Physics 212 Lecture 18, Slide 1

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Physics 212 Lecture 18
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Music
CD

• Whats the name of the band?
• Phish
• String Cheese Incident
• Daves Tune
• Umphreys McGee
• Govt Mule

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Exam II Review Monday, March 24, 5-7 pm Loomis
141 (here) Mats will work through Fall 2004 Exam
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Things you identified as difficult
I'm having some trouble with the oscillation
graphs, and how to relate everything in the
equations. RLC circuits. The concept of damping
and the difference between the oscillation
frequency and the natural frequency. Too much
calculus! AAAHHHHHHHHHHHHHHH!!!!!!!
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I
Q
C
L
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1) 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
capacitor at t 0 ? A)  VC 0 B)  VC
Qmax/C C)  VC Qmax/2C
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1) At time t 0 the capacitor is fully charged
with Qmax and the current through the circuit is
0.
What is the potential difference across the
inductor at t 0 ? A)  VL 0 B)  VL Qmax/C
C)  VL Qmax/2C
Pendulum
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2) 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
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4) The current in an LC circuit is a sinusoidal
oscillation, with frequency w.
If the inductance of the circuit is increased,
what will happen to the frequency ?
A)  increase B)  decrease C)  doesn't change
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5) The current in an LC circuit is a sinusoidal
oscillation, with frequency w.
If the capacitance of the circuit is increased,
what will happen to the frequency ?
A)  increase B)  decrease C)  doesn't change
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7) 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
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8) 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 first time (tgt0) that the charge on
the bottom plate of the capacitor is Q. A)  t
3.14 x 10-3 seconds B)  t 6.28 x 10-3
seconds C)  t 12.6 x 10-3 seconds D)  t 250
x 10-3 seconds E)  t 500 x 10-3 seconds
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9) 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 VC, the maximum voltage across
the capacitor?

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

• 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. What is VC, the maximum voltage across
the capacitor?
IL
V
C
L
R
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
The switch in the circuit shown has been closed
for a long time. At t 0, the switch is
opened. What is VC, the maximum voltage across
the capacitor?
IL
V
C
L
R
IL(t0) gt 0
BUT VL VC since they are in parallel
IMPORTANT NOTE DIFFERENT CONSTRAINTS AFTER
SWITCH OPENED CURRENT through INDUCTOR cannot
change VOLTAGE across CAPACITOR cannot change
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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 VC, the maximum voltage across
the capacitor?
V
C
L
R
VC(t0) 0
IL(t0) gt 0
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. What is VC, the maximum voltage across
the capacitor?
V
C
L
R
VC(t0) 0
IL(t0) gt 0
Current through inductor immediately AFTER switch
is opened IS THE SAME AS the current through
inductor immediately BEFORE switch is opened
dIL/dt 0 ? 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. What is VC, the maximum voltage across
the capacitor?
IL
IL(t0) V/R
VC(t0) 0
Current is maximum at t 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. What is VC, the maximum voltage across
the capacitor?
IL
Imax V/R
Qmax V/(w0R)

ALWAYS TRUE C Q/V