Physics 212 Lecture 11, Slide 1

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Physics 212 Lecture 11
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Music

• Who is the Artist?
• Michael McDonald
• Van Morrison
• Glenn Frey
• Robert Palmer
• David Bowie

CD
My favorite Van the Man album Many of my
friends agree that this one is on the list of 10
albums you must have on a desert island.. What
does that say about my friends?? Did you know
he wrote Gloria.. He did!
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Things you identified as difficult
Exponential change
Making a complicated circuit simple
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This is the value that makes slope equal to the
function
e 2.718281 1/e 0.367879
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This means that
e 2.7182818
Is a solution to equations that look like
So what ??
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dQ -Idt
I
R
Q
C
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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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CD
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How to think about RC circuits Episode 1 When C
is initially charged with Q0
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How to think about RC circuits Episode 2 When
there is a battery, and C is initially uncharged.
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Close S1 at t0 (leave S2 open)
R
C
V
2R
S1
S2
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Open S1 at tbig and close S2
R
C
V
2R
S1
S2
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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. After a long time S is opened How much
energy will ultimately be dissipated in R2 and R3
after S is opened ??

• 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
• S opened and C discharges with some time constant
• Strategic Analysis
• Determine voltage across C a long time after S
  closed
• Determine energy stored in capacitor once S
  opened

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Calculation
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is
closed. After a long time S is opened How much
energy will ultimately be dissipated in R2 and R3
after S is opened ??

• Why??
• VC must be zero because we said C was 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. After a long time S is opened How much
energy will ultimately be dissipated in R2 and R3
after S is opened ??
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

C
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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. After a long time S is opened How much
energy will ultimately be dissipated in R2 and R3
after S is opened ??
R1
R2
R3
C
V

• Why??
• After a long time, the current through C
  approaches 0 !
• Redraw circuit with open circuit in middle leg

• VC V3 IR3 (V/(R1R3))R3

C
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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. After a long time S is opened How much
energy will ultimately be dissipated in R2 and R3
after S is opened ??
R1
R2
R3
C
V

• Why??
• All of the energy stored on C will ultimately be
  dissipated in R2 and R3.
• Energy stored on C ½ CVC2
• VC (V/(R1R3))R3

C
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Follow-Up 1
S
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is
closed. After a long time S is opened How much
energy will ultimately be dissipated in R2 and R3
after S is opened ??
R1
R2
R3
C
V

• Why??
• Redraw Circuit (V1 and R1 gone)

• C discharges through R2 and R3 in series
• td RequivC (R2 R3)C

C
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Follow-Up 2
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is
closed. After a long time S is opened How much
energy will ultimately be dissipated in R2 and R3
after S is opened ??
S
R1
R2
R3
C
V

• Why??
• Plot exponential

• VC decreases to e-2 (14) of its original value
  at t 2RC
• R R2 R3

C
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Challenge
In this circuit, assume V, C, and Ri are known. C
initially uncharged and then switch S is closed.
S
R1
R2
R3
C
V
What is tc, the charging time constant?

• Strategy
• Write down KVR and KCR for the circuit when S is
  closed
• 2 loop equations and 1 node equation
• Use I2 dQ2/dt to obtain one equation that looks
  like simple charging RC circuit ( (Q/C)
  R(dQ/dt) V 0 )
• Make correspondence R ?, then t RC

C