1 / 48

Electromagnetism

Electromagnetism. Zhu Jiongming Department of Physics Shanghai Teachers University. Electromagnetism. Chapter 1 Electric Field Chapter 2 Conductors Chapter 3 Dielectrics Chapter 4 Direct-Current Circuits Chapter 5 Magnetic Field Chapter 6 Electromagnetic Induction

isaac-rogers
Download Presentation

Electromagnetism

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Electromagnetism Zhu Jiongming Department of Physics Shanghai Teachers University

  2. Electromagnetism • Chapter 1 Electric Field • Chapter 2 Conductors • Chapter 3 Dielectrics • Chapter 4 Direct-Current Circuits • Chapter 5 Magnetic Field • Chapter 6 Electromagnetic Induction • Chapter 7 Magnetic Materials • Chapter 8Alternating Current • Chapter 9 Electromagnetic Waves

  3. Chapter 8 Alternating Current • §1. Alternating Current • §2. Three Simple Circuits • §3. Complex Number and Phasor • §4. Complex Impedance • §5. Power and Power Factor • §6. Resonance

  4. i Im o t §1. Alternating Current • Steady current：magnitude and direction not changing magnitude varying ，not reversing Alternating current Varying current • Sinusoidal current：i = Imcos (  t + ) , u ,  • Three important quantities： • Amplitude Im • （or rms I = Im/ ） • Angular frequency  • （ = 2 /T = 2f ） • Initial phase  • （ phase  t + ）

  5. Alternating Current • Features of sinusoidal quantities： • derivative and integral are still sinusoidal • any periodic quantities can expand as a sum of sinusoidal functions with different frequency • Denotation： • instantaneous：little case i , u • rms： capital I , U • amplitude： subscript mIm, Um • ( rms：root-mean-square )

  6. §2. Three Simple Circuits • 1. Introduction • 2. Pure Resistance • 3. Pure Capacitance • 4. Pure Inductance

  7. 1. Introduction • DC R act on current • L short circuit（ideal，no resistance） • C open circuit（ideal，no current） • AC R、L、C all act on current • L self-induced emf • C charge/discharge • Relationship between i and u • i = Imcos (  t + i) • u = Umcos (  t + u) To study： (1) U / I = ? Ratio of rms (2) u- i = ? Difference of phase

  8. i u R u i t 0 2. Pure Resistance • u(t) = i(t) R • or •  U = I R u = i • or U / I = R u - i = 0

  9. C i u u t 0 i 3. Pure Capacitance • Left plate q = Cu •  I = UCi = u +  / 2 • or U / I = 1/C u - i = -  / 2 • Capacitive reactance：XC= 1/C Pure Capacitance ：current leads voltage by  / 2

  10. L u i 自 u i t 0 4. Pure Inductance • L acts as an emf u(t) = -S(t) •  U = LIu = i +  / 2 • or U / I = L u - i =  / 2 • Inductive reactance ：XL= L Pure Inductance ：current lags voltage by  / 2

  11. Exercises • p.361 / 8 - 2 - 1, 2, 3

  12. §3. Complex Number and Phasor • 1. Complex Numbers • Expressions • Calculations • 2. Complex Number Method • 3. Phasors • 4. Complex Form of Relations between u and i • Pure Resistance • Pure Capacitance • Pure Inductance 5. Examples

  13. a = Re() b = Im() +j (a,b) b r +1 0 a Expressions of Complex Numbers • Algebraic：= a + jb • Phasor：r = |  | modulus • a = r cos • b = r sin  • Trigonometric：  = r cos + j rsin • Exponential：  = r ej • （ Euler formula：ej = cos + j sin ）

  14. Calculations of Complex Numbers • Addition/Subtraction： • 1 2 = ( a1 a2 )+ j ( b1  b2 ) • （ parallelogram rule） • Multiplication： • Division：

  15. 2. Complex Number Method • Instantaneous：i = Imcos ( t + ) = Re[ Ime j ( t + ) ] • where Ime j ( t + ) • Complex rms • Definition： • Information：rms, initial phase • Steps ofcalculation： • i, u  calculating result of  of i, u • real complex take real part • 4 theorems：（ Next page ）

  16. Four Theorems • Complex rms of (ki)（ k any real constant） • Complex rms of( i1 i2 ) • Complex rms of di/dt • Complex rms of idt • Pro.： i = Imcos ( t + ) • di/dt = Imcos ( t +  + /2 ) •  complex rms of di/dt = I e j e j/2 •  idt = (1/)Imcos ( t +  - /2 ) •  complex rms of idt = I e j e -j/2 /

  17. +j +1 0 3. Phasors • complex rms phasor • length = I（rms） • angle = （phase）  • parallelogram rule • complex rms of di/dt •  times of length，rotate counterclockwise /2 • complex rms of idt • 1/ times of length，rotate clockwise /2

  18. 4. Complex Form of u , i Relations • Pure Resistance • Pure Capacitance • Pure Inductance

  19. i u R 0 Pure Resistance • Instantaneous： u = i R • Complex rms： • or •  U = I R • u = i

  20. C i u 0 Pure Capacitance • Instantaneous： or • Complex rms ： • or • U = I /C u = i-  / 2 • Acturely, 1/jC includes all information • about relationship between u and i • （ ratio of rms and difference of phase） • Complex capacitive reactance：- j XC= - j /C

  21. L u i 自 0 Pure Inductance • Instantaneous ： • Complex rms ： • or •  U = LI • u = i +  / 2 • Complex inductive reactance：j XL= jL

  22. i u1 R +j u u2 L +1 0 L R Example 1 （p.330/[Ex.1]）(1) • Series RL circuit, relation between u and i. • Sol.：u = u1+ u2 exponential： where If i = Imcost is known, can get u = zImcos(t+) z 

  23. same phase with leads by  / 2 0  Example 1 （p.330/[Ex.1]）(2) • Phasor： • first draw • then • and U2 /U1= L/R • then • get

  24. u1 u2 R u ~ L Example 2（p.332/[Ex.2]） • Fluorescent lamp ( daylight lamp )：tube R，ballast L，in series，emf 220 V，tube U1=110 V. Find U2 of ballast. • Sol.：  U22 = U2- U12 = 220 2- 110 2 = 3  110 2 

  25. i i2 i1 u same phase with leads by  / 2 R C  0 Example 3（p.332/[Ex.3]） • RC in parallel. Find relation between i1and i2 . • Sol.：phasor • in parallel，draw first and I2 /I1 = CR i2leadsi1by  / 2

  26. 0 Example 4（p.332/[Ex.4]） • Continue Ex.3, find phase difference between i and i1 . • Sol.：I2/I1= CR • i2leads i1by /2 R = 138 k = 1.38  10 5  C= 1000 pF = 10-9 F  = 2f = 2  2000 CR 1.73   /3（ileads i1）

  27. §4. Complex Impedance • 1. Three Ideal Elements • 2. Two-Terminal Net without emf • 3. Exponential Formula and Algebraic Formula • Exponential Formula • Algebraic Formula • Impedance Triangle

  28. 1. Three Ideal Elements • Resistoru = Ri • Capacitor • Inductor • introduce ComplexImpedance Z so that • Z determined by R、L、C and ，not U、I • Z representsrelation between i and u • （ U/I andu-i）

  29. i i i2 u u i1 2. Two-Terminal Net without emf • or • Ex.1：RL in series • Ex.2：RC in parallel i = i1+i2

  30. 3. Exponential and Algebraic Formulae • Exponential Formula ：Z = ze j • z impedance —— modulus of Z •  phase constant —— angle of Z • Z representsrelations for i and u（ U/I andu-I） • Algebraic Formula ： Z = r + j x • r effective resistance > 0, not necessarily = R Ex. • x effective reactance > 0 for inductive net < 0 for capacitive net = 0 for resistive net

  31. Z +j jx +1 0 r Impedance Triangle • Z = ze j • Z = r + j x z  z x  r

  32. Complex Form of Laws • 1. Ohm’s Law • DC： U = IR U = - IR • AC： • series connection： Z = Z1 + Z2 + ··· • parallel connection： • 2. Kirchhoff’s Rules • DC：  ( I ) = 0  (  ) =  ( IR ) • AC：

  33. i2 i3 i1 C L R2 R1 A B C R3 i4 G R4 D ~ Example（p.336/[Ex.]） • Condition for balancing an AC bridge. • Sol.：uAC = uAD and or • Maxwell Bridge , for • measuring L

  34. Exercises • p.362 / 8 - 4 - 3, 5, 6, 15

  35. §5. Power and Power Factor • 1. Instantaneous Power, Average Power • and Power Factor • 2. Significance of Raising Power Factor • 3. Method to Raise Power Factor

  36. 1. Power and Power Factor • DC：P = IU keepconstant • AC：p(t) = i(t)u(t) instantaneous power • （ for AC with f = 50 Hz，average is important ） • Average power • Pure Resistance • Pure Inductance • Pure Capacitance • Two-Terminal Net without emf

  37. p P I u i 0 t T Pure Resistance • Resistance： i = Imsin t u = iR p = iu = i2R • Resistor：non-energy-storing， energy  heat

  38. p i u T 0 t External energy M Field energy Never dissipated at all！ Pure Inductance • Inductance：voltage leads current by /2 • i = Imsin t u = Umsin( t + /2) = Umcos t • 0 T/4 and T/2  3T/4： • p > 0, absorb energy and store it in M field • T/4  T/2 and 3T/4T： • p < 0, release energy, field disappear ( i： Im0 )

  39. p i u t 0 T External energy E Field energy Never dissipated at all！ Pure Capacitance • Capacitance：current leads voltage by /2 • u = Umsin t i = Imcos t • 0 T/4 and T/2  3T/4： • p > 0, absorb energy and store it in E field • T/4  T/2 and 3T/4T： • p < 0, release energy, field disappear ( u：  Um0)

  40. p u t 0 T i Two-Terminal Net without emf • u = Umsin t i = Imsin( t -) • ( Trigonometric：cos(- )- cos(+ ) = 2sin sin ） • Resistor：  = 0 P = IU • Inductor：  =  /2 P = 0 • Capacitor： =-  /2 P = 0 cos—— Power factor

  41. I R ~ Z R 2. Significance of Raising Power Factor • S = IU visual power • P = IUcos work power • Q = IUsin workless power • Lost on cable (1) voltage U’ = IR (2) power P’ = I2R • Reduce lost： • R ，thick wire，cost more • I，not decrease consumer’s power P = IUcos —— increase power factor cos • Ex.：inductive load, i lags u by   • Workless current：I Q= I sin • work current： I P= I cos

  42. i’ iC i u ’  3. Method to Raise Power Factor • Workless current：I Q= I sin • work current： I P= I cos • then P = IUcos = I PU • I Q= I sin useless to P , • but a part of total current I , • and a part of energy lost on cable P’ = I2R • increase cos to reduce I Q • inductive net add capacitace • cos’ > cos • P = IUcos = I’Ucos’

  43. Exercises • p.365 / 8 - 5 - 1, 5

  44. L C R uR uL uC u Resonance §6. Resonance • Resonance： • series RLC circuit UL = UC u and i in phase resistive UL > UC u leads i Inductive UL < UC u lags i capacitive

  45. Resonance in Series Circuit （1） • Current： • Complex impedance： Impedance： Current： Resonance： maximumcurrent： Resonance frequency of RLCcircuit： when  = 0，I = I 0 maximum ，resonance

  46. Resonance in Series Circuit （2） • Voltages： UL = IL UC = I/C • Resonance：UL0 = I00L UC0= I0/0C Let thenUL0 = QU UC0 = QU • if R << 0L， Q very large ～ 10 2（ good，bad） • UL0 = UC0 = QU > U • Quality factor：

  47. I I0 0  0 ~ ~ ~ Resonance in Series Circuit （3） • Resonance curve： • Relation for I ~  • keep R、L、C、U constant • Selectivity： • to select the wanted program • —— modulate for a radio • adjust C change • when 0 matches 1ofa signal • for example ( 0 = 1 ) • then I1 >> Ii（ i  1）

  48. Exercises • p.367 / 8 - 7 - 1

More Related