Chapter 31 lecture - Chapter 31 Oscillating emf,...

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Chapter 31 Oscillating emf, transformers, and simple AC circuits Today: begin Ch 31 on AC circuits Tuesday: I, P, and resonance in driven LCR
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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”
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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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Question #1 Why do we power our houses and factories with AC and not DC? 1. DC is more dangerous in terms of electrocution 2. AC can be transformed to higher or lower voltages 3. AC current does not drain electrons like DC 4. DC does not work well at low voltages 5. People trusted Thomas Edison more than George Westinghouse
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Transformers ξ p s s p p s s s s p p s s p p N N V or V N N V and N V dt d N V hence dt d N V dt d N V = = = Φ = Φ - = Φ - = = , 100 years ago AC (Westinghouse) beat out DC (Edison) as the US power standard, primarily because AC voltages can be easily transformed up and down. ξ(t) p s p p s p s s s p p I N N I V V I thus V I V I = = = Energy conservation The “turns ratio” N s /N p is the important parameter here. DEMO
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Question 2 Transformers are often made of laminated iron sheets rather than a solid block of iron because: 1. this increases magnetic permeability 2. eddy currents are reduced 3. the transformer can run hotter 4. it is easier to build
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Chapter 31 lecture - Chapter 31 Oscillating emf,...

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