Physics 212 Lecture 18, Slide 1

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Physics 212 Lecture 18
LC and RLC Circuits
- Oscillation frequency - Energy - Damping
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Note to self

• Exam
• Clicking for friends

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Some of your comments
Sometimes physics makes me cry
This stuff is cool!
Why in the world did I become an Engineer
major!?!?!?!?!?! Time to drop out and go into
radio and movie voice overs!
More about RLC circuits..the prelecture only
focused on LC.
all of it, this stuff is pretty tough
I'm cool, you're cool, this stuff is just cool.
I don't know anything. Is that a problem?
I particularly don't understand the damped
oscillatory behavior of resistors when they are
in circuit with a capacitor and an inductor.
How to use formulas and what happens when
switches open/close
all of it, especially the diff eq.
I have a problem. This class is hard. Give me an
A.
I may just be talking crazy, but the dampening of
the circuit reminded me of Schrodinger's Wave
function. Is there any correlation or is it just
coincidence/me not remembering correctly?
I need an idea for a halloween costume....any
suggestions?
"I'd like to get away from earth awhile and then
come back to it and begin over. May no fate
willfully misunderstand me and half grant what I
wish and snatch me away not to return. Earth's
the right place for love..." -Robert Frost
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WHAT IF I stuck my hand in the LHC beam? Would I
burn? Or like get mega-irradiated? Or would it
just kinda suck...? Would I get annihilated? I
mean have we done and experiment like this on
organic matter? I think we should, just kinda
chuck a plant in there and see if it like mutates
into like an ENT from Lord Of the Rings... or
like a turtle and we end up with DONATELLO...
A live frog levitates inside a 32 mm diameter
vertical bore of a Bitter solenoid in a magnetic
field of about 16 teslas at the Nijmegen High
Field Magnet Laboratory.
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I
Q
C
L
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In a closed Inductor Capacitor loop, the energy
oscillates indefinitely. Well, we know this isn't
really true, because perpetual motion machines
don't exist. Energy can't be transferred over a
given distance (d) via the length of the wire. So
techincally, all LC energy oscillations are
damped. The question is, HOW damped? How much
does the wire REALLY affect the current flow? How
strong REALLY is the wire's resistance over a
given distance d? How does this depend on the
material, orientation, and length of the wire?
Are copper wires more resistant than silicon
wires? Are vertically oriented wires more
resistant than horizontally oriented wires (with
respect to the force of gravity)? How negligible
REALLY is all of this information (i.e., to what
decimal place in LC circuit calculation do energy
values become inaccurate?)? We have always passed
off natural wire resistance throughout this
course. Well if these questions aren't answered I
will be forced to take from this class that
perpetual motion machines exist. Inside of me
would be a void....longing for this unattained
knowledge.
Will an LC circuit really oscillate without any
dampening for an extended period of time, or does
this only happen at the University of Illinois?
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At time t 0 the capacitor is fully charged with
Qmax and the current through the circuit is 0.
CD
What is the potential difference across the
inductor at t 0 ? A)  VL 0 B)  VL Qmax/C
C)  VL Qmax/2C
the voltage across the capacitor is q/v by
Kirchhoff's voltage rule that must be equal to
the voltage across the inductor
Pendulum
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At time t 0 the capacitor is fully charged with
Qmax and the current through the circuit is 0.
CD
What is the potential difference across the
inductor when the current is maximum ? A)  VL
0 B)  VL Qmax/C C)  VL Qmax/2C
dI/dt is zero when current is max
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The capacitor is charged such that the top plate
has a charge Q0 and the bottom plate -Q0. At
time t0, the switch is closed and the circuit
oscillates with frequency w 500 radians/s.
L 4 x 10-3 H
w 500 rad/s
What is the value of the capacitor C? A)  C 1
x 10-3 F B)  C 2 x 10-3 F C)  C 4 x 10-3 F
Omega is 1/sqrt(LC), so simply solving for C
gives 1 x 10-3.
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Which plot best represents the energy in the
inductor as a function of time starting just
after the switch is closed?

• Can UL ever be negative?
• Yes
• No

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Which plot best represents the energy in the
inductor as a function of time starting just
after the switch is closed?
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Just like LC circuit but energy but the
oscillations get smaller because of R
but answer looks kind of complicated
Concept makes sense
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Physics Truth 1
Even though the answer sometimes looks
complicated
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The elements of a circuit are very simple
This is all we need to know to solve for anything
!
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A Different Approach
Start with some initial V, I, Q, VL
Now take a tiny time step dt (1 ms)
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Calculation
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is
opened. What is QMAX, the maximum charge on the
capacitor?

• Conceptual Analysis
• Once switch is opened, we have an LC circuit
• Current will oscillate with natural frequency w0

• Strategic Analysis
• Determine initial current
• Determine oscillation frequency w0
• Find maximum charge on capacitor
• Maximum charge determines maximum voltage

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Calculation
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is opened.
IL
V
C
L
R
What is IL, the current in the inductor,
immediately AFTER the switch is opened? Take
positive direction as shown.

• IL 0

Current through inductor immediately AFTER switch
is opened IS THE SAME AS the current through
inductor immediately BEFORE switch is opened
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Calculation
IL
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is opened.
V
C
L
R
IL(t0) 0
The energy stored in the capacitor immediately
after the switch is opened is zero.

• TRUE (B) FALSE

BUT VL VC since they are in parallel
IMPORTANT NOTE DIFFERENT CONSTRAINTS AFTER
SWITCH OPENED CURRENT through INDUCTOR cannot
change abruptly VOLTAGE across CAPACITOR cannot
change abruptly
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Calculation
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is opened.
V
C
L
R
VC(t0) 0
IL(t0) 0
What is the direction of the current immediately
after the switch is opened?

• clockwise (B) counterclockwise

Current through inductor immediately AFTER switch
is opened IS THE SAME AS the current through
inductor immediately BEFORE switch is opened
BEFORE switch is opened Current moves down
through L
AFTER switch is opened Current continues to
move down through L
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Calculation
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is opened.
V
C
L
R
VC(t0) 0
IL(t0) 0
What is the magnitude of the current right after
the switch is opened?

• (B) (C)
  (D)

Current through inductor immediately AFTER switch
is opened IS THE SAME AS the current through
inductor immediately BEFORE switch is opened
VL 0
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Calculation
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is opened.
IL
Hint Energy is conserved
IL(t0) V/R
VC(t0) 0
What is Qmax, the maximum charge on the capacitor
during the oscillations?

• (B)
  (C) (D)