lect18_handout

lect18_handout - Sin( $ t) Phasor " A...

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Physics 202, Lecture 18 Today’s Topics ! Reminder ! RL Circuits ! RC Circuits ! LC (RLC) Circuits and Electromagnetic Oscillations ! AC Circuits with AC Source ! Phasors Turn on RL Circuit (reminder) Note: the time constant is ! =L/R I = V 0 R (1 " e " t L / R ) Turn off RL Circuit (reminder) Note: the time constant is ! =L/R I = I 0 e " t L / R Charging a Capacitor in RC Circuit Charging Note: ! " RC is called time constant
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Discharging a Capacitor in RC Circuit discharging I ( t ) = " Q RC e " t / RC Note the time constant ! = RC q ( t ) / C + R dq ( t ) dt = 0 Demo: RC Circuit Light Bulb r LC Circuit and Oscillation " Exercise: Find the oscillation frequency of a LC circuit ! ! " eq. of Harmonic Oscillation Total Energy is conserved I AC Power Source " # V = # V max Sin( $ t+ % 0 ) = # V max Sin( $ t) Initial phase, usually set % 0 =0 T=2 / $ $ : angular frequency $ = 2 f t=0
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AC Circuit " Find out current i and voltage difference # V R , # V L , # V C . Notes: Kirchhoff’s rules still apply ! A technique called phasor analysis is convenient. i # V max
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Unformatted text preview: Sin( $ t) Phasor " A sinusoidal function y = A sin % can be represented graphically as a phasor vector with length A and angle % (w.r.t. to horizontal) % A sin % Resistors in an AC Circuit " Ohms Law: # V= I R at any time i i R = # V/R=I max sin $ t, I max = # V max /R # The current through an resistor is in phase with the voltage across it Phasor view Function view Inductors in an AC Circuit " # V - Ldi/dt =0 " i L =I max sin( $ t-& /2) I max = # V max / X L , X L = $ L ! inductive reactance # The current through an inductor is 90 o behind the voltage across it. Phasor view Function view i Capacitors in an AC Circuit " # V - q/C=0, dq/dt =i i " i L =I max sin( $ t+ & /2) I max = # V max / X C , X C = 1/( $ C) ! capacitive reactance # The current through a capacitor is 90 o ahead of the voltage across it. Phasor view Function view...
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lect18_handout - Sin( $ t) Phasor " A...

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