102lect13_handout - Physics 102 Lecture 13 AC Circuit...

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Physics 102: Lecture 13, Slide 1 AC Circuit Phasors Physics 102: Lecture 13 •I = I max sin(2 π ft) •V R = I max R sin(2 π ft) V R in phase with I C = I max X C sin(2 π ft- π/2 ) •V C lags I L = I max X L sin(2 π ft+ π/2 ) •V L leads I I t V L V C V R L R C
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Physics 102: Lecture 13, Slide 2 Peak & RMS values in AC Circuits (REVIEW) L R C When asking about RMS or Maximum values relatively simple expressions ܥ ܮ V R, max = I max R V C, max = I max X C V L, max = I max X L
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Physics 102: Lecture 13, Slide 3 Time Dependence in AC Circuits Write down Kirchoff’s Loop Equation: V gen (t) = V L (t) + V R (t) + V C (t) at every instant of time L R C However … V gen,max V L,max +V R,max +V C,max Maximum reached at different times for R, L, C I t V L V C V R We solve this using phasors V gen
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Physics 102: Lecture 13, Slide 4 I = I max sin(2 π ft ) ( θ = 2 π ft ) V L = I max X L sin(2 π ft + π/2 ) V R = I max R sin(2 π ft ) V C = I max X C sin(2 π ft π/2 ) Graphical representation of voltages θ+π/2 I max X L θ I max R θ−π/2 I max X C L R C
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Physics 102: Lecture 13, Slide 5 Drawing Phasor Diagrams V L,max (2) Inductor vector: upwards Length given by V L,max (or X L ) V C,max (3) Capacitor vector: downwards Length given by V C,max (or X C ) V R,max (1) Resistor vector: to the right Length given by V R,max (or R) V C (t) V R (t) V L (t) (5) Rotate entire thing counter-clockwise Vertical components give instantaneous voltage across R, C, L (4) Generator vector (coming soon)
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Physics 102: Lecture 13, Slide 6 Phasor Diagrams •I = I max sin(2 π ft) •V R = I max R sin(2 π ft) I max R sin(2 π ft) C = I max X C sin(2 π ft– π/2 ) = –I max X C cos(2 π ft) L = I max X L sin(2 π ft + π/2 ) = I max X L cos(2 π ft) I
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This note was uploaded on 02/05/2012 for the course PHYS 102 taught by Professor Carruba during the Spring '09 term at University of Illinois at Urbana–Champaign.

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102lect13_handout - Physics 102 Lecture 13 AC Circuit...

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