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Download November 5th Chapter 33 RLC Circuits
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November 5th Chapter 33 RLC Circuits What’s up for the rest of the term ! (A9) C33 – RLC circuits ! (A10) C34 – Electromagnetic (EM) waves ! (A11) C35 – Optics and images with EM waves ! (A12) C36 – Interference of EM waves C37 – Diffraction of EM waves Summary of Forced Oscillations Element Resistor Reactance/ Resistance R Phase of Phase Amplitude Current angle φ Relation In phase 0° VR=IRR Capacitor XC= 1/ωdC Leads vC (ICE) Inductor XL=ωdL Lags vL (ELI) ! -90° VC=ICXC +90° VL=ILXL ELI (positively) is the ICE man ! ! ! Voltage or emf (E) before current (I) in an inductor (L) Phase constant φ is positive for an inductor Current (I) before voltage or emf (E) in capacitor (C) RLC circuits I= ε m 1 R + ( ωd L − ωd C 2 ! ! ) 2 Current is largest when Or 1 ωd L − =0 ωd C ωd = 1 =ω LC ω is also called the resonance frequency (in the homework) ω =ω d = 2π f d AC circuits ! ! ! ! RLC circuit – resistor, capacitor and inductor in series Apply alternating emf ε =ε m sin ω d t Elements are in series so same current is driven through each i = I sin ω t − φ d From the loop rule, at any time t, the sum of the voltages across the elements must = vR + vC + vL equal the applied emf ( ε ) AC circuits - Equations ε ! = IZ m Define impedance, Z to be Z = R + (X L − XC ) 2 ! XL − XC tan φ = R Resonant frequency – natural freq = driving freq ω =ω d = 2π f d where 2 X L = ωd L 1 XC = ωd C AC circuit Examples AC circuits ! Instantaneous rate which energy is dissipated (power) in a resistor is 2 P=i R ! But i = I sin(ωd t − φ ) P = I R sin (ωd t − φ ) 2 ! 2 Want average (rms) rate ! Average over complete cycle T 〈sin θ 〉 = 1 2 2 AC circuits ! For alternating current circuits define rootmean-square or rms values for i, V and emf I V I rms = V rms = rms = 2 2 2 ε ! ! Ammeters, voltmeters - give rms values The average (rms) power dissipated by resistor in an ac circuit is 2 Prms ! ε 2 I R I = = R 2 2 (Called Pave in the book) Prms = I 2 rms R AC circuits ! If ac circuit has only resistive load Z=R (e.g. at the resonance frequency) Prms = ε rms I rms ! Trade-off between current and voltage ! ! ! For general use want low voltage Means high current but rms P =I 2 rms R General energy transmission rule: Transmit at the highest possible voltage and the lowest possible current AC circuits ! Transformer – device used to raise (for transmission) and lower (for use) the ac voltage in a circuit, keeping iV constant ! Has 2 coils (primary and secondary) wound on same iron core with different #s of turns AC circuits Alternating primary current induces alternating magnetic flux in iron core ! Same core in both coils so induced flux also goes through the secondary coil ! Using Faraday’s law dΦ B dΦ B VP = − N P VS = − N S dt dt ! VP VS = NP NS AC circuits ! Transformation of voltage is NS VS = VP NP ! ! If NS > NP called a step-up transformer If NS < NP called a step-down transformer AC circuits ! Conservation of energy I PVP = I SVS VP NP IS = IP = IP VS NS AC circuits ! The current IP appears in primary circuit due to R in secondary circuit. I S = VS / R I PVP = I SVS 2 VS VS 1 V 1 NS V P = IP = V P = R VP RV R NP 2 S 2 P ! Has for of IP = VP/Req where 2 R eq NP R = NS