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Physics 2112 Unit 21

Physics 2112 Unit 21. Outline:. Resonance Power/Power Factor Q factor What is means A useful approximation Transformers. From last time…. C. L. R. X L. R. X C. “Ohms Law” for each element. (impedance). where:. (inductive reactance). (capacitive reactance). w of generator.

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Physics 2112 Unit 21

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  1. Physics 2112Unit 21 • Outline: • Resonance • Power/Power Factor • Q factor • What is means • A useful approximation • Transformers

  2. From last time….. C L R XL R XC • “Ohms Law” for each element (impedance) • where: (inductive reactance) (capacitive reactance) w of generator

  3. This means….. C L L C R Current is largest when or Where have we seen this before? (Natural Frequency) When wd = wo resonance

  4. Resonance Z = R at resonance Z R XC XL w0 Frequency at which voltage across inductor and capacitor cancel R is independent of w XL increases with w XC increases with 1/w is minimum at resonance Resonance: XL=XC

  5. Example 21.1 (Tuning Radio) C L R • A radio antenna is hooked to signal filter consisting of a resistor, a variable capacitor and a 50uH inductor. • If we would like to get maximum current for the signal from our favorite country music station, US 99 (99.5MHz), what should we set the capacitor to? amplifier

  6. Example 21.2 (Peak Current) C L R A generator with peak voltage 15 volts and angular frequency 25 rad/sec is connected in series with an 8 Henry inductor, a 0.4 mF capacitor and a 50 ohm resistor. What is the peak current through the circuit?

  7. CheckPoint 1(A) Imax XL Imax XL Imax R Imax R Imax XC Case 1 Imax XC Case 2 Consider two RLC circuits with identical generators and resistors. Both circuits are driven at the resonant frequency. Circuit II has twice the inductance and 1/2 the capacitance of circuit I as shown above. • Compare the peak voltage across the resistor in the two circuits. • VI> VII • VI= VII • VI< VII Resonance: XL=XC Z=R Same since R doesn't change

  8. CheckPoint 1(B) Imax XL Imax XL Imax R Imax R Imax XC Case 1 Imax XC Case 2 Consider two RLC circuits with identical generators and resistors. Both circuits are driven at the resonant frequency. Circuit II has twice the inductance and 1/2 the capacitance of circuit I as shown above. • Compare the peak voltage across the inductor in the two circuits • VI> VII • VI= VII • VI< VII Voltage in second circuit will be twice that of the first because of the 2L compared to L.

  9. CheckPoint 1(C) Imax XL Imax XL Imax R Imax R Imax XC Case 1 Imax XC Case 2 Consider two RLC circuits with identical generators and resistors. Both circuits are driven at the resonant frequency. Circuit II has twice the inductance and 1/2 the capacitance of circuit I as shown above. • Compare the peak voltage across the capacitor in the two circuits • VI> VII • VI= VII • VI< VII The peak voltage will be greater in circuit 2 because the value of XC doubles.

  10. CheckPoint 1(D) Imax XL Imax XL Imax R Imax R Imax XC Case 1 Imax XC Case 2 • At the resonant frequency, which of the following is true? • The current leads the voltage across the generator • The current lags the voltage across the generator • The current is in phase with the voltage across the generator

  11. Resonance….what it means….. A circuit is in resonance when…. • frequency of the signal generator is the same as the natural frequency of the circuit. • Imax = e/R • Voltage drop across the resistor is maximum • XL = XC • Z has minimum value • phase angle, f, is zero • voltage and current are in sync at the signal generator. “

  12. Power C L R • What is the power put into circuit by signal? • At any instant P=VI  varies with time. • But V and I not in sync at genarator

  13. Power C L R • PIN = POUT RMS=Root Mean Square Changes electrical energy into thermal energy

  14. Example 21.3 (Power lost) • How much electrical energy was turned into thermal energy every minute in the three situations we had in example 20.2? • Recall w=60rad/sec f =-72o • w=400rad/sec f=55.7o • w =206rad/sec f = 0o • In the circuit to the right • L=500mH • Vmax = 6V • C=47uF • R=100W

  15. Example 21.4 A bright electric light bulb and a small window air conditioner both are plugged into a wall socket with puts out Vrms=120V. Both draw Irms= 1amp of current. The light bulb has a power factor of 1 and the AC unit has a power factor of 0.85. How much electrical energy do they consume in 1 hour?

  16. Power Line Calculation • If you want to deliver 1,500Watts at 100Volts over transmission lines w/ resistance of 5Ohms. How much power is lost in the lines? • Current Delivered: I=P/V= 15 Amps • Loss =IV (on line) =I2R= 15*15 * 5 = 1,125 Watts! • If you deliver 1,500 Watts at 10,000Volts over the same transmission lines. How much power is lost? • Current Delivered: I=P/V= .15 Amps • Loss =IV(on line) =I2R= 0.125 Watts Lower, but not zero!!!

  17. Cost to you Utility companies charge a surcharge for industrial customers with large power factors (e.g. large AC loads). Customers can correct power factor with capacitors. Assumed power factor for residential > 0.95.

  18. Warning!!!! About to talk about “Quality Factor”, Q Just to confuse you….we’re also going to be talking about the charge on a capacitor, Q We’ll go through the math quickly…. Hang in there. We’ll show what it means conceptually and do an example problem in the end.

  19. Recall Damped Harmonic Motion Damping factor Natural oscillation frequency Damped oscillation frequency

  20. What does Q mean algebraically…. Energy Charge2 Energy Lost Define Quality Factor (Maximum energy Stored) Q = 2p (Energy Lost per Cycle)

  21. Second way to look at Q How fast you fall away from current at resonance How far you are from resonance Bigger Q, fall off faster

  22. What does Q mean graphically….. Q=0.5 Q=1.0 Imax/(e/R) Imax/(e/R) x=w/wo x=w/wo Q=5.0 Q=20.0 Imax/(e/R) Imax/(e/R) x=w/wo x=w/wo

  23. Useful approximationfrom Q • Often used approximation for Q>2 Q=5.0 • “Full Width at Half Maximum”

  24. Example 21.5 (FWHM) An electronic filter is made up of an inductor, L=0.5H, a capacitor, C=2.0uF and resistor, R=20W. It has an input signal with Vmax = 0.1V. 1) What is the resonant frequency for this filter? 2) What is the average output power at this frequency? 3) What is the quality factor Q for this filter? 4) Use this Q to estimate FWHM. 5) What is the average power output at a frequency of wo + FWHM/2?

  25. Transformers Secondary (S) DVP DIP Primary (P)  DBP  DFS  DIS  DVS  DBS  DFP Difficult to calculate step by step

  26. Transformers Note by energy conservation

  27. Example 21.6 (Coil in your car) • In the old days, the high voltage needed to fire the spark plugs in your car was created by “the coil”. On a typical coil, there were 200 turns the primary side and 400,000 turns on the secondary side. • If the car’s alternator provided 12 volts to the coil, what was the voltage provided to the spark plugs?

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