Lect13 handout

AC Circuit Phasors Physics 102: Lecture 13 ,[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

Peak & RMS values in AC Circuits (REVIEW) When asking about RMS or Maximum values relatively simple expressions V R, max = I max R V C, max = I max X C V L, max = I max X L L R C

Time Dependence in AC Circuits ,[object Object],[object Object],[object Object],[object Object],[object Object],I t V L V C V R We solve this using phasors V gen L R C

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  I max X L  I max R  I max X C L R C

Drawing Phasor Diagrams (4) Generator vector (coming soon) V L,max ,[object Object],[object Object],V C,max ,[object Object],[object Object],V R,max ,[object Object],[object Object],V C (t) V R (t) V L (t) ,[object Object],[object Object]

Phasor Diagrams ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Voltage across resistor is always in phase with current! Voltage across capacitor always lags current! Voltage across inductor always leads current! Instantaneous Values: I max R I max R sin(2  ft) I max X L cos(2  ft) -I max X C cos(2  ft) I max X L I max X C

Phasor Diagram Practice ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],V L V C V R Inductor Leads Capacitor Lags R: It has largest vertical component Decreasing, spins counter clockwise Inductor, it has longest line. Example

Kirchhoff: generator voltage ,[object Object],V L,max -V C,max V L,max =I max X L V C,max =I max X C V R,max =I max R V gen,max =I max Z  V gen (t) = V R (t) +V C (t) +V L (t) Define impedance Z: V gen,max ≡ I max Z “ Impedance Triangle” “ phase angle”

Phase angle  I = I max sin(2  ft ) V gen = I max Z sin(2  ft +  )  is positive in this particular case. 2  ft I max I max Z 2  ft + 

Drawing Phasor Diagrams V C V R V L ,[object Object],[object Object],V L,max ,[object Object],[object Object],V C,max ,[object Object],[object Object],V R,max ,[object Object],[object Object],[object Object],[object Object],V gen,max V gen

ACTS 13.1, 13.2, 13.3 When does V gen = V R ? When does V gen = 0 ? The phase angle is: (1) positive (2) negative (3) zero? time 1 time 2 time 3 time 4

Problem Time! ,[object Object],I max = 2.5/2.76 = .91 Amps I max = V gen,max /Z Example L R C

ACT: Voltage Phasor Diagram At this instant, the voltage across the generator is maximum. What is the voltage across the resistor at this instant? 1) V R = I max R 2) V R = I max R sin(  ) 3) V R = I max R cos(  ) I max X L I max X C I max R V gen,max 

Resonance and the Impedance Triangle R (X L -X C ) Z  X L and X C point opposite. When adding, they tend to cancel! When X L = X C they completely cancel and Z = R. This is resonance! V max,gen = I max Z I max (X L -X C ) I max X L I max X C I max R V gen,max  L R C

Resonance R is independent of f R X L increases with f X L X C decreases with f X C Z : X L and X C subtract Z X C = 1/(2  fC ) X L = 2  fL Resonance: X L = X C f 0 Z is minimum at resonance frequency!

Resonance R is independent of f X L increases with f X C decreases with f Z : X L and X C subtract Z X C = 1/(2  fC ) X L = 2  fL Resonance: X L = X C Current I max = V gen,max /Z f 0 Current is maximum at resonance frequency!

ACT: Resonance ,[object Object],[object Object],[object Object],[object Object],[object Object],L R C

Summary of Resonance ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],I max (X L -X C ) I max X L I max X C I max R V gen,max 

Power in AC circuits ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

AC Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Lect13 handout

Recommandé

Recommandé

Contenu connexe

Tendances

Tendances (20)

Similaire à Lect13 handout

Similaire à Lect13 handout (20)

Plus de oyunbileg06

Plus de oyunbileg06 (20)

Dernier

Dernier (20)

Lect13 handout

Notes de l'éditeur