Transcript Document
Admin: • Assignment 9 is posted • 2 more AC analysis problems • RC circuits • Due Monday (May 4th) • • • • Second mid-term date is Wednesday May 6th The test will cover everything after Thevenin’s theorem Review Lecture Monday (May 4th). Any requests? Any students with accommodations can use the test center – fill out the DSS form. • Extra Office hours: • Thursday 2pm – 4pm • Monday 2pm – 4pm • Tuesday 2pm – 4pm. Copyright © 2009 Pearson Education, Inc. AC circuit 1 Find the equivalent impedance Copyright © 2009 Pearson Education, Inc. AC circuit 2 Find the current through Z3 Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations An LC circuit is a charged capacitor shorted through an inductor. Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations The charge and current both oscillate, but with different phases. . Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations The total energy in the circuit is constant; it oscillates between the capacitor and the inductor: http://en.wikipedia.org/wiki/LC_circuit#/med a/File:Tuned_circuit_animation_3.gif Copyright © 2009 Pearson Education, Inc. 30-5 LC Circuits and Electromagnetic Oscillations Many applications: Oscillators Crystal set radio tuner Tuners Resonators Filters Mixers https://www.youtube.com/wat ch?v=qAvVjGZnBrw Copyright © 2009 Pearson Education, Inc. Security tags 30-5 LC Circuits and Electromagnetic Oscillations Example 30-7: LC circuit. A 1200-pF capacitor is fully charged by a 500-V dc power supply. It is disconnected from the power supply and is connected, at t = 0, to a 75mH inductor. Determine: (a) the initial charge on the capacitor; (b) the maximum current; (c) the frequency f and period T of oscillation; (d) the total energy oscillating in the system. U Copyright © 2009 Pearson Education, Inc. 30-6 LC Oscillations with Resistance (LRC Circuit) Any real (nonsuperconducting) circuit will have resistance. Copyright © 2009 Pearson Education, Inc. 30-6 LC Oscillations with Resistance (LRC Circuit) Now the voltage drops around the circuit give The solutions to this equation are damped harmonic oscillations. The system will be underdamped for R2 < 4L/C, and overdamped for R2 > 4L/C. Critical damping will occur when R2 = 4L/C. Copyright © 2009 Pearson Education, Inc. 30-6 LC Oscillations with Resistance (LRC Circuit) This figure shows the three cases of underdamping, overdamping, and critical damping. Copyright © 2009 Pearson Education, Inc. 30-6 LC Oscillations with Resistance (LRC Circuit) The angular frequency for underdamped oscillations is given by . The charge in the circuit as a function of time is . Copyright © 2009 Pearson Education, Inc. 30-6 LC Oscillations with Resistance (LRC Circuit) Example 30-8: Damped oscillations. At t = 0, a 40-mH inductor is placed in series with a resistance R = 3.0 Ω and a charged capacitor C = 4.8 μF. (a) Show that this circuit will oscillate. (b) Determine the frequency. (c) What is the time required for the charge amplitude to drop to half its starting value? (d) What value of R will make the circuit nonoscillating? Underdamped R2 < 4L/C, overdamped for R2 > 4L/C. Critical damping will occur when R2 = 4L/C. Copyright © 2009 Pearson Education, Inc.