2. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Electricity Principles & Applications Eighth Edition Chapter 13 R, C, and L Circuits (student version) Richard J. Fowler McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. 13 - 1

3. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. INTRODUCTION RC, RL, and RCL Circuits Resonance (f r ) Quality ( Q ) Bandwidth (BW) Filters 13 - 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. 13 - 3

5. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Preview Phasors can be added graphically or mathematically. (Page 340) Voltage drops in series RC circuits are added by phasor addition. (Page 343) Oppositions in series RC circuits are added by phasor addition. (Page 343) Currents in parallel RC circuits are added by phasor addition. (Page 346) 13 - 4

6. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Facts About R, C, and L Circuits Impedance (Z) is the combined opposition of R and X. The ohm is the base unit of impedance. Except at resonance, Z is always larger than R or X in a series circuit. Except at resonance, Z is always smaller than R plus X in a series circuit. Except at resonance, Z always causes phase shift. ___ For all impedance circuits, Z = V T / I T and f r = 1 / (6.28  LC ). The current phasor is the reference for series circuits. The voltage phasor is the reference for parallel circuits. A given L and C are resonant at only one frequency. At a given f, BW is inversely proportional to Q. 13 - 5

7. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Two right angle phasorscan be added graphically by completing the rectangleand bisecting it diagonally. The bisecting line is the phasor resulting from the addition. 3 4 5 Mathematical addition can be done with this equation. C = A 2 + B 2 = 3 2 + 4 2 = 5 Substituting for A and B, and solving the equation yields 5 which is the value of the resultant phasor (C). Graphical and Mathematical Addition of Phasors (Page 340) 13 - 6

8. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Series RC Circuit (Page 000) VRVR + VC+ VC does not equal V T because these voltages are out-of-phase. V T =  V R 2 + V C 2 =  30 2 + 40 2 =  2500 = 50 V Solution: These voltages must be added using phasor addition. V 50 V V 40 V V 30 V VRVR VCVC VT VT ITIT 13 - 7

9. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Series RC Impedance (Page 000) Z does not equal R + X C because R and X C are  out-of-phase.  8 0 2 + 60 2 =  10000 = 100  Determine Z using I V 150 V R XCXC Z X C = 60  R = 80  A 1.5 A and V.Z = V / I = 150 V / 1.5 A = 100  Or, using phasor addition: Z =  R 2 + X C 2 = 13 - 8

10. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Parallel RC Circuit (Page 000) IRIR + IC+ IC does not equal I T because these currents are out-of-phase. I T =  I R 2 + I C 2 =  0.4 2 + 0.3 2 =  0. 25 = 0.5 A Solution: These currents must be added using phasor addition. A 0.5 A A 0.4 A A 0.3 A IRIR ICIC IT IT VTVT 13 - 9

11. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. RC-Circuits Quiz V T = ____ when V R = 20 V and V C = 15 V in a series circuit. I T ____ V T in a series RC circuit. Z = ____ when R = 400  and X C = 300  in a series circuit. In a parallel RC circuit, I T ____ V T. When I R = 0.5A, I C = 0.8A, and V T = 30V, Z of a parallel RC circuit will be ____  25 V leads 500  leads 33.7 13 - 10

12. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Review Repeat Segment Phasors can be added graphically or mathematically. Voltage drops in series RC circuits are added by phasor addition. Oppositions in series RC circuits are added by phasor addition. Currents in parallel RC circuits are added by phasor addition. 13 - 11

13. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Preview Impedance is a combination of resistance and reactance. (Page 343) Voltage drops in series RL circuits are added by phasor addition. (Page 349) Oppositions in series RL circuits are added by phasor addition. (Page 349) Currents in parallel RL circuits are added by phasor addition. (Page 251) 13 - 12

14. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Series RL Circuit (Page 349) VRVR + VL+ VL does not equal V T because these voltages are out-of-phase. V T =  V R 2 + V L 2 =  6 0 2 + 80 2 =  10000 = 100 V Solution: These voltages must be added using phasor addition. V 100 V V 80 V V 60 V VRVR VLVL VT VT ITIT 13 - 13

15. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Series RL Impedance (Page 349) Z does not equal R + X L because R and X L are  out-of-phase.  8 0 2 + 60 2 =  10000 = 100  Determine Z using I V 150 V and V.Z = V / I = 150 V / 1.5 A = 100  Or, using phasor addition: Z =  R 2 + X L 2 = R XLXL Z X L = 60  R = 80  A 1.5 A 13 - 14

16. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. IRIR ILIL IT IT VTVT Parallel RL Circuit (Page 351) IRIR + IL+ IL does not equal I T because these currents are out-of-phase. I T =  I R 2 + I L 2 =  0.9 2 + 1.2 2 =  2.25 = 1.5 A Solution: These currents must be added using phasor addition. A 1.5 A A 0.9 A A 1.2 A 13 - 15

17. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. RL-Circuits Quiz V T = ____ when V R = 15 V and V L = 12 V in a series circuit. In a series RL circuit, I T ____ V T. In a series circuit, Z = ____ when R = 600  and X L = 800 . In a parallel RL circuit, I T ____ V T. Z of a parallel RL circuit will be ____  when I R = 0.7A, I L = 0.4A, and V T = 25 V. 19.2 V lags 1000  lags 38.5 13 - 16

18. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Review Repeat Segment Impedance is a combination of resistance and reactance. (Page 343) Voltage drops in series RL circuits are added by phasor addition. (Page 349) Oppositions in series RL circuits are added by phasor addition. (Page 349) Currents in parallel RL circuits are added by phasor addition. (Page 351) 13 - 17

19. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Preview X L and X C are 180  out-of-phase. (Page 353) V L and V C are 180  out-of-phase in series RCL circuits. (Page 352) Either (or both) X L and X C can be > Z in series RCL circuits. (Page 353) I L and I C are 180  out-of-phase in parallel RCL circuits. (Page 354) 13 - 18

20. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Series RCL Circuits (Page 352) because these voltages are out-of-phase. V 15 V V T can be calculated using phasor addition: V T =  V R 2 + (V L - V C ) 2 = L R C VRVR VLVL VT VT VCVC VXVX Notice that either (or both) V C and V L can be greater than V T. Also, V T must be greater than V X or V R. V 38 V V 26 V V 9 V does not equal V T V C +VRVR  9 2 + 12 2 =  225 = 15 V VL +VL + 13 - 19

21. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Series RCL Impedance (Page 353) Z does not equal R +X C + X L because R and X are  out-of-phase.  15 2 + 20 2 =  625 = 25  Determine Z using I V 15 V and V.Z = V / I = 15 V / 0.6A = 25  Or, using phasor addition: Z =  R 2 + (X L -X C ) 2 = X L = 50  R = 15  X C = 30  A 0.6 A R XLXL Z XCXC X Notice that either (or both) X C and X L can be greater than Z. Also, Z must be greater than X or R. 13 - 20

22. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Parallel RCL Circuits (Page 000) because these currents are out-of-phase. I T can be calculated using phasor addition: I T =  I R 2 + (I C - I L ) 2 = VT VT IRIR ICIC ITIT ILIL IXIX Notice that either (or both) I C and I L can be greater than I T. Also, I T must be greater than I X or I R. does not equal I T IC +IC +IRIR  0.8 2 + 0.4 2 =  0.8 = 0.894 A IL +IL + A 0.89 A A 0.8 A A 1.0 A A 0.6 A 13 - 21

23. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. RCL-Circuit Quiz The current will ____ the voltage in a series RCL circuit in which R = 20 , X C = 45  and X L = 65 . The current will ____ the voltage in a parallel RCL circuit in which R = 30 , X C = 50  and X L = 75 . In a series RCL circuit, V T is always ____ than V X. In a series RCL circuit, if X L is ____ than X C, then I leads V. In a parallel RCL circuit, the ____ current can be less than the ____ current or the _____ current. Z = ____ for a parallel RCL circuit in which R = 20 , X C = 30  and X L = 60 . 19  total capacitor inductor lag lead greater less 13 - 22

24. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Review Repeat Segment X L and X C are 180  out-of-phase. V L and V C are 180  out-of-phase in series RCL circuits. Either (or both) X L and X C can be > Z in series RCL circuits. I L and I C are 180  out-of-phase in parallel RCL circuits. 13 - 23

25. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Preview A circuit is resonant when X L equals X C. (Page 355) Many LC combinations can be resonant at the same frequency. (Page 356) Selectivity is determined by bandwidth. (Page 360) Q and BW are inversely proportional. (Page 361) Both low-pass and high-pass filters can be either RC or RL circuits. (Page 364) 13 - 24

26. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Resonant Circuits (Page 000) Resonance occurs when X L equals X C. There is only one resonant frequency for each LC combination. However, an infinite number of LC combinations have the same f r. frfr Frequency Reactance XL3XL3 XL2XL2 XL1XL1 XC3XC3 XC1XC1 XC2XC2 L1 and C3 are resonant at f r2. f r2 13 - 25

27. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Frequency Impedance or Current Effects Of Q On The BW Of Resonant Circuits BW Response curveand BWfor a high-Q circuit. The curve plots I for series circuits and Z for parallel circuits. 0.707 A low-Q circuit has a flatter curveand a wider bandwidth. A high-Q produces a narrow BW and good selectivity. (Page 000) 13 - 26

28. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Low-Pass Filters (Page 364) Frequency V output X C decreases as f increases. Thus, less V develops across C as f increases. Multiple- frequency input Output voltage Multiple- frequency input Output voltage Frequency V output X L increases as f increases. Thus, more V develops across L as f increases. 13 - 27

29. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. High-Pass Filters (Page 365) Frequency V output X C decreases as f increases. Thus, less V develops across C as f increases. Frequency V output X L increases as f increases. Thus, more V develops across L as f increases. Multiple- frequency input Output voltage Multiple- frequency input Output voltage 13 - 28

30. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Resonance and Filters Quiz A given value of inductance and capacitance produces ____ value(s) of resonant frequency(ies). A circuit is ____ when the inductive reactance is equal to the capacitive reactance. The ____ the Q, the wider the BW of the circuit. The ____ the bandwidth, the more selective the circuit. An RC filter with the output taken across the capacitor is a ____ pass filter. An RL filter with the output taken across the inductor is a ____ pass filter. one resonant lower narrower low- high- 13 - 29

31. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. Concept Review Repeat Segment A circuit is resonant when X L equals X C. Many LC combinations can be resonant at the same frequency. Selectivity is determined by bandwidth. Q and BW are inversely proportional. Both low-pass and high-pass filters can be either RC or RL circuits. 13 - 30

32. McGraw-Hill © 2013 The McGraw-Hill Companies Inc. All rights reserved. REVIEW RC, RL, and RCL Circuits Resonance Quality Bandwidth Filters 13 - 31