Applied Electricity II 2024.pdf 2.pptx t

EENG220

1. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES APPLIED ELECTRICITY II EENG 222 1

2. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Applied Electricity II. 2024 Min. & Civil Fridays 9 to 11 Elec. & Mech. Mondays 11 to 1:00

3. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES METHOD OF ASSESSMENT Attendance 5% Assignments 5% Classwork 5% Tests 15% Final Exam 70% TOTAL 100% 3

4. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES SECOND SEMESTER SYLLABUS INTRODUCTION 2. A.C. BASIC THEORY (A.C. Power Generation) 3. SINUSOIDAL WAVES (Terms and Definition) 3.1. Instantaneous Values 3.2. Maximum Values 3.3. R.M.S. Values 3.4. Effective Values 3.5. Peak-to-peak Values 4

5. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 4. A.C . CIRCUITS (Components ) 5. CALCULATION OF REACTANCES 5.1. Capacitive Reactance 5.2. Inductive Reactance 5.3. Impedance 6. CALCULATION OF A.C. CURRENT 7 . VECTOR REPRESENTATION 8. PHASE ANGLE OF SINUSOIDAL VOLTAGE AND CURRENT 5

6. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 9. A.C. SERIES CIRCUITS 9.1. R-C 9.2. R-L 9.3. L.C 9.4. R-L-C 10. A.C. PARALLEL CIRUITS 10.1 . R-C 10.2 . R-L 10.3 . L.C 10.4 RL-C POWER FACTOR CALCULATION 6

7. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES POWER FACTOR CORRECTION 13. RESONANCE 13.1 Series Resonance 13.2 Parallel Resonance TERMS ASSOCIATED WITH A.C. RESONANCE THREE PHASE POWER SYSTEM THREE PAHSE 4-WIRE SYSTEM SATR CONNECTED LOADS 7

8. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES CALCULATION OF 3-ph VOLTAGE CURRENT AND POWER BALANCE 3-ph LOADS UNBALANCE 3-ph LOADS (Current in the Neutral) TRANSFORMERS 21.1. Single Phase Transformers CONSTRUCTION TRANSFORMER LOSSES 8

9. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES INDUCED VOLTAGE IN THE PRIMARY AND SECONDARY WINDINGS EQUIVALENT CIRCUITS OF AN IDEAL TRANSFORMER 25.1. ON LOAD 25.2. ON NO-LOAD IMPEDANCE TRANSFER EQUIVALENT CIRCUIT OF AN EXACT TRANSFORMER TRANSFORMER EFFICIENCY 9

10. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES APPLIED ELECTRICITY II Year 2. 10

11. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 11 Faraday’s Laws of Electromagnetic Induction Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced, which is called induced current.

12. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 1. INTRODUCTION Unlike D.C Current we have so far studied, alternating current (A.C) is the current that changes in magnitude direction continuously with respect to time. In many design applications, alternating current offers substantial advantages over direct current. Transmitted over long distances. Storage is not necessary Conversion to DC is easier. For these reasons, alternating current (a.c) has become accepted as a more suitable and versatile power source than direct current (d.c.). Although there are many situations in which d.c. is a proper choice as a fundamental source of power such as the automobile where a d.c. storage battery represents an initial source of power, there are correspondingly many more situation in which it becomes essential to utilize and understand alternating current. 12

13. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 13

14. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG212) LECTURER’S NOTES 14

15. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG212) LECTURER’S NOTES 15

16. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG212) LECTURER’S NOTES 16

17. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Electricity is produced by generators at power stations and then distributed by a vast network of transmission lines (called the National Grid system) to industry and for domestic use. It is easier and cheaper to generate alternating current (a.c.) than direct current (d.c.) and a.c. is more conveniently distributed than d.c. since its voltage can be readily altered using transformers . Whenever d.c. is needed in preference to a.c., devices called rectifiers are used for conversion. If values of quantities which vary with time t are plotted to a base of time , the resulting graph is called a waveform . Some typical waveforms are shown in the figure below. A waveform of the type shown above is called a sine wave . It is the shape of the waveform of e.m.f. produced by an alternator and thus the mains electricity supply is of ‘sinusoidal’ form. 17

18. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES One complete series of values is called a cycle The time taken for an alternating quantity to complete one cycle is called the period or the periodic time , T , of the waveform . The number of cycles completed in one second is called the frequency , f , of the supply and is measured in hertz , Hz . The standard frequency of the electricity supply in Great Britain is 50 Hz . 18

19. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Problem 1. Determine the periodic time for frequencies of (a ) 50 Hz and (b) 20 kHz Problem 2. Determine the frequencies for periodic times of (a) 4 ms, (b) 4 μ s Problem 3. An alternating current completes 5 cycles in 8 ms. What is its frequency? 19

20. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES A.C VALUES Instantaneous values are the values of the alternating quantities at any instant of time. 20

21. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES A.C VALUES Instantaneous values are the values of the alternating quantities at any instant of time. The largest value reached in a half cycle is called the peak value or the maximum value or the crest value or the amplitude of the waveform. Such values are represented by V m , I m , etc. A peak-to-peak value of e.m.f . is the difference between the maximum and minimum values in a cycle. The average or mean value of a symmetrical alternating quantity , ( such as a sine wave), is the average value measured over a half cycle , ( since over a complete cycle the average value is zero). 21

22. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 22 ROOT MEAN SQUARE VALUE (RMS VALUE)

23. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 23 V rms or V = 0.707 V max

24. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES A.C VALUES The area under the curve is found by approximate methods such as the trapezoidal rule, the mid-ordinate rule or Simpson’s rule. Average values are represented by V AV , I AV , etc. The effective value of an alternating current is that current which will produce the same heating effect as an equivalent direct current. The effective value is called the root mean square (rms) value and whenever an alternating quantity is given, it is assumed to be the rms value. For example , the domestic mains supply in Great Britain is 240 V and is assumed to mean ‘240 V rms’. The symbols used for rms values are I, V , E, etc. 24

25. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES A.C VALUES Problem 4. Calculate the rms value of a sinusoidal current of maximum value 20 A Problem 5. Determine the peak and mean values for a 240 V mains supply. Problem 6. A supply voltage has a mean value of 150 V. Determine its maximum value and its rms value 25

26. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES The equation of a sinusoidal waveform In the figure above, OA represents a vector that is free to rotate anticlockwise about 0 at an angular velocity of ω rad/s . A rotating vector is known as a phasor. After time t seconds the vector OA has turned through an angle ω t . If the line BC is constructed perpendicular to OA as shown, then 26

27. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES If all such vertical components are projected on to a graph of y against angle ω t (in radians), a sine curve results of maximum value OA. Any quantity which varies sinusoidally can thus be represented as a phasor . A sine curve may not always start at 0°. To show this a periodic function is represented by y = sin( ω t + Φ ), where is the phase (or angle) difference compared with y = sin ω t . Given the general sinusoidal voltage, v = V m sin( ωt + Φ ), then 27

28. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 28

29. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES 29 Problem 7. An alternating voltage is given by: v = 282.8 sin 314t volts. Find (a) the rms voltage, (b) the frequency and (c) the instantaneous value of voltage when t = 4 ms Problem 8 . An alternating voltage is given by: v = 75 sin(200 t - 0.25) Volts. Find ( a) the amplitude, ( b) the peak-to-peak value, ( c) the rms value , ( d) the periodic time, ( e) the frequency, and ( f) the phase angle (in degrees and minutes ) relative to 75 sin 200 π t .  

30. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Exercise 1. Purely Resistive AC Series Circuit R = 15 Ω 120 ∠0 o V I Determine the current I flowing in the circuit above and sketch the waveforms and phasor diagrams. + _ Ans. 30 SINGLE PHASE A. C. CIRCUITS

31. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Single Phase Series AC Circuits Purely Inductive AC Series Circuit L = 35 mH 132 ∠45 o V 50 Hz I Exercise 2 . Determine the current I flowing in the circuit above and sketch the waveforms and phasor diagrams. + _ 31

32. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Single Phase Series AC Circuits Purely Capacitive AC Series Circuit C = 0.15 mF 140 ∠60 o V 60 Hz I Exercise 4. Determine the current I flowing in the circuit above and sketch the waveforms and phasor diagrams. Exercise 5 . Calculate the current taken by a 23 μF capacitor when connected to a 240 V, 50 Hz supply. + _ 32 Exercise 3. Determine the capacitive reactance of a capacitor of 10 μF when connected to a circuit of frequency ( a) 50 Hz (b ) 20 kHz

33. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Single Phase Series AC Circuits A.C. R-C Series Circuit C = 35 µF 140 ∠60 o V 50 Hz I Exercise 6. Determine the current I flowing in the circuit above and sketch the waveforms and phasor diagrams. + _ Exercise 7. A capacitor C is connected in series with a 40 Ω resistor across a supply of frequency 60 Hz . A current of 3 A, flows and the circuit impedance is 50 Ω . Calculate: ( a) the value of capacitance , C , ( b) the supply voltage, ( c) the phase angle between the supply voltage and current, ( d) the p.d. across the resistor, and ( e) the p.d. across the capacitor. Draw the phasor diagram. R = 12 Ω 33

34. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Single Phase Series AC Circuits A.C. R-L Series Circuit L = 35 mH 110 ∠60 o V 60 Hz I Exercise 8 . Determine the current I flowing in the circuit above and sketch the waveforms and phasor diagrams. + _ Exercise 9 . In a series R–L circuit the p.d. across the resistance R is 12 V and the p.d. across the inductance L is 5 V. Find the supply voltage and the phase angle between current and voltage . Exercise 10 . A coil has a resistance of 4 Ω and an inductance of 9.55 mH. Calculate at 50 Hz, ( a) the inductive reactance , ( b) the impedance, and (c) the current taken from a 240 V supply . Determine also the phase angle between the supply voltage and current. R = 12 Ω 34

35. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES A.C. R-L-C Series Circuit 35 In an a. c. series circuit that contains a resistor R, an inductor L, and a capacitor C, the applied voltage V is the phasor sum of the resistor voltage V R , the inductor voltage V L and the capacitor voltage V C . That is V = V R + JV L + (-JV C ) Or V = V R + J(V L -V C ) The current flowing round the circuit is the same so that: IZ = IR + I(JX L ) + I(-JX C ) Z = R + J(X L – X C ) + _ V L V R V C V R L C Z R X C (XL-XC) X L φ

36. FOURAH BAY COLLEGE ELECTRICAL & ELECTRONIC ENGINEERING DEPARTMENT APPLIED ELECTRICITY II (EENG222) LECTURER’S NOTES Single Phase Series AC Circuits R-L-C AC Series Circuit L = 35 mH 124 ∠30 o V 50 Hz I Exercise 11. Determine the current I flowing in the circuit above and sketch the waveforms and phasor diagrams. + _ R = 12 Ω C = 25 µ F 36 Exercise 12. A coil of resistance 5 Ω and inductance 120 mH in series with a 100 μF capacitor, is connected to a 300 V, 50 Hz supply . Calculate ( a) the current flowing, ( b) the phase difference between the supply voltage and current, ( c) the voltage across the coil and ( d) the voltage across the capacitor.