Lect20 - I t I max sin t I max t Actual current I(t) is the...

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Unformatted text preview: I t I max sin t I max t Actual current I(t) is the projection of the "phasor" onto the y-axis at time t. VR I t IR VR RI max sin Vmax R I max t Vmax t I t I max sin t L VL dI L dt LI max cos t Inductor phasor I max t VL max LI max VL max LI max X L I max 90o Inductive "reactance" I t I max sin Q C VC t I t C VC , dQ dt I max cos C 90o I max t VC max I max C X C I max $ $ $ $ ! " % " # " & $ $ & ' " ! ' " "# " " ) $1 ) #& * + % )$ & " " ) " " ) "# & % && R ," ). /. $ $. & * &# " & " & " "# " % 0 & & " " ( ) " *" & " "" + 1 ' * " + VR VC VL VC $ If phasors satisfy Khirchoff's Law, then so will their projections. VL VL VR VC VR The projections are the actual voltages. 2 $ VR VC VL $ max VL VR max $ VC $ $ max 3 $ ) " " % " " + max $ VR VC VL 4 5 $. $ ! max I max Z 4 5 $. Define total circuit impedance Z( ) max = 6 4 5 $. 7 $ $ $ $ max max 6 6 5 $. max 8 7 $ max max $ ' " : " & " max A B C 9 $ ' " % : " & " max A B C ; $ ' " 1 $< 8= 1 1 > 8 $< 8= 1 max A B C D % & " $ ' " A B C ( $ ' " % A B C 2 $ ' " A B C 3 $ $" ) 9 & ' " B + "# " " " " " *" & % ; " " $ " + $ " * A 1 $ # " - C " ? $" @ @ 1 1 ) *" " *" & & #" & #" + " % ? @ @ @ & < < < ) " & $ 6 " & " ! $ $" ) 9 & ' " B + "# $ " $ " + $ " * A " *" & % ; " 1 $ " # - C $" 4) . # $ 4$. #" @ $ D $ 4/ . 7 E " $ 4:. = " *" & " & # " #" " ?1 4 $ $ "# . $ $ $" ) 9 & ' " B + "# " " *" & % ; " " $ " + $ " * A 1 $ # - C B 6 4) . 2 + ' 2 " 4/ . ' "# 4$. 9 + ' ; C 4:. + ' Vmax Z I max 100V 2mA 50k $ $" ) 9 & ' " B + "# " " *" & % ; " " $ " + $ " * A 1 $ 6 # C ' 4; . + 2 2 " 4; . + 2 2 + ' B C 2 4) . 2 + ' ?: # " 4/ . ' 4$. 9 + ' ; & 4:. cos(45) 6 ' 4 $5 . R Z 6 " 4; ' 9 + ' ; ". + 2 2 $ $" ) 9 & ' " B 2 4) . 2 + ' B & 7 + "# " ; 4$. 9 + ' " *" & % ; " " $ " + $ " * A 1 $ 6 # C ' 9 +' ; 4/ . ' 4:. + ' XC R XL tan 45 1 B $ 5 $ C $ 6 4 $5 . $ (+ ' @9 + ' ; XC 113 56.5k 2 9 ...
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This document was uploaded on 03/08/2012.

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