Applied Electricity 4 MODULE RESOURCE MANUAL NUE056/2 Second Edition
Contents INTRODUCTION 5 1. TRIGONOMETRY 7 2. CATHODE RAY OSCILLOSCOPE OPERATION 13 3. ALTERNATING QUANTITIES 33 4. VECTOR/PHASOR DIAGRAMS 45 5. RESISTIVE AC CIRCUITS 63 6. INDUCTIVE AC CIRCUITS 73 7. CAPACITIVE AC CIRCUITS 83 8. RL SERIES AC CIRCUITS 93 9. RC SERIES AC CIRCUITS 107 10. RLC SERIES AC CIRCUITS 117 11. RL, RC AND LC PARALLEL AC CIRCUITS 129 12. RLC PARALLEL AC CIRCUITS 143 13. THE IDEAL TRANSFORMER 155 REVIEW QUESTIONS - ANSWERS 167 ASSESSMENT 177 THEORY TEST 1 - ANSWERS 201 THEORY TEST 2 - ANSWERS 204 APPENDIX - THEORY SUMMARY 207
1. Trigonometry Purpose In this topic you will learn how to apply trigonometric methods to solve electrical problems when dealing with a.c. circuits. Objectives At the end of this topic you should be able to: state and apply the sine, cosine and tangent ratios of a right-angle triangle use a scientific calculator to find the sine, cosine and tangent of any angle apply Pythagoras s Theorem to a right-angled triangle. Technical information You will find the information to undertake this topic in the following references. At least one reference text should used. References for this topic Jenneson JR., Electrical Principles for the Electrical Trades 5th Ed., 2003. McGraw Hill, Sydney, Chapter 1. Phillips Peter, Electrical Principles 2, Thomas Nelson, Melbourne, 1996, Chapter 5. Batty Ian, More Electrical Principles, Prentice Hall, Sydney,1997, Chapters 6 and 7. Mychael A., A.C. Principles, Thomas Nelson, Melbourne, 1994, Chapter 1. 7
Exercises In the following exercises, a right angled triangle is assumed to have sides ABC or XYZ. 1. The hypotenuse AB of a right-angle triangle is 20 mm long, the side AC is 12 mm. Determine: (a) The values of the angles CAB and ABC (b) Length of side BC. 2. In a right-angle triangle with hypotenuse AB, the side AC is 170 mm and the side BC is 34 mm. Determine the angle ABC and the length of the hypotenuse AB. 8
3. If the hypotenuse BC of a right-angle triangle is 200 mm, and the side AB is 160 mm, calculate the values of: (a) Sin B; Cos B and Tan B. (b) Sin C; Cos C and Tan C. 4. Complete the table below. Angle θ Sin θ Cos θ Tan θ 10 0 27 0 0.4142 0.7314 0.8480 57 0 1.9626 101 0 0.5592 0.3584 163.7 0-0.8988 9
Review questions These questions will help you revise what you have learnt in topic 1. 1. In a right-angle triangle, the ratio is termed the tangent of the angle. 2. A sine curve repeats itself every degrees. 3. A cosine curve is a sine curve shifted by degrees. 4. The sine of any angle ranges between. 5. In a right-angle triangle when the cosine of one of the complementary angles is 0.5 the size of the other angle in degrees is. 6. Complete the following table: Angle φ Sin φ Angle φ Cos φ Angle φ Tan φ 135 0 93 0 200 0 225 0 295 0 105 0 400 0 2 0 150 0 75 0 195 0 285 0 264 0 27' 230 0 42' 250 0 130 0 200 0 146 0 36' 260 0 162 0 28' 178 0 180 0 330 0 198 0 200 0 270 0 270 0 7. The hypotenuse AB of a right-angle triangle is 250 mm in length and the side BC is 100 mm in length. Determine: (a) The values of the angles A and B; (b) Length of side AC. 8. The hypotenuse YZ of a right-angle triangle is 250 units in length and the side XZ is 150 units in length. Determine: (a) Length of side XY. (b) The values of the two unknown angles 10