Physics 212 Lecture 8, Slide 1

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Physics 212 Lecture 8
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Music

• Who is the Artist?
• Ray Charles
• Solomon Burke
• Henry Butler
• Johnny Adams
• Otis Redding

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I like this format a lot better than last year,
but I would still like to be doing more
quantitative questions in lecture since those are
the harder ones.
Even though i feel like i am learning, i also
feel that if i were to take a test on this
material i would not do well.
I liked the format of PHYS211 last semester
better I was able to learn the material better
in lecture than at home on my laptop, especially
when I'm pressed for time and have to rush it.
I would like more quantitative examples.
Try to explain concepts as well as do problems.
I think this lecture system is much better than
last semester, 211.
I think overall the experience has been great
because I learn more. However, I do seem to be
spending quite alot of time on the prelectures
and preflights in my attempt to understand
everything fully.
I like the enthusiasm in lecture now, but I
dislike how figuring out how to do the actual
calculations of the concepts is essentially
placed on us. We maybe do one example calculation
a week I would love to see more. We don't need
the whole hour on conceptual stuff. That can be
read up on, it's harder to learn calculating
stuff on your own.
I think this set up is very good and helpful. I
wasn't happy about the extra work at first, but
they definitely make the lectures more beneficial
since I already have some ideas about the
material heading in. I would continue to do more
problems in class.
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Things you identified as difficult

• Wire up capacitors in different ways in a
  circuit - What is Q, V, C, E etc. -
  Comparing cases, when is V the same, when Q the
  same, etc. - How do I know what changes from one
  case to the next ?
• Dielectrics - Does it take work to stick some
  into a capacitor?

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Simple Capacitor Circuit
V
C
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Dielectrics
By adding a dielectric you are just making a new
capacitor with larger capacitance (factor of k)
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Parallel Capacitor Circuit
C2
C1
V
Key point V is the same for both capacitors
Key Point Qtotal Q1 Q2 VC1 VC2 V(C1
C2)
Ctotal C1 C2
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Series Capacitor Circuit
V
Key point Q is the same for both capacitors
Key point Q VCtotal V1C1 V2C2
Also V V1 V2
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Preflight 1
Which has lowest total capacitance
C
C
C
C
C
1/Ctotal 1/C 1/C
2/C
Ctotal 2C
Ctotal C/2
Ctotal C
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Preflight 4
Which has lowest total capacitance
C
C
C
C
C
Ctotal C
Ctotal Cleft Cright
Same
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Preflight 7
CD
Ctotal

• Which of the following is NOT true
• V0 V1
• Ctotal gt C1
• V2 V3
• Q2 Q3
• V1 V2 V3

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Preflight 7
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Energy in a Capacitor
In pre-lecture 7 we calculated the work done to
move charge Q from one plate to another
Q
C
V
U 1/2QV
-Q
This is potential energy waiting to be used
(big bang)
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Energy in a Capacitor with dielectric
Its simple just use the new capacitance C1 kC0
Case 1 If Q is constant (not attached to
battery) then V changes
C0
Q
Q
C1kC0
V0
V1
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Energy in a Capacitor with dielectric
Case 2 If V is constant (cap attached to
battery) then Q changes
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Preflight 10
For dielectric, there's field created that is
opposing the field by the conductors, so the
field is smaller, which means the voltage is
smaller as well since V Ed.
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Preflight 12
For dielectric, there's field created that is
opposing the field by the conductors, so the
field is smaller, which means the voltage is
smaller as well since V Ed.
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Preflight 15
CD
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Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
fx0
Q
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Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
fx0
Q

• Strategic Analysis
• Calculate new capacitance C
• Apply definition of capacitance to determine Q

(A) Vleft lt Vright (B) Vleft Vright
(C) Vleft gt Vright
The conducting plate is an equipotential !!
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Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
fx0
Q

• Can consider capacitor to be two capacitances,
  C1 and C2

In general. For parallel plate capacitor C
e0A/d
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Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
fx0
C2
Q
C1

C1 (1-f)C0
In general. For parallel plate capacitor filled
with dielectric C ke0A/d
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Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
fx0
C2
C
Q
C1

C1 (1-f)C0
C2 kfC0
C parallel combination of C1 and C2 C C1
C2
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Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
fx0
C2
C
Q
C1

C1 (1-f)C0
C2 kfC0
C C0 (f(k-1) 1)
What is Q?
Q increases linearly from Q0 to kQ0
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Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
fx0
C2
C
Q
C1

C1 (1-f)C0
C2 kfC0
C C0 (f(k-1) 1)
U ½ QV Q increased V remained same
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Different Problem

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V
  and then battery is disconnected.
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Vf, the final voltage on the capacitor?

Q0
C0
V
V
x0
fx0
Q
(A) Vf lt V (B) Vf V (C) Vf
gt V
Q stays same no way to add or subtract
We know C (property of capacitor)
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Different Problem

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V
  and then battery is disconnected.
• A dielectric (k) of width fx0 is inserted into
  the gap as shown.
• What is Vf, the final voltage on the capacitor?

Q0
C0
V
V
x0
fx0
Vf Q/C V / (f(k-1) 1)
How did energy stored in capacitor change when
dielectric inserted?

• U increased (B) U stayed same (C) U
  decreased

U ½ QV Q remained same V decreased
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Extra 1
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Extra 2
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Extra 3