Physics 212 Lecture 21, Slide 1

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Physics 212 Lecture 21
dude--you're killing me. that prelecture made me
want to explode. i have no idea what happened.
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Some of your comments
1. Can the guy reading the pre-lectures be my
life coach? I feel inspired after he reads to me.
2. Can we get a breakfast buffet in the back of
the lecture hall. I think this class is early
enough and all of us pay enough for "engineering
tuition" that this wouldn't be too crazy. 3. Can
you float a frog across the room in B-field for
us? I've heard it is possible and I'm guessing
you could explain what's happening with the
material we've learned. 4. Can we go over average
power per cycle in LCR circuits?
And why does our equation sheet lack most of
these equations mentioned? It has the bare
minimum for the LC and LCR circuits - that's just
not nice. I mean, are we supposed to memorize the
equations??
do the physics gods just love to pick on us? I
understand v and V being velocity and and
voltage, but do we have to use Q again when it
already is charge?
I missed one question on the last lecture because
I was discussing it with the person next to me.
(
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Peak AC Problems
07

• Ohms Law for each element
• Vgen I Z
• VResistor I R
• Vinductor I XL
• VCapacitor I 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?

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Peak AC Problems
12

• Ohms Law for each element
• Vgen I Z
• VResistor I R
• Vinductor I XL
• VCapacitor I 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 0.004 Farad
  capacitor and a 50 ohm resistor. What is the peak
  current through the circuit?

Which element has the largest peak voltage across
it? A) Generator E) All the same. B) Inductor C)
Resistor D) Capacitor
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Peak AC Problems
14

• Ohms Law for each element
• Vgen I Z
• VResistor I R
• Vinductor I XL
• VCapacitor I 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?

Which happens to the impedance if we decrease the
angular frequency to 20 rad/sec? A) Z
increases B) Z remains the same C) Z decreases
w 25 (XL-XC)2 (200-100)2 w 20 (XL-XC)2
(160-125)2
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Phasor Recap
Imax Z
Imax(XL-XC)
Imax R
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Resonance
Light-bulb Demo
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Resonance
Frequency at which voltage across inductor and
capacitor cancel
R is independent of w
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Off Resonance
Z
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Off Resonance
Qualitatively, what is the quality factor? Why
does a larger quality factor make the voltage
graph have a sharper spike up at the resonant
frequency?
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Same since R doesn't change
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Imax XL
Imax XL
Imax R
Imax R
Imax XC
Case 1
Case 2
Imax XC
voltage in second circuit will be twice that of
the first because of the 2L compared to L
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Imax XL
Imax XL
Imax R
Imax R
Imax XC
Case 1
Case 2
Imax XC
The peak voltage will be greater in circuit 2
because the value of X_c doubles.
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Imax XL
Imax XL
Imax R
Imax R
Imax XC
Case 1
Case 2
The voltage across the inductor and the capacitor
are equal when at resonant frequency, so there is
no lag or lead.
Imax XC
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Follow Up from Last Lecture
Consider the harmonically driven series LCR
circuit shown. Vmax 100 V Imax 2 mA VCmax
113 V ( 80 sqrt(2)) The current leads generator
voltage by 45o (cossin1/sqrt(2)) L and R are
unknown. How should we change w to bring
circuit to resonance?
(A) decrease w (B) increase w
(C) Not enough info
At resonance XL XC
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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 Power
• Inductor/Capacitor 0
• Resistor
• ltI2Rgt ltI2 gt R ½ I2peak R
• I2rms R
• Average Power Generator Average Power Resistor

RMS Root Mean Square Ipeak Irms sqrt(2)
What is Root Mean Square? Why are we using it and
what is the significance of it?
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Do you feel better?

• A) Much Better
• B) A Bit Better
• C) About the Same
• D) Worse
• E) Not Applicable

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Power Line (Demo) Calculation

• If you want to deliver 1500 Watts at 100 Volts
  over transmission lines w/ resistance of 5 Ohms.
  How much power is lost in the lines?

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Power Line Calculation

• If you want to deliver 1500 Watts at 100 Volts
  over transmission lines w/ resistance of 5 Ohms.
  How much power is lost in the lines?
• I P/V 15 Amps
• Loss IV (on line) I2 R 1515 5 1,125
  Watts!
• If you deliver 1500 Watts at 10,000 Volts over
  the same transmission lines. How much power is
  lost?
• I P/V .15 Amps
• Loss IV (on line) I2R 0.125 Watts

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Transformers

• Application of Faradays 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

Demos
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Have a GREAT Weekend!
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Calculation
Consider the harmonically driven series LCR
circuit shown. Vmax 100 V Imax 2 mA XC
56.5 kW The current leads generator voltage by
45o L and R are unknown. What is XL, the
reactance of the inductor?

• Conceptual Analysis
• The maximum voltages for each component is
  related to its reactance and to the maximum
  current.
• The maximum voltages for the components are
  related via the impedance triangle

• Strategic Analysis
• Use Vmax and Imax to determine Z
• Use impedance triangle to determine R

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Calculation
Consider the harmonically driven series LCR
circuit shown. Vmax 100 V Imax 2 mA XC
56.5 kW The current leads generator voltage by
45o L and R are unknown.
Compare XL and XC at this frequency (A) XL lt XC
(B) XL XC (C) XL gt XC (D)
Not enough information
IR

• This information is determined from the phase
• Current leads voltage

45o
V
VL ImaxXL VC ImaxXC
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Calculation
Consider the harmonically driven series LCR
circuit shown. Vmax 100 V Imax 2 mA XC
56.5 kW The current leads generator voltage by
45o L and R are unknown.
What is the total impedance of the circuit
Z? (A) (B)
(C) (D)
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Calculation
Consider the harmonically driven series LCR
circuit shown. Vmax 100 V Imax 2 mA XC
56.5 kW The current leads generator voltage by
45o L and R are unknown.
What is R? (A) (B)
(C) (D)

• Determined from impedance triangle

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Calculation
Consider the harmonically driven series LCR
circuit shown. Vmax 100 V Imax 2 mA XC
56.5 kW The current leads generator voltage by
45o L and R are unknown.
What is XL? (A) (B)
(C) (D)