FUNDAMENTALS OF ELECTRICAL ENGINEERING ENT 163 LECTURE 2

FUNDAMENTALS OF ELECTRICAL ENGINEERING [ ENT 163 ] LECTURE #2 INTRODUCTION TO ELECTRIC CIRCUIT Siti Marhainis Othman, MEng, Programme of Mechatronics, School of Mechatronics Engineering, Uni. MAP. Email: marhainis@unimap. edu. my

CONTENTS l l l Introduction The International System of Units Current And Charge Voltage Power and Energy

Introduction : An Overview of Electrical Engineering: Electrical engineering is the profession concerned with the systems that transmit, and measure of electric signal. Electrical system can be classified into 5 classification: • Communication systems -electrical systems that generate, transmit and distribute information. • Computer systems -use electric signals to process information ranging from word processing to mathematical computations • Control systems -use electric signals to regulate processes. Eg. , control of temperature, pressure.

Introduction : An Overview of Electrical Engineering: Power Systems -generate and distribute electric power. Signal-processing system -act on electric signals that represent information.

The International System of Units (SI) SI – International System of Units (International Measurement Language). The SI is based on seven fundamental units : Quantity Basic Unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mol Luminous intensity candela cd

The International System of Units (SI) Defined quantities are combines to form derived units: Quantity Unit Name (Symbol) Formula Frequency hertz (Hz) s-1 Force newton (N) kg. m/ s 2 Energy of work joule (J) n. m Power watt (W) J/s Electric charge coulomb (C) A. s Electric potential volt (V) J/C Electric resistance ohm ( ) V/A Electric conductance siemen (S) A/V Electric capacitance farad (F) C/V Magnetic flux weber (Wb) V. s Inductance henry (H) Wb/A

Scientific and Engineering Notation Scientific Notation: l Provide a convenient method to represent large and small numbers. Engineering Notation: l A specialized form of scientific notation to represent large and small quantities. l only uses multiples of 3 for the power of ten notation exponent

Engineering Notation Prefix Symbol Power pico p 10 -12 nano n 10 -9 micro µ 10 -6 milli m 10 -3 kilo k 103 mega M 106 giga G 109 tera T 1012

Examples 47, 000 = 4. 7 x 107 (Scientific Notation) = 47. x 106 (Engineering Notation) = 47 M 0. 000 027 = 2. 7 x 10 -5 (Scientific Notation) = 27 x 10 -6 (Engineering Notation) = 27µ 0. 605 = 6. 05 x 10 -1 (Scientific Notation) = 605 x 10 -3 (Engineering Notation) = 605 m

Charge and Current • The basic quantity in an electric circuit is the electric charge. Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). • The charge on an electron is negative and equal in magnitude to 1. 602 x 10 -19 Note: 1. The Coulomb is a large unit for charges. In 1 C of charge, there are 1/(1. 602 x 10 -19) = 6. 24 x 1018 electrons. 2. The law of conservation charge states that charge can be neither be created nor destroyed, only transferred. • Electric current is the time rate of change of charge, measured in ampere (A). Where, current is measured in amperes (A), 1 ampere= 1 coulomb/ second

Charge and Current • The charge transferred between time to time is obtained by integrating both side. • Two types of current: 1. A direct current (dc) is a current that remains constant with time (I) 2. An alternating current (ac) is a current that varies sinusoidally with time (i).

Example 1: 1. How much charge is represented by 4600 electrons? (ans: -7. 369 x 10 -19)

Example 2: 2. The total charge entering a terminal is given by q = 5 t sin 4πt m. C. Calculate the current at t = 0. 5 s. (ans: 31. 42 m. A)

Example 3: 3. If in Example 2, q = (10 – 10 e-2 t) m. C, find the current at t = 0. 5 s. (ans: 7. 36 m. A)

Example 4: 4. Determine the total charge entering a terminal between t=1 s and t=2 s, if the current passing the terminal is i =(3 t 2 -t)A. (ans: 5. 5 C)

Exercise 1: 1. How many coulombs are represented by these amount of electrons: (a) 6. 482 x 1017 (b) 1. 24 x 1018 3. Determine the current flowing through an element if the charge flow is given by: (a) q(t) = 3 e-t-5 e-2 t m. C (b) q(t) = 20 e-4 tcos 50 tμC

Exercise 1(cont’) 3. Find the charge q(t) flowing through a device if the current is: (a) i(t)=3 A, q(0)=1 C (b) i(t)=(2 t+5)m. A, q(0) = 0 (c) i(t)=20 cos(10 t+π/6)μA, q(0)=2μC 4. The current flowing through a device is i(t) = 5 sin 6πt A. Calculate the total charge flow through the device from t = 0 to t = 10 ms.

Example 5: 5. The current flowing through an element is, i={ 2 A 0<t<1 { 2 t 2 A t>1 Calculate the charge entering the element from t = 0 to t = 2 s. (ans: 6. 667 C)

Voltage • To move the electron in a conductor in a particular direction requires some work or energy transfer. • Performed by an external electromotive force (emf). • Also known as voltage or potential difference. • The voltage between two point a and b in electric circuit is the energy ( work ) needed to move 1 C of charge from a to b : w =energy (J), q = charge (C) 1 volt= 1 joule/coulomb= 1 newton meter/ coulomb Voltage (or potential difference) is the energy required to move a unit charge through an element , measured in volts (V).

Voltage • Two ways in interpreting polarity: 1) Point a is at a potential of vab volts higher than point b , 2) The potential at point a with respect to point b is vab +a vab -b • Two common types of voltage: 1) Direct voltage (dc voltage): a constant voltage (V); commonly produced by a battery. 2) Alternating voltage (ac voltage): a sinusoidally time-varying voltage (v); produced by an electric generator.

Power and Energy Power is the time rate of expending or absorbing energy, measured in watts (W). w =energy (J), t = time (s) or (instantaneous power) • + sign power is being delivered to/ absorbed by the element • - sign power is being supplied by the element. • To determine polarity, use passive sign convention.

Power and Energy Passive sign convention is satisfied when the current enters through the positive terminal of an element and p=+vi. If the current enters through the negative terminal, p=-vi. +Power absorbed = - Power supplied + 4 V - 3 A 4 V + Fig. 1: Cases of absorbing power + 3 A 4 V - 3 A 4 V + Fig. 2: Cases of supplying power

Power and Energy • Law of conservation energy: total power supplied to the circuit must balance the total power absorbed. • Energy is the capacity to do work , measured in joules (J)

Example 6: 6. An energy source forces a constant current of 2 A for 10 s to flow through a light bulb. If 2. 3 k. J is given off in the form of light and heat energy, calculate the voltage drop across the bulb. (ans: 115 V)

Example 7: 7. To move charge q from point a to point b requires -30 J. Find the voltage drop vab if : (a) q=2 C (b) = -6 C (ans : (a) -15 V (b) 5 V )

Example 8: 8. Find the power delivered to an element at t = 3 ms if the current entering its positive terminal is i = 5 cos 60πt A and the voltage is: (a) v =3 i (b) v = 3 di/dt (ans : (a) p = 53. 48 W, (b) p = -6. 396 W)

Circuit Elements • • An electric circuit is simply an interconnection of the elements. There are two types of elements: • • Passive elements – not capable of generating energy (resistors, capacitors, inductors. ) Active elements – capable of generating energy( generators, batteries, operational amplifiers) The most important active elements are voltage or current sources Two kinds of sources: independent and dependent sources An ideal independent sources is an active element that provides a specified voltage or current that is completely independent of other circuit elements An ideal dependent (controlled) sources is an active element in which the source quantity is controlled by another voltage or current.

Example 9 9. Calculate the power supplied or absorbed by each element in Fig 3. Figure 3

Example 10: 10. Compute the power absorbed or supplied by each component of the circuit in Fig 4 Figure 4

Power and Energy + - + V- v i Fig. 5: Symbol for independent sources v + - Fig 6: Symbol for dependent sources • There are four possible types of dependent sources: 1. 2. 3. 4. A A i voltage – controlled voltage sources (VCVS) current – controlled voltage sources (CCVS) voltage – controlled current sources (VCCS) current – controlled current sources (VCVS)

References 1. Charles K. Alexander, Matthew N. O. Sadiku, “Fundamentals of Electric Circuits”, 2 nd Ed, Mc. Graw Hill, 2004. 2. 2. James W. Nilsson, Susan A. Reidel, “Electric Circuits”, 6 th Ed, Prentice Hall, 2004.