1 / 42

Class 26: Outline

This educational outline delves into driven harmonic motion as observed in RLC circuits through a series of lectures and experiments. It covers the principles of damped LC oscillations, resonance in systems, and the differences between alternating current (AC) and direct current (DC). Hands-on demonstrations highlight phasor diagrams, impedance plots, and resonance behavior at varying frequencies. Students will engage in experiments to observe current and voltage relationships in driven RLC circuits, applying theoretical concepts to real-world scenarios.

marshall-george
Download Presentation

Class 26: Outline

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Class 26: Outline • Hour 1: • Driven Harmonic Motion (RLC) • Hour 2: • Experiment 11: Driven RLC Circuit

  2. Last Time:Undriven RLC Circuits

  3. LC Circuit It undergoes simple harmonic motion, just like a mass on a spring, with trade-off between charge on capacitor (Spring) and current in inductor (Mass)

  4. Damped LC Oscillations Resistor dissipates energy and system rings down over time

  5. Mass on a Spring:Simple Harmonic Motion`A Second Look

  6. Mass on a Spring (2) (1) We solved this: (4) (3) Simple Harmonic Motion Moves at natural frequency What if we now move the wall? Push on the mass?

  7. Demonstration:Driven Mass on a SpringOff Resonance

  8. Driven Mass on a Spring Now we get: F(t) Assume harmonic force: Simple Harmonic Motion Moves at driven frequency

  9. Resonance • Now the amplitude, xmax, depends on how close the drive frequency is to the natural frequency xmax Let’s See… w0 w

  10. Demonstration:Driven Mass on a Spring

  11. Resonance • xmax depends on drive frequency xmax Many systems behave like this: Swings Some cars Musical Instruments … w0 w

  12. Electronic Analog:RLC Circuits

  13. Analog: RLC Circuit • Recall: • Inductors are like masses (have inertia) • Capacitors are like springs (store/release energy) • Batteries supply external force (EMF) • Charge on capacitor is like position, • Current is like velocity – watch them resonate • Now we move to “frequency dependent batteries:” • AC Power Supplies/AC Function Generators

  14. Demonstration:RLC with Light Bulb

  15. Start at Beginning:AC Circuits

  16. Alternating-Current Circuit • direct current (dc) – current flows one way (battery) • alternating current (ac) – current oscillates • sinusoidal voltage source

  17. AC Circuit: Single Element • Questions: • What is I0? • What is f ?

  18. AC Circuit: Resistors IR and VR are in phase

  19. AC Circuit: Capacitors ICleadsVC by p/2

  20. AC Circuit: Inductors ILlagsVL by p/2

  21. AC Circuits: Summary Although derived from single element circuits, these relationships hold generally!

  22. PRS Question:Leading or Lagging?

  23. Phasor Diagram • Nice way of tracking magnitude & phase: Notes: (1) As the phasor (red vector) rotates, the projection (pink vector) oscillates (2) Do both for the current and the voltage

  24. Demonstration:Phasors

  25. Phasor Diagram: Resistor IR and VR are in phase

  26. Phasor Diagram: Capacitor ICleadsVC by p/2

  27. Phasor Diagram: Inductor ILlagsVL by p/2

  28. PRS Questions:Phase

  29. Put it all together:Driven RLC Circuits

  30. Question of Phase • We had fixed phase of voltage: • It’s the same to write: (Just shifting zero of time)

  31. Driven RLC Series Circuit

  32. Driven RLC Series Circuit I(t) VS Now we just need to read the phasor diagram!

  33. Driven RLC Series Circuit Impedance

  34. Plot I, V’s vs. Time

  35. PRS Question:Who Dominates?

  36. RLC Circuits:Resonances

  37. Resonance At very low frequencies, C dominates (XC>>XL): it fills up and keeps the current low At very high frequencies, L dominates (XL>>XC): the current tries to change but it won’t let it At intermediate frequencies we have resonance I0 reaches maximum when

  38. Resonance C-like: f < 0 I leads L-like: f > 0 I lags

  39. Demonstration:RLC with Light Bulb

  40. PRS Questions:Resonance

  41. Experiment 11: Driven RLC Circuit

  42. Experiment 11: How To • Part I • Use exp11a.ds • Change frequency, look at I & V. Try to find resonance – place where I is maximum • Part II • Use exp11b.ds • Run the program at each of the listed frequencies to make a plot of I0 vs. w • Part III • Use exp11c.ds • Plot I(t) vs. V(t) for several frequencies

More Related