Physics 212 Lecture 11, Slide 1

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Physics 212 Lecture 11
Today's Concept RC Circuits (Circuits with
resistors capacitors batteries)
Where do I Start? This is pretty confusing to
me......
Differential equations?! Yuk.
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Your Thoughts
Where the exponential equations come from, which
ones we'll need to know and why circuits went
from being fun little puzzles to calculus-induced
headaches
??? I have no idea who and what the heck this
Kirchoff dude did???
I have no idea how you guys got the RC circuit
equations in the prelectures, once again physics
has made me fail at life.
For the powerpoint lectures you post online, can
it be the saved/marked version with the
work/correct answers selected on it, please.
Please go over the opening and closing of
switches in a circuit with capacitors and
resistors.
How we used KCL and KVL to come to the
differential equations, and demonstrate how to
use KCL and KVL to analyze a more complex circuit
(i.e., more than one capacitor/resistor in
series/parallel).
these concepts are a little confusing with the
derivatives.. are we supposed to take them or is
that just how the formulas for found?
How was your trip? Are you a part of the super
collider team for the US?
I have been attending all lectures and
discussions. I have also been reading from the
text in the spiral bound textbook. Why are so
many of these homework problems including
concepts that I have not seen in class. Am I not
reading far ahead enough? Am I missing something?
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Key Concepts

• Understanding the behavior of capacitors in
  circuits with resistors
• Understanding the RC time constant

Todays Plan

• Examples with switches closing and opening
• What changes?
• What is constant?
• Example problem
• Exponentials

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4
RC Circuit (Charging)
what is the meaning of time dependent???

• Capacitor uncharged, Switch is moved to position
  a
• Kirchoffs Voltage Rule
• Short Term (qq0)
• Long Term (Ic 0)

Intermediate
Will we have to know the equations for the exam
or will they be provided?
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immediately after the switch is closed the
capacitor does nothing until some charge builds
up on it
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After closing S1 for a long time, the capacitor
will be fully charged and there will be no more
current in the circuit. By the equation VIR, we
can conclude that the voltage of resistor R is
zero. Hence the voltage of the battery must be
all distributed on the capacitor.
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Close S1 at t0 (leave S2 open)
R
C
V
2R
S1
S2
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RC Circuit (Discharging)

• Capacitor has q0 CV, Switch is moved to
  position b
• Kirchoffs Voltage Rule
• Short Term (qq0)
• Long Term (Ic 0)

Intermediate
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A B C D
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Open S1 at tbig and close S2
R
C
V
2R
S1
S2
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A B C
Now the voltage is "shared" between all
components as modeled by Kirchhoff voltage rule..
.
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12
Close both S1 and S2 andwait a long time
R
C
V
2R
S1
S2
VC 2V/3
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DEMO ACT 1
Bulb 2
CD
S
R
R
V
Bulb 1
C

• What will happen after I close the switch?
• Both bulbs come on and stay on.
• Both bulbs come on but then bulb 2 fades out.
• Both bulbs come on but then bulb 1 fades out.
• Both bulbs come on and then both fade out.

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DEMO ACT 2
Bulb 2
CD
R
S
R
V
Bulb 1
C

• Suppose the switch has been closed a long time.
• Now what will happen after open the switch?
• Both bulbs come on and stay on.
• Both bulbs come on but then bulb 2 fades out.
• Both bulbs come on but then bulb 1 fades out.
• Both bulbs come on and then both fade out.

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Calculation
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is closed.
What is the voltage across the capacitor after
a long time ?

• Conceptual Analysis
• Circuit behavior described by Kirchhoffs Rules
  
• KVR SVdrops 0
• KCR SIin SIout
• S closed and C charges to some voltage with some
  time constant
• Strategic Analysis
• Determine currents and voltages in circuit a long
  time after S closed

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Calculation
S
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is closed.
What is the voltage across the capacitor after
a long time ?
R1
R2
R3
C
V
Immediately after S is closed what is I2,
the current through C what is VC, the voltage
across C?
(A) Only I2 0 (B) Only VC 0 (C) Both I2
and VC 0 (D) Neither I2 nor VC 0

• Why??
• We are told that C is initially uncharged (V
  Q/C)
• I2 cannot be zero because charge must flow in
  order to charge C

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Calculation
I1
S
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is closed.
What is the voltage across the capacitor after
a long time ?
R1
R2
R3
C
V

• Why??
• Draw circuit just after S closed (knowing VC 0)

• R1 is in series with the parallel combination of
  R2 and R3

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Calculation
S
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is closed.
What is the voltage across the capacitor after
a long time ?
R1
R2
R3
C
V
After S has been closed for a long time, what
is IC, the current through C ?
(A) (B) (C)

• Why??
• After a long time in a static circuit, the
  current through any capacitor approaches 0 !
• This means we Redraw circuit with open circuit in
  middle leg

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Calculation
S
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is closed.
What is the voltage across the capacitor after
a long time ?
R1
R2
R3
C
V
I
I

• Why??

• VC V3 IR3 (V/(R1R3))R3

R1
R3
VC
V
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Fraction of initial charge that remains
How many time constants worth of time that have
elapsed
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RC 2
RC 1
Time constant t RC The bigger this is, the
longer it takes to getthe same change
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• Which circuit has the largest time constant?
• Circuit 1
• Circuit 2
• Same

CD
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CD
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(No Transcript)
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See you Thursday!