W9_parallel_resonance.eps
Week 9: Alternating Current Circuits 319 In the figure above, the capacitorCon the left is initially charged up to chargeQ 0. At ...
320 Week 9: Alternating Current Circuits +Q C S L R Figure 122: UndrivenLRCcircuit where I=−dQ dt (713) If we substitute this re ...
Week 9: Alternating Current Circuits 321 To go on, we need to introduce a classical harmonic oscillating voltagelike that produc ...
322 Week 9: Alternating Current Circuits We observe in this result a quantity that behaves like the “resistance” of the capacito ...
Week 9: Alternating Current Circuits 323 with a peak current given by: I 0 = V 0 ωL = V 0 χL (733) We see that the current isπ/ ...
324 Week 9: Alternating Current Circuits The remaining particular solutionQp(t) is therefore called thesteady statepart of the s ...
Week 9: Alternating Current Circuits 325 R Z φ χL− χC Figure 128: The impedance diagram for theLRCcircuit. so that I 0 = V 0 Z ( ...
326 Week 9: Alternating Current Circuits Again we don’t much care about the peak values, but the averages are important. The tim ...
Week 9: Alternating Current Circuits 327 Next, let’s factor the power into a slightly more convenient form: Pav = Vrms^2 R R^2 + ...
328 Week 9: Alternating Current Circuits In a later section we’ll see at least one or two places one canusean seriesLRCcircuit t ...
Week 9: Alternating Current Circuits 329 ωt Vo Vo Vo φ Vo Z χL χC R I(t) Figure 131: A phasor diagram for the parallelLRCcircuit ...
330 Week 9: Alternating Current Circuits Far from resonance on either side, eitherχCorχLwill be verysmall– in particular much le ...
Week 9: Alternating Current Circuits 331 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 Power in R ω Resonance of Parallel LRC Circuit R = 10R ...
332 Week 9: Alternating Current Circuits -1 0 2 4 6 8 10 -0.5 0 0.5 1 t carrier (^00246810) 1 2 3 4 t signal -4 0 2 4 6 8 10 -2 ...
Week 9: Alternating Current Circuits 333 r L C R V(t) sin( t)ωo diode (crystal) Figure 135: A very simple, idealized crystal rad ...
334 Week 9: Alternating Current Circuits Figure 136: A full-wave rectifier made out of four diodes. The “headphones” are the res ...
Week 9: Alternating Current Circuits 335 adding theMaxwell Displacement Currentto Ampere’s (broken) Law. When we do, we will dis ...
336 Week 9: Alternating Current Circuits Homework for Week 9 Problem 1. Physics Concepts Make this week’s physics concepts summa ...
Week 9: Alternating Current Circuits 337 high frequency pulses while maintaining a steadyDCvoltage across the fully charged capa ...
338 Week 9: Alternating Current Circuits We wish to evaluate theQ-factorfor this resonant circuit, as this is an important desig ...
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