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Resonance Electromagnetic Waves

Physics 102: Lecture 14. Resonance Electromagnetic Waves. Today’s lecture will cover Textbook Sections 21.6, 22.1, 4-5, 9. Review: Impedance Triangle and Resonance. V max,gen = I max Z. I max X L. Z. (X L -X C ). V gen,max. f. I max (X L -X C ). R. f. I max R.

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Resonance Electromagnetic Waves

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  1. Physics 102:Lecture 14 ResonanceElectromagnetic Waves • Today’s lecture will coverTextbook Sections 21.6, 22.1, 4-5, 9 Physics 102: Lecture 14, Slide 1

  2. Review:Impedance Triangle and Resonance Vmax,gen = Imax Z ImaxXL Z (XL-XC) Vgen,max f Imax(XL-XC) R f ImaxR XL and XC point opposite. When adding, they tend to cancel! When XL = XC they completely cancel and Z = R. This is resonance! ImaxXC Physics 102: Lecture 14, Slide 2

  3. Z is minimum at resonance frequency! f0 Resonance R is independent of f XL increases with f XC increases with 1/f Z R Z: XL and XC subtract XC XL Resonance: XL = XC Physics 102: Lecture 14, Slide 3

  4. Power is maximum at resonance frequency! Resonance R is independent of f XL increases with f XC increases with 1/f Z: XL and XC subtract Z Power f0 Resonance: XL = XC Physics 102: Lecture 14, Slide 4

  5. f0 Preflight 14.1 L R As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: C Always increases Only increases for lowering the frequency Only increases for raising the frequency Z Physics 102: Lecture 14, Slide 5

  6. f0 Preflight 14.1 L R As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: C Always increases Only increases for lowering the frequency Only increases for raising the frequency Z Z is minimum at fo! Any other frequency will have higher Z! Physics 102: Lecture 14, Slide 6

  7. ACT: Resonance L R The AC circuit to the right is being driven at its resonance frequency. Compare the maximum voltage across the capacitor with the maximum voltage across the inductor. • VC > VL • VC = VL • VC < VL • Depends on R C Physics 102: Lecture 14, Slide 7

  8. ACT: Resonance L R The AC circuit to the right is being driven at its resonance frequency. Compare the maximum voltage across the capacitor with the maximum voltage across the inductor. • VC > VL • VC = VL • VC < VL • Depends on R C At resonance XL = XC. Since everything has the same current we can write XL = XC XLImax = XCImax VL = VC Also VGenerator is in phase with current! Physics 102: Lecture 14, Slide 8

  9. Preflight 14.3 At the resonant frequency, which of the following is true? VL I leads Vgenerator I lags Vgenerator Vgen f = 0 I is in phase with Vgenerator VR VC Physics 102: Lecture 14, Slide 9

  10. At resonance, VL = VC, so f= 0. Vgen is in phase with VR! VR is always in phase with I so Vgen is also! Preflight 14.3 At the resonant frequency, which of the following is true? VL I leads Vgenerator I lags Vgenerator Vgen f = 0 I is in phase with Vgenerator VR VC Physics 102: Lecture 14, Slide 10

  11. Resonance in Radios L Example R An AC circuit with R= 2 W, L = 0.30 mH and variable capacitance is connected to an antenna to receive radio signals at the resonance frequency. If you want to listen to music broadcasted at 96.1 MHz, what value of C should be used? C Physics 102: Lecture 14, Slide 11

  12. Resonance in Radios L Example R An AC circuit with R= 2 W, L = 0.30 mH and variable capacitance is connected to an antenna to receive radio signals at the resonance frequency. If you want to listen to music broadcasted at 96.1 MHz, what value of C should be used? C Physics 102: Lecture 14, Slide 12

  13. Electromagnetic Waves • Light, Radio, TV, Microwaves, Satellites, X-Rays Physics 102: Lecture 14, Slide 13 40

  14. Direction wave travels Electromagnetic Waves Generator creates E field up and down. - + Physics 102: Lecture 14, Slide 14

  15. Direction wave travels Electromagnetic Waves Generator creates E field up and down. - - + + Physics 102: Lecture 14, Slide 15

  16. Direction wave travels Electromagnetic Waves Generator creates E field up and down. - + Physics 102: Lecture 14, Slide 16

  17. Direction wave travels Electromagnetic Waves Generator creates E field up and down. Physics 102: Lecture 14, Slide 17

  18. Direction wave travels Electromagnetic Waves Generator creates E field up and down. + - Physics 102: Lecture 14, Slide 18

  19. Direction wave travels Electromagnetic Waves Generator creates E field up and down. + + - - Physics 102: Lecture 14, Slide 19

  20. Direction wave travels Electromagnetic Waves Generator creates E field up and down. + - Physics 102: Lecture 14, Slide 20

  21. Direction wave travels + - ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical 2) Horizontal 3) 45 Degrees Physics 102: Lecture 14, Slide 21

  22. Direction wave travels ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical 2) Horizontal 3) 45 Degrees + - Alternating E field moves charges up and down thru antenna! Physics 102: Lecture 14, Slide 22

  23. + - y x z Electromagnetic Waves(Preflight 14.5) Generator also creates B field into and out of the page! Physics 102: Lecture 14, Slide 23

  24. Physics 102:Lecture 14 ResonanceElectromagnetic Waves • Today’s lecture will coverTextbook Sections 21.6, 22.1, 4-5, 9 Physics 102: Lecture 14, Slide 24

  25. Review:Impedance Triangle and Resonance Vmax,gen = Imax Z ImaxXL Z (XL-XC) Vgen,max f Imax(XL-XC) R f ImaxR XL and XC point opposite. When adding, they tend to cancel! When XL = XC they completely cancel and Z = R. This is resonance! ImaxXC Physics 102: Lecture 14, Slide 25

  26. Z is minimum at resonance frequency! f0 Resonance R is independent of f XL increases with f XC increases with 1/f Z R Z: XL and XC subtract XC XL Resonance: XL = XC Physics 102: Lecture 14, Slide 26

  27. Power is maximum at resonance frequency! Resonance R is independent of f XL increases with f XC increases with 1/f Z: XL and XC subtract Z Power f0 Resonance: XL = XC Physics 102: Lecture 14, Slide 27

  28. f0 Preflight 14.1 L R As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: C Always increases Only increases for lowering the frequency Only increases for raising the frequency Z Physics 102: Lecture 14, Slide 28

  29. ACT: Resonance L R The AC circuit to the right is being driven at its resonance frequency. Compare the maximum voltage across the capacitor with the maximum voltage across the inductor. • VC > VL • VC = VL • VC < VL • Depends on R C Physics 102: Lecture 14, Slide 29

  30. Preflight 14.3 At the resonant frequency, which of the following is true? VL I leads Vgenerator I lags Vgenerator Vgen f = 0 I is in phase with Vgenerator VR VC Physics 102: Lecture 14, Slide 30

  31. Resonance in Radios L Example R An AC circuit with R= 2 W, L = 0.30 mH and variable capacitance is connected to an antenna to receive radio signals at the resonance frequency. If you want to listen to music broadcasted at 96.1 MHz, what value of C should be used? C Physics 102: Lecture 14, Slide 31

  32. Electromagnetic Waves • Light, Radio, TV, Microwaves, Satellites, X-Rays Physics 102: Lecture 14, Slide 32 40

  33. Direction wave travels Electromagnetic Waves Generator creates E field up and down. + - Physics 102: Lecture 14, Slide 33

  34. Direction wave travels + - ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical 2) Horizontal 3) 45 Degrees Physics 102: Lecture 14, Slide 34

  35. + - y x z Electromagnetic Waves(Preflight 14.5) Generator also creates B field into and out of the page! Physics 102: Lecture 14, Slide 35

  36. y x z Electromagnetic Waves • Transverse (vs. sound waves – longitudinal) • E perpendicular to B and always in phaseE & B increase and decrease at same times • Can travel in empty space (sound waves can’t!) • “Speed of light”: v = c = 1/ (e0m0) = 3 x 108 m/s (186,000 miles/second!) • Frequency:f = v/l = c/l Physics 102: Lecture 14, Slide 36

  37. Preflight 14.6 – 14.12 Which of the following are transverse waves? • sound • light • radio • X-ray • microwave • water waves • “The Wave” (i.e. at football games) Physics 102: Lecture 14, Slide 37

  38. Preflight 14.6 – 14.12 Which of the following are transverse waves?  • sound • light • radio • X-ray • microwave • water waves • “The Wave” (i.e. at football games)   All but sound!     Physics 102: Lecture 14, Slide 38

  39. E x Example EM Waves Practice Shown below is the E field of an EM wave broadcast at 96.1 MHz and traveling to the right. (1) What is the direction of the magnetic field? (2) Label the two tic marks on the x axis (in meters). Physics 102: Lecture 14, Slide 39

  40. E x Example EM Waves Practice Shown below is the E field of an EM wave broadcast at 96.1 MHz and traveling to the right. (1) What is the direction of the magnetic field? (2) Label the two tic marks on the x axis (in meters). Perpendicular to E, v: Into/out of the page 3.1 6.2 Physics 102: Lecture 14, Slide 40

  41. observed frequency emitted frequency Doppler Effect • fo = fe (1 + u/c) moving toward each other • fo = fe (1 - u/c) moving away from each other Note: These are easier than equations for sound! • Finding relative velocity: u = v1 + v2 moving in opposite directions u = v1 – v2 moving in same direction Physics 102: Lecture 14, Slide 41

  42. observed frequency emitted frequency Doppler Effect Doppler Example Audio Doppler Example Visual • fo = fe (1 + u/c) moving toward each other • fo = fe (1 - u/c) moving away from each other Note: These are easier than equations for sound! • Finding relative velocity: u = v1 + v2 moving in opposite directions u = v1 – v2 moving in same direction Physics 102: Lecture 14, Slide 42

  43. Example Doppler Practice V = 32 m/s V = 50 m/s In the jeep, the frequency of the light from the troopers car will appear: (1) higher (more blue) (2) Lower (more red) What value should you use for u in the equation? (1) 32 (2) 50 (3) 50+32 (4) 50-32 Physics 102: Lecture 14, Slide 43

  44. Example Doppler Practice V = 32 m/s V = 50 m/s In the jeep, the frequency of the light from the troopers car will appear: (1) higher (more blue) (2) Lower (more red) What value should you use for u in the equation? (1) 32 (2) 50 (3) 50+32 (4) 50-32 Cars are getting closer together: fo = fe (1 + u/c) Cars are moving in same directions: u = v1 – v2 Physics 102: Lecture 14, Slide 44

  45. Exam Prep Questions • Draw an impedance triangle for an AC circuit being driven with f=30 degrees • How would this triangle change if it was being driven at resonance? The figure to the right illustrates a plane electromagnetic wave. Compare the z‑component of the electric field at the points a and b. (A) Ea > Eb (B) Ea = Eb (C) Ea < Eb Physics 102: Lecture 14, Slide 45

  46. ACT: Radios Your radio is tuned to FM 96.1 MHz and want to change it to FM 105.9 MHz, which of the following will work. • Increase Capacitance • Decrease Capacitance • Neither, you need to change both Physics 102: Lecture 14, Slide 46

  47. See you later! • Read Sections 22. 7-8 Physics 102: Lecture 14, Slide 47

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