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AC Circuits Physics 102:  Lecture 12 L R C
Review:  Generators  and EMF v v • x  r ,[object Object],[object Object],[object Object],t 1 2 Frequency = How fast its spinning Amplitude = Maximum voltage Voltage across generator:  20  V max -V max
AC Source  ,[object Object],[object Object],[object Object],[object Object],0.25 0.5 2  f t = 8  t f = 4 Hz T=(1/4)seconds/cycle Example +24 -24 RMS: Root Mean Square  V rms =V max / √ 2
RMS? ,[object Object],RMS: Root Mean Square  V rms =V max / √ 2 +V max -V max V max 2 Square: V max 2  / 2 Mean: square Root: V max   / √2
Preflight 12.1, 12.2 ,[object Object],[object Object],[object Object],Well…  We know that the maximum value  sine is 1. So the maximum current is 10! I max  = 10 A Just like  V rms =V max /√2  … I rms =I max /√2 =10/ √ 2 A =  7.07 A L R C
Resistors in AC circuit ,[object Object],[object Object],R ,[object Object],[object Object],I t t V R Frequency Resistance (R) Frequency  does not  affect Resistance!
C Capacitors in AC circuit ,[object Object],[object Object],[object Object],I t ,[object Object],[object Object],t V C Frequency Reactance (X C ) Frequency  does  affect Reactance!
Inductors in AC circuit L ,[object Object],[object Object],[object Object],I t ,[object Object],[object Object],t V L Frequency Reactance (X L ) Frequency  does  affect Reactance!
ACT/Preflight 12.4, 12.5 ,[object Object],[object Object],[object Object],The  inductor  can be ignored when… (a)   frequency is very large (b) frequency is very small L R C
AC Circuit Voltages ,[object Object],[object Object],= 0.5    2 = 1 Volt = 0.5    1/(8  0.015) = 1.33 Volts = 0.5    8  0.03 = 0.38 Volts V C,max  = I max  X C V L,max  = I max  X L Example L R C
ACT: AC Circuit Voltages ,[object Object],Now the frequency is  increased  so I(t) = 0.5 sin(16  t).  Which element’s maximum voltage  decreases? 1) V R,max 2) V C,max 3) V L,max L R C
Summary so far… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],I t V L V C V R L R C
Kirchhoff: generator voltage ,[object Object],[object Object],[object Object],[object Object],[object Object],We solve this using  phasors V gen L R C I t V L V C V R
A reminder about sines and cosines ,[object Object],[object Object],[object Object],[object Object],x y    a a a
I  = I max sin(2  ft )  (   = 2  ft ) V L  = I max X L   sin(2  ft  +   )   V R  = I max R  sin(2  ft ) V C  = I max X C  sin(2  ft  –   ) Graphical representation of voltages L R C  I max X L  I max R  I max X C
Phasor Diagrams:  A Detailed Example ,[object Object],[object Object], V R,max sin(  ) t = 1  f=1/12 2  ft =   /6 Length of vector = V max  across that component Vertical component = instantaneous value of V V R,max
Phasor Diagrams ,[object Object],[object Object], V R,max sin(  ) t = 2 2  ft =   /3 Length of vector = V max  across that component Vertical component = instantaneous value of V V R,max
Phasor Diagrams ,[object Object],[object Object], V R,max sin(  )=V 0 t = 3 2  ft =   /2 Length of vector = V max  across that component Vertical component = instantaneous value of V V R,max
Phasor Diagrams ,[object Object],[object Object], V R,max sin(4  ) t = 4 2  ft = 4  /6 V R,max Length of vector = V max  across that component Vertical component = instantaneous value of V
Phasor Diagrams ,[object Object],[object Object], t = 6 2  ft =   V R,max sin(  )=0 Length of vector = V max  across that component Vertical component = instantaneous value of V V R,max
Phasor Diagrams ,[object Object],[object Object], V R,max sin(8  ) t = 8 2  ft = 8  V R,max Length of vector = V max  across that component Vertical component = instantaneous value of V
Phasor Diagrams ,[object Object],[object Object], V R,max sin(10  ) t = 10 2  ft = 10  V R,max Length of vector = V max  across that component Vertical component = instantaneous value of V
AC circuit summary ,[object Object],[object Object],[object Object],I t V L V C V R Kirchoff’s Loop Equation always holds true: V gen  = V L  + V R  + V C  ,[object Object],[object Object],Phasors  represent  instantaneous voltages L R C

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Lect12 handout

  • 1. AC Circuits Physics 102: Lecture 12 L R C
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  • 15. I = I max sin(2  ft ) (  = 2  ft ) V L = I max X L sin(2  ft +  ) V R = I max R sin(2  ft ) V C = I max X C sin(2  ft –  ) Graphical representation of voltages L R C  I max X L  I max R  I max X C
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Notes de l'éditeur

  1. 1
  2. Ave V = 0 Ave V^2: Vmax/2
  3. Ave V = 0 Ave V^2: Vmax/2
  4. 85% and 78% correct respectively
  5. Changing voltage tries to charge/discharge capacitor. Low frequency limit: open circuit High frequency limit: closed circuit (capacitor never has time to build up charge) Lag: charge (voltage drop) lags behind current.
  6. Low frequency: no voltage drop…nothing is changing High frequency: large rate of change of current implies large emf (as per Faraday) Voltage leads current. (rate is initially large, current then grows as rate drops)
  7. “ can be ignored” means “behaves like a wire”…no voltage drop
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  9. 1 whole system rotates, theta=2pi*ft
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  11. Phasor Animation
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