Physics 212 Lecture 19, Slide 1

1
Physics 212 Lecture 20
2
Music

• Who is the Artist?
• Delbert McClinton
• Elvis Costello
• Jimmy Buffett
• Randy Newman
• John Prine

Why? The Day After (the exam) Something
Familiar? Also Spring Break??
Also He closes Jazzfest on Sat May 3 on Acura
Stage His competition at that same time? Diana
Krall, Irvin Mayfield, Kenny Wayne Shepherd,
Nathan the Zydeco Cha Chas, and Joe Krown !!
p.s. all of the above choices will be at
Jazzfest
3
Summary
05

• Driven LCR Circuits
• Resonance
• Q factor
• Power
• Transformers

4
06
Your Comments
Peak Voltages across elements in a circuit What
is the deal with Z and Erms and Irms and Average
power? Could you give a general summary of
this prelecture? A prelecture due at 6pm the
day of an exam, thats just asking for a
half-assed effort... Really guys? come on....
5
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?

6
Peak AC Problems
08

• Ohms Law for each element
• A) Vgen I Z
• B) VResistor I R
• C) Vinductor I XL
• D) 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 Equation should we use?
7
Peak AC Problems
10

• 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?

8
Peak AC Problems

• 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?

9
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
10
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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Resonance
Frequency at which voltage across inductor and
capacitor cancel!
R is independent of w
XL increases with f
XC increases with 1/w
Z
R
Z XL and XC subtract
XC
XL
Resonance XL XC
10
12
Preflight 6
16

• At Resonance Voltage across capacitor exactly
  cancels voltage across inductor!
• Just like have generator and resistor
• Voltage across generator is in phase w/ current

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Preflight 7-11
18
This circuit is being driven __________ its
resonance frequency. (53) A) Above (too
fast) B) below (two slow) C) exactly at
XL gt XC so w is too large
The generator voltage is __________ the current.
(53) A) Leading B) Lagging C) in phase
Phasors rotate counter clockwise Generator
(green) phasor is leading current (R) phasor.
To increase power dissipated in the
resistor Decrease L, Decrease C R is tricky..
depends on values of R,L and C.
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Preflights 2-5
22
2
1
Circuits have identical generators and resistors.
Both are at resonance.
Compare the peak current through two circuits. A)
I1 gt I2 B) I1 I2 C) I1 lt I2
2) Compare the peak voltage across resistor in
the two circuits. (75) A) V1 gt V2 B) V1 V2
C) V1 lt V2
3) Compare the peak voltage across capacitor in
the two circuits. (50) A) V1 gt V2 B) V1 V2
C) V1 lt V2
4) Compare the peak voltage across inductor in
the two circuits. (50) A) V1 gt V2 B) V1 V2
C) V1 lt V2
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Power
25

• 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 ½ I2peak R
• I2rms R
• Average Power Generator Average Power Resistor

RMS Root Mean Square Ipeak Irms sqrt(2)
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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

17
Calculation
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. What is VL, the maximum voltage across
the inductor?
OK!
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Follow Up 1
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. What does the phasor diagram look like
at t 0? (assume V Vmaxsinwt)
V Vmax sinwt ? V is horizontal at t 0 (V
0)
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Follow Up 2
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 does VL vary with time? (assume V
Vmaxsinwt)

• EQUATIONS
• I leads Vgen by 45o
• I sin(wtp/4)
• dI/dt cos(wtp/4)

VL L dI/dt ? VL cos(wtp/4)
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Follow Up 3
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. If we increase w slightly, How does
average power delivered to the circuit change?
(A) ltPgt decreases (B) ltPgt increases
(C) ltPgt remains the same
XL increases XC decreases
How does phase change??
21
Follow Up 4
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