ELECTRICITY & MAGNETISM (Fall 2011)

1. ELECTRICITY & MAGNETISM (Fall 2011) LECTURE # 1 BY MOEEN GHIYAS

2. ENGINEERING DEFINITIONS & CHAPTER 1 – Introductory Circuit Analysis by Boylested TODAY’S lesson

3. 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

4. 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.

5. 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).

6. 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.

7. 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.

8. 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.

9. 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.

10. 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. • Voltafter Count Alessandro Volta, (Italian Physicist) • Ampere after André Ampère, (Italian Physicist) • Ohmafter Georg Ohm. (German Physicist)

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. System of Units

18. System of Units - Comparison The meter was originally defined in 1790 to be 1/10,000,000 the distance between the equator and either pole at sea level, a length preserved on a platinum-iridium bar at the International Bureau of Weights and Measures at Sèvres, France. The meter is now defined with reference to the speed of light in a vacuum, which is 299,792,458 m/s.

19. System of Units - Comparison The kilogram is defined as a mass equal to 1000 times the mass of one cubic centimeter of pure water at 4°C.

20. System of Units - Comparison

21. System of Units - Comparison • The second was originally defined as 1/86,400 of the mean solar day. However, since Earth’s rotation is slowing down by almost 1 second every 10 years, • the second was redefined in 1967 as 9,192,631,770 periods of the electromagnetic radiation emitted by a particular transition of cesium atom.

22. 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

23. 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

24. 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)

25. 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,

26. 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

27. 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.

28. 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)

29. 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)

30. 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.

31. 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.

32. 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.

33. 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

34. 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

35. 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

36. Powers of Ten • The product of powers of ten: • The division of powers of ten: • The power of powers of ten: • Multiplication,

37. Powers of TensPrefixes of SI Units

38. 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.

39. 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.

40. Powers of Ten (Example) • Example 1.1 - Determine appropriate prefixes • Last part solution is it correct in engineering notation?

41. 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