Unformatted text preview: Physics 212
Ph
Lecture 20
AC Circuits Maximum currents & voltages
Phasors: A Simple Tool
Simple Physics 212 Lecture 20, Slide 1 Music
Who is the Artist?
A)
B)
C)
D)
E) Derek Trucks Band
Trucks Band
Robert Plant & Alison Kraus
CCR
Emmylou Harris & Gregg Allman
Led Zeppelin Theme of the week
Bluegrass fiddlers (Mark O’Connor, Alison Kraus) doing something different !!
Also: From today’s Lecture Thoughts:
“You should ALTERNATE your CURRENT music pattern and put up a song  sister
rosetta walks before us, preferably  from Raising Sand  please and thanks!”
P.S. Did you know this is Alison Kraus’ hometown?
Physics 212 Lecture 20, Slide 2 Your
Your Comments
“I need more practice reading the phasor
phasor diagrams, and please explain what exactly is
meant by two elements being "in phase" or
"out of phase." Think about what the voltage across
each element is proportional to:
Q, I, dI/dt
C, R, L “This was rather confusing.... Can you please explain the phasor diagrams and a circuit with
all 3 elements (capacitors, inductors, and
resistors) in it?”
“Where does Z come from? I don't understand
how wL and wC could be related to each
other... And the units are weird too...”.” Absolutely
Absolutely Will Do !
Impedance
Impedance Triangle ﬂ Phases !!
Rotation of Phasors ﬂ Voltages at any time “explain the check points!! I seem to be LAGGING behind the
prelecture by something greater than 90 degrees.”
th 90 “I just finished the midterm 2 just in time for me to do more
physics. Right now, I'm all "phased" out.”
“Obvious Star Trek/phasor pun goes here”
Trek/phasor
05 Physics 212 Lecture 20, Slide 3 Resistors = Vmaxsin(t) R I = VR/R = Vmax/R sin(t) Amplitude = Vmax/R Physics 212 Lecture 20, Slide 4 Capacitors
Q = CV = CVmaxsin(t)
CV CV
I = dQ/dt = Vmaxsin(t) C I = VmaxC cos(t) Amplitude = Vmax/XC 90o where XC = 1/C
is like the “resistance”
of
of the capacitor
XC depends on Physics 212 Lecture 20, Slide 5 Inductors
dI/dt = VL = Vmaxsin(t) = Vmaxsin(t) L I =  Vmax/L cos(t) Amplitude = Vmax/XL 90o where XL = L
is like the “resistance”
of
of the inductor
XL depends on Physics 212 Lecture 20, Slide 6 RL ACT
An RL circuit is driven by an AC generator as shown in the
figure.
XL = L L R As Ø 0, so does XL
As Ø 0,
resistance of circuit Ø R
current gets bigger For what driving frequency of the generator will the
th
current
current through the resistor be largest
A) large
B) Current through R doesn’t depend on C) small
Physics 212 Lecture 20, Slide 7 Summary
Summary
R Imax = Vmax/R VR in phase with I Because resistors are simple C Imax = Vmax/XC
XC = 1/C VC 90o behind I
Current comes first since it
charges capacitor
Like a wire at high L Imax = Vmax/XL
XL = L VL 90o ahead of I Opposite of capacitor
Like a wire at low Physics 212 Lecture 20, Slide 8 Makes sense to write everything in
Makes
terms of I since this is the same
everywhere in a oneloop circuit:
one Phasors make this
simple to see
Imax XL Vmax = Imax XC
V 90o behind I C max L
R Imax R Vmax = Imax XL
V 90o ahead of I Vmax = Imax R
V in phase with I
Simulation from the Prelecture Imax XC
Always looks the same.
Only the lengths will
change
change
Physics
Physics 212 Lecture 20, Slide 9 Imax XC The
The voltages still add up
C max But now we are adding
vectors:
Imax XL L
R Imax R Imax XL Imax R max
Imax R Imax R Imax XC Imax XC Imax XL Imax XC Imax XL max
Physics 212 Lecture 20, Slide 10 Imax XC Making
Making this simpler…
C max
Imax XL L Imax XL R
Imax R Imax XL max
Imax R Imax XC Imax R Imax XC
Physics 212 Lecture 20, Slide 11 Imax XC Making
Making this simpler…
C max L Imax XL R
Imax R Imax XL max = Imax Z
max
max
Imax R Imax(XLXC)
Imax R Imax XC
Physics 212 Lecture 20, Slide 12 Imax XC Making
Making this simpler…
C max L Imax XL R
Imax R max = Imax Z
max
max
Imax(XLXC)
Imax R Physics 212 Lecture 20, Slide 13 Imax XC Making
Making this simpler…
C max Imax XL R max = Imax Z Imax R Imax(XLXC) L Imax R (XLXC) Impedance Triangle R X L XC
tan R
Physics 212 Lecture 20, Slide 14 Imax XC Summary:
Summary:
C VCmax= Imax XC max VLmax= Imax XL L Imax XL R VRmax= Imax R Imax R max = Imax Z
Imax = max / Z
max Z R X L XC 2 X L XC
tan R 2 XLXC) R Physics 212 Lecture 20, Slide 15 Example:
Example: RL Circuit Xc=0 max L Imax XL R
Imax R Imax XL max
Imax R Physics 212 Lecture 20, Slide 16 CheckPoint
CheckPoint 1a
Draw Voltage Phasors
Imax XL max
Imax R A
B
C 60
50
40 “I lags V for the inductor by 90° and V(resistor) is IR, that
means that the voltage across the resistor lags the
generator voltage” 30
20
10
0 “The generator is always in phase with resistors.” Physics
Physics 212 Lecture 20, Slide 17 CheckPoint 1b
Draw Voltage Phasors
Imax XL max
Imax R A
B
C 60
50
40
30 “The voltages across the resistor and the inductor are always 90
degrees out of phase.” 20
10
0 “As we saw from the prelecture, the voltage across the inductor
is again always in phase with the generator.” Physics
Physics 212 Lecture 20, Slide 18 CheckPoint 1c
The CURRENT is THE CURRENT
Imax XL A
B
C
D
“The same current passes through the resistor and the inductor.”
“The current through the resistor and inductor will always be 90
degrees, since the voltage across the resistor and inductor is
always in phase.” max
Imax R is the phase between
generator and current
40
30
20
10
0 Physics 212 Lecture 20, Slide 19 CheckPoint
CheckPoint 2a A
B
C What does the voltage
phasor diagram look
lik
like when the current
th
IXL
is a maximum? IXL IR 40 IR
IXc
IXc 30
20
10
0 Physics 212 Lecture 20, Slide 20 IXL IR IR A
B
C IXc CheckPoint
CheckPoint 2b 30 IXc 20
10 IXL What does the voltage
phasor diagram look
lik
like when the capacitor
th
is fully charged? 40 0 Physics 212 Lecture 20, Slide 21 IXL IR IR A
B
C IXc CheckPoint
CheckPoint 2c 40 IXc 30
20
10 IXL What does the voltage
phasor diagram look
lik
like when the voltage
th
across capacitor is at
its positive maximum? 50 0 Physics 212 Lecture 20, Slide 22 Calculation
Calculation
Consider the harmonically driven series LCR circuit shown.
Vmax = 100 V
Imax = 2 mA
VCmax = 113 V
The current leads generator voltage by 45o
L and R are unknown. C V~ L
R What is XL, the reactance of the inductor, at this frequency? • Conceptual Analysis
–
– The maximum voltage for each component is related to its
reactance and to the maximum current.
The impedance triangle determines the relationship between the
maximum voltages for the components • Strategic Analysis
–
–
– Use Vmax and Imax to determine Z
Use impedance triangle to determine R
Use
Use VCmax and impedance triangle to
determine XL
Physics
Physics 212 Lecture 20, Slide 23 Calculation
Calculation
Consider the harmonically driven series LCR circuit shown.
Vmax = 100 V
Imax = 2 mA
VCmax = 113 V
The current leads generator voltage by 45o
L and R are unknown. C V~ L
R What is XL, the reactance of the inductor, at this frequency? Compare XL and XC at this frequency:
(A) XL < XC
(B) XL = XC
(C) XL > XC (D) Not enough information • This information is determined from the phase
– Current leads voltage VL VL = ImaxXL
VC = ImaxXC VR (phase of current)
V
VC IR
V leads
Physics 212 Lecture 20, Slide 24 Calculation
Calculation
Consider the harmonically driven series LCR circuit shown.
Vmax = 100 V
Imax = 2 mA
VCmax = 113 V
The current leads generator voltage by 45o
L and R are unknown. C V~ L
R What is XL, the reactance of the inductor, at this frequency? What is Z, the total impedance of the circuit?
(A) 70.7 k
(B) 50 k
(C) 35.4 k (D) 21.1 k Vmax 100V 50k Z
I max 2mA Physics 212 Lecture 20, Slide 25 Calculation
Calculation
Consider the harmonically driven series LCR circuit shown.
Vmax = 100 V
Imax = 2 mA
VCmax = 113 V
The current leads generator voltage by 45o
L and R are unknown. C V~ L
R
Z = 50k What is XL, the reactance of the inductor, at this frequency? sin(45)=.707 What is R?
(A) 70.7 k cos(45)=.707 (B) 50 k (C) 35.4 k (D) 21.1 k • Determined from impedance triangle
R Z=50k (XCXL) R
cos(45) Z R = Z cos(45o)
= 50 kx 0.707
= 35.4 k
Physics 212 Lecture 20, Slide 26 Calculation
Calculation C Consider the harmonically driven series LCR circuit shown.
Vmax = 100 V
Imax = 2 mA
VCmax = 113 V
The current leads generator voltage by 45o
L and R are unknown. V~
R Z = 50k What is XL, the reactance of the inductor, at this frequency? (A) 70.7 k (B) 50 k We start with the
impedance triangle: R Z (C) 35.4 k XC X L tan 45 1
R L R = 35.4k
35.4k (D) 21.1 k XL = XC  R
What is XC ? (XCXL) VCmax = ImaxXC
XL = 56.5 k – 35.4 k 113
XC 56.5k
2
Physics 212 Lecture 20, Slide 27 ...
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 Fall '08
 Kim
 Physics, Current, Alternating Current, Inductor, Electrical impedance, IMAX, Imax XL

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