-like") is a general term that
encompasses a variety of phenomena
resulting from the presence and flow of
electric charge.
• Electrostatics deals with static electricity i.e
static electric charges and field exerted by the
them in their surroundings.
Definitions
• Electrostatics & Electricity in more precise
terms
– Electric charge – a property of some subatomic
particles, which determines their electromagnetic
interactions. Electrically charged matter is
influenced by, and produces, electromagnetic fields.
– Electric current – a movement or flow of
electrically charged particles, typically measured in
amperes.
Definitions
– Electric field – an influence produced by an electric
charge on other charges in its vicinity.
– Electric potential – the capacity of an electric field
to do work on an electric charge, typically measured
in volts.
– Electromagnetism – a fundamental interaction
between the magnetic field and the presence and
motion of an electric charge.
System of Units
• The International Bureau of Weights and Measures
located at Sèvres, France, has been the host for the
General Conference of Weights and Measures,
attended by representatives from all nations of the
world.
• In 1960, the General Conference adopted a system
called Le Système International d’Unités (International
System of Units), which has the international
abbreviation SI.
System of Units
• SI has been adopted by the Institute of
Electrical and Electronic Engineers, Inc. (IEEE)
in 1965 and by the United States of America
Standards Institute in 1967 as a standard for all
scientific and engineering literature.
System of Units
System of Units - Comparison
The The meter was originally defined meter was originally defined in 1790 to be 1/10,000,000 in 1790 to be 1/10,000,000
the the distance between the equator and either pole at sea level, a distance between the equator and either pole at sea level, a
length preserved on a platinum-iridium bar at the International length preserved on a platinum-iridium bar at the International
Bureau of Weights and Measures at Sèvres, France.Bureau of Weights and Measures at Sèvres, France.
The The meter is now defined meter is now defined with reference to the speed of with reference to the speed of
light in a vacuum, which is 299,792,458 m/s.light in a vacuum, which is 299,792,458 m/s.
System of Units - Comparison
The The kilogram is defined kilogram is defined as a mass equal to 1000 times the as a mass equal to 1000 times the
mass of one cubic centimeter of pure water at 4°C.mass of one cubic centimeter of pure water at 4°C.
System of Units - Comparison
System of Units - Comparison
• The The secondsecond was was originally defined originally defined as 1/86,400 of as 1/86,400 of
the mean solar the mean solar day. However, since Earth’s rotation day. However, since Earth’s rotation
is slowing down by almost 1 second every 10 years,is slowing down by almost 1 second every 10 years,
• the second was the second was redefined in 1967 redefined in 1967 as 9,192,631,770 as 9,192,631,770
periods of the electromagnetic radiation emitted periods of the electromagnetic radiation emitted
by a particular transition of cesium atom.by a particular transition of cesium atom.
Units of Measurement
• Students often generate a numerical solution but often
they are unsure of which unit of measurement should
be applied. Consider, for example
d = 4000 ft
t = 1 min
V =? mi /hr
Units of Measurement
• To state that v = 45.37 without including the unit of
measurement mi/h is meaningless.
• Note while working with an equation, each quantity is in
the same system of units
Conversion Within and Between System of Units
• This operation is performed incorrectly most often
• Just convert the conversion factor into ratio or fraction
with required system of units in numerator and the other
in denominator.
• For conversion factor of 1m = 39.37 in
• To convert inches to meter (1m/39.37in) or
• To convert meter to inches (39.37in/1m)
Conversion Within and Between System of Units
• Let us convert 48 in. (4 ft) to meters
– We know conversion factor, 1 m = 39.37 in.
• Dividing both sides of the conversion factor by 39.37 in.
will result in the following format:
• Substituting we have,
Problems – Ch 1
• # 38 - Each spring there is a race up 86 floors of the 102-
story Empire State Building in New York City. If you were able to
climb 2 steps/second, how long would it take you to reach the
86th floor if each floor is 14 ft. high and each step is about 9 in.?
• Solution
– Steps – Find no of steps (distance) up to 86th floor and then time taken to
cover that
distance
Significant Figures
• All nonzero numbers are considered significant
figures, with zeros being significant in only some
cases.
• For instance, the zeros in 1005 are considered
significant because they define the size of the number
and are surrounded by nonzero digits.
• For the number 0.4020, the zero to the left of the
decimal point is not significant, but the other two are
because they define the magnitude and the fourth-
place accuracy of the reading.
Accuracy (or Precision in Measurement)
• Measurements of 22.1 and 22.10 imply different levels
of accuracy. The first suggests that the measurement
was made by an instrument accurate only to the tenths
place; the latter was obtained with instrumentation
capable of reading to the hundredths place.
• In the addition or subtraction of approximate numbers,
the entry with the lowest level of accuracy determines
the format of the solution. For example,
532.6 + 4.02 + 0.036 = 536.656 ≈ 536.7
(as determined by 532.6)
Accuracy (or Precision in Measurement)
• For the multiplication and division of approximate
numbers, the result has the same number of significant
figures as the number with the least number of
significant figures.
0.0046/0.05 = 0.0920 ≈ 0.09 (as determined by the one
significant digit of 0.05)
Rounding off
• For approximate numbers (and exact, for that matter)
there is often a need to round off the result; that is, you
must decide on the appropriate level of accuracy.
• The accepted procedure is simply to note the digit
following the last to appear in the rounded-off form, and
add a 1 to the last digit if it is greater than or equal to 5,
and leave it alone if it is less than 5.
• For example, 3.186 ≈ 3.19 ≈ 3.2, depending on the
level of precision desired.
Fixed-point, Floating-point, Scientific & Engg Notation
• There are four ways in which numbers appear when
using a computer or calculator
• Fixed-point – The fixed-point format defines the no. of
digits appearing after decimal point each time.
• Floating-point – In the floating-point format, the no. of
digits appearing after the decimal point are defined by
the number to be displayed.
Fixed-point, Floating-point, Scientific & Engg Notation
• Scientific (also called standard) notation and
engineering notation make use of powers of ten.
• Scientific notation requires that the decimal point
appear directly after the first digit greater than or equal
to 1 but less than 10.
• A power of ten (notation E or x10y ) will then appear
with the number, even if it has to be to the zero power.
Fixed-point, Floating-point, Scientific & Engg Notation
• Within the scientific notation, the fixed- or floating-point
format can be chosen.
• Floating Point Scientific
• If Fixed Point Scientific is chosen and set at the
thousandths-point accuracy, we have
Fixed-point, Floating-point, Scientific & Engg Notation
• Engineering Notation – Specifies that all powers of ten
must be multiples of 3, and the mantissa must be
greater than or equal to 1 but less than 1000.
• This restriction on the powers of ten is due to the fact
that specific powers of ten have been assigned
prefixes e.g. Kilo, micro etc
• Engineering notation with three-place accuracy (fixed
point notation) will result in
Powers of Ten• An important mathematical equation pertaining to
powers of ten is:
• Shifting a power of ten from the denominator to the
numerator, or the reverse, requires simply changing
the sign of the power.
• 1 = 100 1/10 = 0.1 = 10-1
• 10 = 101 1/100 = 0.01 = 10-2
• 100 = 102 1/1000 = 0.001 = 10-3
• 1000 = 103 1/10,000 = 0.0001 = 10-4
Powers of Ten
• The product of powers of ten:
• The division of powers of ten:
• The power of powers of ten:
• Multiplication,
Powers of Tens
Prefixes of SI Units
Conversion Between Levels of Powers of Ten
• An increase or a decrease in the power of ten must be
associated with the opposite effect on the multiplying
factor. For example
– Convert 20 kHz to megahertz.
Conversion Between Levels of Powers of Ten
• An increase or a decrease in the power of ten must be
associated with the opposite effect on the multiplying
factor. For example
– Convert 0.01 ms to microseconds.
Powers of Ten (Example)
• Example 1.1 - Determine appropriate prefixes
• Last part solution is it correct in engineering notation?
Summary / Conclusion
• A Brief History & Definitions
• Units of Measurement & System of Units
• Conversion Within and Between System of Units
• Problem # 38 Solving – Ch 1
• Significant Figures, Accuracy and Rounding off
• Fixed-point, Floating-point, Scientific & Engineering
Notation and Prefixes
• Powers of Ten
• Conversion Between Levels of Powers of Ten