Physics 212 Lecture 21, Slide 1 Physics 212 Lecture 21.
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Transcript of Physics 212 Lecture 21, Slide 1 Physics 212 Lecture 21.
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 11
Physics 212Physics 212Lecture 21Lecture 21
Main Point 1
First, we defined the condition of resonance in a driven series LCR circuit to occur at the frequency w 0 that produces the largest value for the peak current in the circuit. At this frequency, which is also the natural oscillation frequency of the corresponding LC circuit, the inductive reactance is equal to the capacitive reactance so that the total impedance of the circuit is just resistive.
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 22
Main Point 2
Second, we determined that the average power delivered to the circuit by the generator was equal to the product of the rms values of the emf and the current times the cosine of the phase angle phi. The sharpness of the peak in the frequency dependence of the average power delivered was determined by the Q factor, which was defined in terms of the ratio of the energy stored to the energy dissipated at resonance.
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 33
Main Point 3
Third, we examined the properties of an ideal transformer and determined that the ratio of the induced emf in the secondary coil to that of the generator was just equal to the ratio of the number of turns in secondary to the number of turns in the primary. We also determined that when a resistive load is connected to the secondary coil, the ratio of the induced current in the primary to that in the secondary is also equal to the ratio of the number of turns in secondary to the number of turns in the primary.
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 44
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 55Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 55
Peak AC Problems
• “Ohms” Law for each element – NOTE: Good for PEAK values only)
– Vgen = Imax Z
– VResistor = Imax R
– Vinductor = Imax XL
– VCapacitor = Imax XC
• Typical Problem 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?
LX L
22L CZ R X X
1CX C
07
L
R
C
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 66
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 77
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 88
Resonance
Light-bulb DemoLight-bulb Demo
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 99
Resonance
R is independent of
XL increases with fLLX
is minimum at resonance
22 )( CL XXRZ
XC increases with 1/1CCX
Resonance: XL = XC 0
1LC
10
Frequency at which voltage across inductor and capacitor cancel
Resonance in AC Circuits
frequency
Imp
edan
ce
0
Resonance
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1010
Off Resonance
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1111
Checkpoint 1a
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 circuitsA. VI > VII B. VI = VII C. VI < VII
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1212
Checkpoint 1b
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 circuitsA. VI > VII B. VI = VII C. VI < VII
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1313
Checkpoint 1c
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 circuitsA. VI > VII B. VI = VII C. VI < VII
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1414
Checkpoint 1d
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.
At the resonant frequency, which of the following is true?A. Current leads voltage across the generatorB. Current lags voltage across the generator C. Current is in phase with voltage across the generator
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1515
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1616
Power
• P = IV instantaneous always true– Difficult for Generator, Inductor and Capacitor because of
phase– Resistor I,V are ALWAYS in phase!
P = IV = I2 R
• Average PowerInductor/Capacitor = 0Resistor<I2R> = <I2 > R = ½ I2peak R
= I2rms R
Average Power Generator = Average Power Resistor
RMS = Root Mean Square
Ipeak = Irms sqrt(2)
L
R
C
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1717
Transformers
• Application of Faraday’s Law– Changing EMF in Primary creates changing flux– Changing flux, creates EMF in secondary
• Efficient method to change voltage for AC.– Power Transmission Loss = I2R– Power electronics
p s
p s
V VN N
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1818
Follow Up from Last LectureFollow Up from Last LectureConsider the harmonically driven series LCR circuit shown. Vmax = 100 VImax = 2 mAVCmax = 113 V (= 80 sqrt(2))The current leads generator voltage by 45o
(cos=sin=1/sqrt(2))L and R are unknown.
How should we change to bring circuit to resonance?
CC
RR
LLVV ~~
(A) decrease (B) increase (C) Not enough info
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 1919
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 2020
Current Follow UpCurrent Follow UpConsider the harmonically driven series LCR circuit shown. Vmax = 100 VImax = 2 mAVCmax = 113 V (= 80 sqrt(2))The current leads generator voltage by 45o
(cos=sin=1/sqrt(2))L and R are unknown.
What is the maximum current at resonance ( Imax(0) )
CC
RR
LLVV ~~
(A) (B) (C)max 0I ( ) 2 mA max 0I ( ) 2 2 mA max 0I ( ) 8 / 3 mA
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 2121
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 2222
Phasor Follow Up Phasor Follow Up Consider the harmonically driven series LCR circuit shown. Vmax = 100 VImax = 2 mAVCmax = 113 V (= 80 sqrt(2))The current leads generator voltage by 45o
(cos=sin=1/sqrt(2))L and R are unknown.
What does the phasor diagram look like at t = 0? (assume V = Vmaxsint)
CC
RR
LLVV ~~
(A) (B) (C) (D)V L
V R
V C
V
VL
VR
VC
V
VL
VR
VC V
V L
V R
V C
V
Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide 2323