Time Domain to Phasor Domain (Linear Transformation)

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Presentation transcript:

Time Domain to Phasor Domain (Linear Transformation) Sources 150 cos(377t + 20o) V 150 /20o V Resistors 20  20 /0o  Inductors 50 mH  (5010-3) /90o  Capacitors 100 F 1/[ (10010-6)] /90o  In a DC circuit, inductors act like a short circuit. In a DC circuit, capacitors act like an open circuit.

AC Circuits 1/(jC) = 20 /90o v(t) = 10 cos (200t + 10o) 10 /10o 40 mH v(t) = 10 cos (200t + 10o) 10 /10o Find i(t) jL = 8 /90o

AC Circuits 10.6 /90o v(t) = 50 V @ 60 Hz Find vc(t) 50 /0o 40 mH v(t) = 50 V @ 60 Hz Find vc(t) 50 /0o  = 2 (60) = 377 rad/s 15.1 /90o

AC Circuits 500 /– 90o i(t) = 5 cos (2000t – 35o) 5 /– 35o 80 /90o Find v(t) and iL(t)

AC Circuits Find the equivalent (Thevenin) impedance at 1 kHz.  = 2 (1000) = 6283 rad/s R = 20 /0o L1 = 12.57 /90o L2 = 6.28 /90o C = 0.159 /– 90o