Physics 102: Lecture 14, Slide 1 Resonance Electromagnetic Waves Today’s lecture will cover Textbook Sections 21.6, 22.1, 4-5, 9 Physics 102: Lecture 14

Physics 102: Lecture 14, Slide 2 Review: Impedance Triangle and Resonance R (X L -X C ) Z  X L and X C point opposite. When adding, they tend to cancel! When X L = X C they completely cancel and Z = R. This is resonance! I max (X L -X C ) I max X L I max X C I max R V gen,max  V max,gen = I max Z

Physics 102: Lecture 14, Slide 3 Resonance R is independent of f X L increases with f X C increases with 1/f Z: X L and X C subtract R XCXC Z Resonance: X L = X C XLXL f0f0 Z is minimum at resonance frequency!

Physics 102: Lecture 14, Slide 4 Resonance R is independent of f X L increases with f X C increases with 1/f Z: X L and X C subtractPowerZ f0f0 Resonance: X L = X C Power is maximum at resonance frequency!

Physics 102: Lecture 14, Slide 5 Preflight 14.1 As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: L R C Always increases Only increases for lowering the frequency Only increases for raising the frequency f0f0 Z

Physics 102: Lecture 14, Slide 6 Preflight 14.1 As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: L R C Always increases Only increases for lowering the frequency Only increases for raising the frequency f0f0 Z is minimum at f o ! Any other frequency will have higher Z! Z

Physics 102: Lecture 14, Slide 7 ACT: Resonance 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. 1)V C > V L 2)V C = V L 3)V C < V L 4)Depends on R L R C

Physics 102: Lecture 14, Slide 8 ACT: Resonance 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. 1)V C > V L 2)V C = V L 3)V C < V L 4)Depends on R At resonance X L = X C. Since everything has the same current we can write X L = X C X L I max = X C I max V L = V C Also V Generator is in phase with current! L R C

Physics 102: Lecture 14, Slide 9 Preflight 14.3 At the resonant frequency, which of the following is true? I is in phase with V generator I leads V generator I lags V generator VLVL VCVC VRVR V gen 

Physics 102: Lecture 14, Slide 10 Preflight 14.3 At the resonant frequency, which of the following is true? I is in phase with V generator I leads V generator I lags V generator VLVL VCVC VRVR V gen  At resonance, V L = V C, so   = 0. V gen is in phase with V R ! V R is always in phase with I so V gen is also!

Physics 102: Lecture 14, Slide 11 Resonance in Radios L R C An AC circuit with R= 2 , L = 0.30  H 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?

Physics 102: Lecture 14, Slide 12 Resonance in Radios L R C An AC circuit with R= 2 , L = 0.30  H 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?

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

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

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

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

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

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

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

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

Physics 102: Lecture 14, Slide 21 ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical2) Horizontal 3) 45 Degrees +-+- Direction wave travels

Physics 102: Lecture 14, Slide 22 ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical2) Horizontal 3) 45 Degrees +-+- Direction wave travels Alternating E field moves charges up and down thru antenna!

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

Physics 102: Lecture 14, Slide 24 Resonance Electromagnetic Waves Today’s lecture will cover Textbook Sections 21.6, 22.1, 4-5, 9 Physics 102: Lecture 14

Physics 102: Lecture 14, Slide 25 Review: Impedance Triangle and Resonance R (X L -X C ) Z  X L and X C point opposite. When adding, they tend to cancel! When X L = X C they completely cancel and Z = R. This is resonance! I max (X L -X C ) I max X L I max X C I max R V gen,max  V max,gen = I max Z

Physics 102: Lecture 14, Slide 26 Resonance R is independent of f X L increases with f X C increases with 1/f Z: X L and X C subtract R XCXC Z Resonance: X L = X C XLXL f0f0 Z is minimum at resonance frequency!

Physics 102: Lecture 14, Slide 27 Resonance R is independent of f X L increases with f X C increases with 1/f Z: X L and X C subtractPowerZ f0f0 Resonance: X L = X C Power is maximum at resonance frequency!

Physics 102: Lecture 14, Slide 28 Preflight 14.1 As the frequency of the circuit is either raised above or lowered below the resonant frequency, the impedance of the circuit: L R C Always increases Only increases for lowering the frequency Only increases for raising the frequency f0f0 Z

Physics 102: Lecture 14, Slide 29 ACT: Resonance 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. 1)V C > V L 2)V C = V L 3)V C < V L 4)Depends on R L R C

Physics 102: Lecture 14, Slide 30 Preflight 14.3 At the resonant frequency, which of the following is true? I is in phase with V generator I leads V generator I lags V generator VLVL VCVC VRVR V gen 

Physics 102: Lecture 14, Slide 31 Resonance in Radios L R C An AC circuit with R= 2 , L = 0.30  H 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?

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

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

Physics 102: Lecture 14, Slide 34 ACT: EM Waves Which direction should I orient my antenna to receive a signal from a vertical transmission tower? 1) Vertical2) Horizontal 3) 45 Degrees +-+- Direction wave travels

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

Physics 102: Lecture 14, Slide 36 Electromagnetic Waves x z y Transverse (vs. sound waves – longitudinal) E perpendicular to B and always in phase E & B increase and decrease at same times Can travel in empty space (sound waves can’t!) “Speed of light”: v = c = 1/  (  0  0 ) = 3 x 10 8 m/s (186,000 miles/second!) Frequency: f = v/  = c/

Physics 102: Lecture 14, Slide 37 Preflight 14.6 – 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 38 Preflight 14.6 – 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 39 EM Waves Practice E x 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 40 EM Waves Practice E x 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

Physics 102: Lecture 14, Slide 41 Doppler Effect f o = f e (1 + u/c) moving toward each other f o = f e (1 - u/c) moving away from each other Note: These are easier than equations for sound! Finding relative velocity: u = v 1 + v 2 moving in opposite directions u = v 1 – v 2 moving in same direction observed frequency emitted frequency

Physics 102: Lecture 14, Slide 42 Doppler Effect Doppler Example Audio Doppler Example Visual f o = f e (1 + u/c) moving toward each other f o = f e (1 - u/c) moving away from each other Note: These are easier than equations for sound! Finding relative velocity: u = v 1 + v 2 moving in opposite directions u = v 1 – v 2 moving in same direction observed frequency emitted frequency

Physics 102: Lecture 14, Slide 43 Doppler Practice V = 32 m/sV = 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 44 Doppler Practice V = 32 m/sV = 50 m/s Cars are getting closer together: f o = f e (1 + u/c) Cars are moving in same directions: u = v 1 – v 2 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 45 Draw an impedance triangle for an AC circuit being driven with  =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) E a > E b (B) E a = E b (C) E a < E b Exam Prep Questions

Physics 102: Lecture 14, Slide 46 ACT: Radios Your radio is tuned to FM 96.1 MHz and want to change it to FM MHz, which of the following will work. 1.Increase Capacitance 2.Decrease Capacitance 3.Neither, you need to change both

Physics 102: Lecture 14, Slide 47 See you later! Read Sections