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Lecture 11 Electromagnetic Oscillations and Alternating Current Ch. 31 • Topics – – – – – – – Transformers LC Circuit Qualitatively Electrical and Magnetic energy oscillations Alternating current Pure R and L circuits Series RLC circuit Power and Transformers • Demos • • Elmo Polling Quiz 2 • • • • Resistivity and currents Apply Kirchhoff Laws to circuits B fields from simple current geometries Faraday’s and Lenz’s Law. Electric fields from changing B fields • Find acceleration and velocity of partikcles in E and B fields • RL circuits What is a Generator? Coil of wire ! • " m = B ! nˆ dA ! ! = B ! dA = B cos!dA n̂ θ B d# d(BAcos $ ) d cos $ d$ !=" =" = "BA = BAsin $ dt dt dt dt d$ = BA% sin $ but $ = %t so =% dt ! = BA" sin "t ! = !m sin "t ω= 2πf and f= 60 Hz Where ω is the rotational angular frequency of the generator Driven RLC Series Circuit Series RLC • Show Generator voltage vs time on scope. •Vary frequency • Show voltage across resistor compared to signal voltage •How is signal voltage related to voltage across resistor •Vary frequency - ELI the ICE man • Show voltage across inductor compared to resistor. •Voltage across resistor is in phase with current through resistor • Does voltage across inductor lead or lag the current • Show voltage across capacitor compared to resistor. •Voltage across resistor is in phase with current through resistor • Does voltage across the capacitor lead or lag the current • Show phase angle is related to impedance in circuit and is frequency dependent • Show resonance by varying frequency. • Need table of numbers for some frequency and at resonance. Series LCR circuit f Hz 6.28fL 4.2mH 1/6.28fC R Z I=V/Z φ 1uF Ohms Ohms Amps Deg 100 2.7 1600 10 40 0.25 1000 27 160 10 133 2445 65.3 65.3 10 16 10 10000 270 1 #L " #C ) ! = tan "1 ( R VR Volts VL VC -89.6 .05 .05 10 0.075 -85.7 .25 1 10 10 1 0 9.0 20 -20 270 0.037 87.7 0.2 10 0.6 2.7 " 1600 ! = tan ( ) = "89.6 10 "1 Peak value Effective Power 2 rms P=I R I Irms = 2 rms=root-mean-square High Pass Filter Low Pass Filter Chapter 13 Problem 17 In an oscillating LC circuit, L = 28.0 mH and C = 7.50 µF. At time t = 0 the current is 9.50 mA, the charge on the capacitor is 3.20 µC, and the capacitor is charging. (a) What is the total energy in the circuit? (b) What is the maximum charge on the capacitor? (c) What is the maximum current? (d) If the charge on the capacitor is given by q = Q cos(ωt + ϕ), what is the phase angle ϕ? (e) Suppose the data are the same, except that the capacitor is discharging at t = 0. What then is ϕ? Chapter 31 Problem 21 In an oscillating LC circuit with C = 62.0 µF, the current as a function of time is given by I = (1.10) sin(2500t + 0.670), where t is in seconds, I in amperes, and the phase angle in radians. (a) How soon after t = 0 will the current reach its maximum value? (b) What is the inductance L? (c) What is the total energy?