2. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Electricity Principles & Applications Eighth Edition Chapter 9 Power in AC Circuits (student version) Richard J. Fowler McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. 9 - 1

3. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. INTRODUCTION Phase Shift True Power Apparent Power Angle Theta Power Factor 9 - 2

4. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Dear Student: This presentation is arranged in segments. Each segment is preceded by a Concept Preview slide and is followed by a Concept Review slide. When you reach a Concept Review slide, you can return to the beginning of that segment by clicking on the Repeat Segment button. This will allow you to view that segment again, if you want to. 9 - 3

5. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Preview (Page 231) In pure resistance ac circuits, there are only two power pulses per cycle. In pure resistance ac circuits, both power pulses are positive. In pure resistance ac circuits, current and voltage are in-phase. In pure resistance ac circuits, use the the power formula used for dc circuits. 9 - 4

6. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Ac- Power Facts Resistance doesn’t cause phase shift. Reactance causes 90  of phase shift. Theta is the angle by which the current leads or lags the voltage. Trigonometric functions can be used to find the resistive and reactive parts of a phasor. Apparent power calculations ignore phase shift. It is advantageous for a system to operate with a power factor close to one. 9 - 5

7. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Power In A Resistive Ac Circuit (Page 232) P = IV in an ac circuit containing only resistance. P =2 A x 0.707 x5 W5V x 0.707 = 2 A 5V Note that both power pulses are positive. There are only two pulses per cycle. Voltage and current are in-phase. I V P 9 - 6

8. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Resistive-Power Quiz Power equals current times voltage in an ac circuit when the only load is ____. Use ____ values of current and voltage when calculating power. Without phase shift, there are ____ power pulses for each cycle. There are no ____ power pulses when current and voltage are in phase. An ac circuit with a 30-V P-P source and a 10-  resistor load uses ____ watts of power. resistance rms two negative 11.25 9 - 7

9. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Review Repeat Segment In pure resistance ac circuits, there are only two power pulses. In pure resistance ac circuits, both power pulses are positive. In pure resistance ac circuits, current and voltage are in-phase. In pure resistance ac circuits, use the the power formula used for dc circuits. 9 - 8

10. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Preview Capacitance causes I to lead V. (Page 232) Inductance causes V to lead I. (Page 233) Circuits with both R and X (reactance) cause theta to be >0  and <90 . (Page 233) I t (or V t ) can be divided into its resistive and reactive parts. (Page 235) 9 - 9

11. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Reactance Causes Phase Shift (Page 232) A combination circuit with capacitance causes I to lead V. 50  I V 9 - 10

12. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Reactance Causes Phase Shift (Page 232) A combination circuit with inductance causes V to lead I. 60  I V 9 - 11

13. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Working With Right Triangles (Page 236) The hypotenuse can be either the total voltage or the total current. Of course, the sides must be the same quantity as the hypotenuse. hypotenuse adjacent side opposite side  tan  opposite adjacent opposite hypotenuse adjacent hypotenuse sin  cos  = I resistive I reactive I source V source  I resistive I reactive I source  9 - 12

14. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Combination-Loads Quiz Capacitance causes current to ____ voltage. Inductance causes current to ____ voltage. The ____ of a triangle of current phasors represents the total current. The resistive current is ____ amperes when theta is 40  and the total current is 12 amperes. The total voltage is ____ volts when theta is 25  and the reactive voltage is 40 volts. lead lag hypotenuse 9.2 94.6 9 - 13

15. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Review Repeat Segment Capacitance causes I to lead V. Inductance causes V to lead I. Circuits with both resistance and reactance cause theta to be >0  and <90 . I t (or V t ) can be divided into its resistive and reactive parts. 9 - 14

16. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Preview (Page 240) Phase-shifted circuits produce two positive and two negative power pulses. In pure reactance circuits the negative and positive pulses are equal. Wattmeters measure true power. Apparent power ignores angle theta. Power factor = power  apparent power. 9 - 15

17. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. 2 A Power In A Phase-Shifted Circuit (Page 241) 3V The power pulse is negative when I and V have opposite signs. 30° P = I V cos  2 A x 0.707 x2.6 W3V x 0.707 x0.866 = cos 30° = 0.866 I V P 9 - 16

18. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Power in a Pure Reactance Circuit This circuit has capacitance because I leads V. 90  VI P The negative power pulses cancel the positive power pulses. There is no true power. (Page 231) 9 - 17

19. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Power (true power) is measured with a wattmeter P = IV cos  Apparent power is determined by measuring P app = IV. currentand voltage and then using the formula When the load is all resistance, power (P) = apparent power (P app ). Combination of resistance and reactance W 80 W V 25 V A 4 A P app = 4 A x 25 V = 100 VA Measured P = 80 W. or calculated using the formula (Page 240) Two Types Of Power In Ac Circuits 9 - 18

20. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Determining Power Factor (PF) and Angle Theta (  ) Combination of resistance and reactance W 75.5 W V 30 V A 3 A The measured power,current,and voltage can be used to determine power factor and angle theta. P app = 3 A x 30 V = 90 VA PF = cos  = P / P app = 75.5 W / 90 VA = 0.839  = arccos 0.839 = 33  ( Arccos means the angle that has this cos.) (Page 241) 9 - 19

21. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Calculating Currents (Page 238) Determine the resistive and reactive currents when the source current is 43 A and the power factor is 0.92. cos  = I resistive / I T Therefore, I resistive = I T x cos  I resistive = 43 A x 0.92 = 39.56 A arccos 0.92 = 23.1  And, tan 23.1  tan  reactive   I resistive Therefore, I reactive = I resistive x tan  I reactive = 39.56 A x 0.426 = 16.85 A ( Arccos means the angle that has this cos.) 9 - 20

22. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Combination-Load-Power Quiz There are ____ negative power pulses per cycle when current and voltage are out of phase. With combination loads, P = IV cos  will yield the ____ power. With combination loads, P = IV  will yield the ____ power. The unit for apparent power is the _____. The power is ____ watts when I = 16 A, V = 240 V, and  20  The power factor is ____ when P = 860 W, I = 10 A, and V = 120 V. two true apparent VA 3608.4 0.717 9 - 21

23. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Review Repeat Segment Phase-shifted circuits produce two positive and two negative power pulses. In pure reactance circuits the negative and positive pulses are equal. Wattmeters measure true power. Apparent power ignores angle theta. Power factor = power  apparent power. 9 - 22

24. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. REVIEW Phase Shift True Power Apparent Power Angle Theta Power Factor 9 - 23