lecture13 - AC Circuit Phasors Physics 102: Lecture 13 I =...

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Unformatted text preview: AC Circuit Phasors Physics 102: Lecture 13 I = I max sin(2 ft) V R = I max R sin(2 ft) V R in phase with I V C = I max X C sin(2 ft- /2 ) V C lags I V L = I max X L sin(2 ft+ /2 ) V L leads I I t V L V C V R L R C Peak & RMS values in AC Circuits (REVIEW) L R C 5 ,max max C C V I X = ,max max R V I R = ,max max L L V I X = When asking about RMS or Maximum values relatively simple expressions 1 C X C = L X L = Time Dependence in AC Circuits Write down Kirchoffs Loop Equation: V G (t) = V L (t) + V R (t) + V C (t) at every instant of time L R C 5 However V G,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 Here is a problem that we will now learn how to solve: An AC circuit with R= 2 , C = 15 mF, and L = 30 mH is driven by a generator with voltage V(t)=2.5 sin(8 t) Volts. Calculate the maximum current in the circuit, and the phase angle. L R C 41 A reminder about sines and cosines Recall: y coordinates of endpoints are a sin( + /2) a sin( ) a sin( - /2) + / 2 -/2 a a a x y I = I max sin(2 ft ) ( = 2 ft ) V L = I max X L sin(2 ft + /2 ) V R = I max R sin(2 ft ) V C = I max X C sin(2 ft- /2 ) Graphical representation of voltages + /2 I max X L I max R -/2 I max X C L R C Phasor Diagrams: A Detailed Example I = I max sin(2 ft) V R = V R,max sin(2 ft) /6 V R,max sin( /6 ) t = 1 f=1/12 2 ft = /6 Length of vector = V max across that component Vertical component = instantaneous value of V 10 V R , m a x /3 Phasor Diagrams V R,max sin( /3 ) t = 2 2 ft = /3 V R , m a x I = I max sin( /3) V R = V R,max sin( /3) Length of vector = V max across that component Vertical component = instantaneous value of V Phasor Diagrams...
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This note was uploaded on 01/25/2012 for the course PHYS 102 taught by Professor Lee during the Spring '08 term at University of Illinois, Urbana Champaign.

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lecture13 - AC Circuit Phasors Physics 102: Lecture 13 I =...

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