Lecture 22 preview mar27

# Lecture 22 preview - Lecture 22 Oscillating emf transformers and simple AC circuits Today begin Ch 31 on AC circuits Tuesday I P and resonance in

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Lecture 22 Oscillating emf, transformers, and simple AC circuits Today: begin Ch 31 on AC circuits Tuesday: I, P, and resonance in driven LCR Thursday: EM waves, ( and exam #3)

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The LCR circuit 0 1 0 0 2 2 2 2 = + + = + + - = = - - + Q LC dt dQ L R dt Q d or dt Q d L dt dQ R C Q dt dQ i and dt di L iR C Q L +Q -Q i Take a CCW walk around Kirchhoff’s loop: R Add in just a little R (under-damped): The oscillations get gradually smaller 2 2 2 0 4 1 ' ), ' cos( ) ( L R LC t e Q t q t L R - = + = - ϖ ϕ “ring down effect”
Highly Damped LCR No oscillations when LC L R 1 2 But we can force the LCR circuit to oscillate by driving the circuit with a oscillating emf. Our primary goal in ch 31 is to understand the (series) LCR driven by a sinusoidal emf. Like a pendulum in thick molasses Like a car with new shock absorbers

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Oscillating emf, an AC power source ξ(t) = ξ max cos(ωt) or ξ max sin(ωt) or ξ max cos(ωt + φ) You control the amplitude and frequency 2 ) ( 2 ) ( 0 ) ( ) cos( ) ( 2 2 m ave m ave rec ave m t t t t t ξ π ϖ = < = < = < = V ξ m ξ m cos(ωt) Phasor representation rectified
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## This note was uploaded on 04/04/2008 for the course PHYSICS 240 taught by Professor Davewinn during the Spring '08 term at University of Michigan.

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Lecture 22 preview - Lecture 22 Oscillating emf transformers and simple AC circuits Today begin Ch 31 on AC circuits Tuesday I P and resonance in

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