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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max 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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