Physics 212 Lecture 20, Slide 1

1
Physics 212 Lecture 20
AC Circuits Maximum currents voltages Phasors
A Simple Tool
UHhhhh....yeahhhh....to put it tactfully....HELP!!
!!!!!!!!!!
2
Some of your comments
While I normally make outlandish requests in this
text box, demanding that you inspire me to some
Nobel prize winning status of greatness, today is
different. For today, just do your thing and I
will listen.
Do some more examples of this one in lecture.
It's kind of a lot of information for one
prelecture.
I dont understand how an inductor can exist in
the same circut as the ac generator, would these
force two different currents? is the key that
there can be different currents through different
circut elements at the same time? Because without
that possibility the rest of the circut seemes
impossible
the impedance triangle
Bring in the imaginary friends! Also, it was
kinda weird that reactance was on the homework
due this tuesday - thank goodness we have wiki.
Phases especially, and their relationships
We use so many types of appliances, each with
different resistance. If we have more than one
appliance plugged into an extension cord, do both
of these appliances get voltage which is in phase
with each other?
More examples of this with different orientations
of the resistor, inductor, and capacitor. Maybe
even using multiple resistors, inductors, or
capacitors.
3
So, in the prelecture, the generator has a a
voltage associated with it-- does that mean it
eventually runs out of charge since it takes
torque to keep the generator spinning? Or do we
just ignore this question entirely and use ideal
generators?
Did that guy that promised you chocolate ever
come through?
It seems like we are getting farther away from
doing straight calculations because the math is
getting a bit tricky, is that just for this part
of the course or is this pattern going to
continue onto future topics.
I thought you said this was going to get
easier...Don't lie to us!
You said this was supposed to get easier... But
this definitely got harder... And there's a test
this week!?!
Captain, we have landed on a hostile planet where
the current is constantly changing! Set phasors
to confused!
4
Resistors
e emaxsin(wt)
I VR/R
Vmax/R sin(wt)
Why is V given by the vertical component of the
phasor diagram?
5
Capacitors
Why does changing the frequency affect the
magnitude of a capacitor's or an inductor's
voltage?
Q VC Cemaxsin(wt)
I dQ/dt
e emaxsin(wt)
I VmaxwC cos(wt)
where XC 1/wC is like the resistanceof the
capacitor XC depends on w
6
Capacitor Act
1) A capacitor is connected to an AC generator as
shown.
CD
If the frequency of the generator is doubled, the
maximum current in the circuit
willA)  increase by a factor of 2 B)  stay the
same C)  decrease by a factor of 2
7
Inductors
dI/dt VL emaxsin(wt)
e emaxsin(wt)
I - Vmax/wL cos(wt)
where XL wL is like the resistanceof the
inductor XC depends on w
8
RL Act
  An RL circuit is driven by an AC generator as
shown in the figure.
CD
L
R
For what driving frequency w of the generator
will the current through the resistor be largest
A)  w large B) Current through R doesnt depend
on w C)  w small
9
Summary
phasors, and where in jebus lice's name did they
come from, how are we supposed to remember how
all of these things relate, meaning what is an
easy way to relate them all in our minds.
Imax Vmax/R
V in phase with I
Because resistors are simple
Current comes first since itcharges capacitor
Like a wire at high w
Opposite of capacitor
Like a wire at low w
10
please help, I'm confused on how to interpret
the current in the voltage phasor diagram
Makes sense to write everything in terms of I
since this is the same everywhere in a one-loop
circuit
Vmax Imax XC
V 90o behind I
Vmax Imax XL
emax
V 90o ahead of I
Vmax Imax R
Always looks the same. Only the lengths will
change
V in phase with I
Prelecture animation
11
The voltages still add up
But now we are adding vectors
12
Making this simpler
Imax XL
emax
Imax R
Imax XC
13
Making this simpler
emax Imax Z
Imax(XL-XC)
Imax R
14
Making this simpler
15
Making this simpler
what exactly is impedence?
(XL-XC)
R
Impedance Triangle
16
Summary
VCmax Imax XC
VLmax Imax XL
VRmax Imax R
emax Imax Z
Imax emax / Z
(XL-XC)
f
R
17
Example RL Circuit Xc0
Imax XL
Imax R
18
A B C
19
A B C
20
A B C
21
V
Imax XL
emax
Imax R
Imax XC
22
V
emax
Imax R
Imax XL
Imax XC
When current is maximumthe voltage across the
resistor is maximum
23
A B C
The description in the prelecture shows that the
voltage across a resistor is in phase with the
current an the current in this circuit is
determined by the generator so it is in phase
with it.
24
V
Imax XC
Imax R
emax
When the voltage across the capacitor is
maximum(fully charged) then
Imax XL
25
A B C
26
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

27
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
28
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)
29
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)
30
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)