Physics 212 Lecture 8, Slide 1

1
Physics 212 Lecture 8
Today's Concept Capacitors Capacitors in a
circuits Dielectrics Energy in capacitors
The weight allowance of a sparrow. African or
European, your choice.
This is pretty easy. You should have started
with this stuff first. But, I understand why you
did it. Let's face it - every professor wants a
smaller class size.....
2
Some Exam Stuff

• Exam next Wednesday at 700
• Covers material through lecture 8
• Bring your ID
• Review session Tuesday night. Mats will work
  through Spring/08 exam
• Old exams are online (for practice)
• Conflict exam at 515 sign up in your gradebook
  if you need to
• If you have conflicts with both of these contact
  us immediately

3
How confident are you in your understanding of
the concepts presented in the prelecture? A  I
am confused by all of it. B  I understand a
little but I am confused by most of it. C  I
understand some parts and I am confused by other
parts. D  I understand most of itE  I
understand everything
4
Your Thoughts
And an explanation of WHYYYY parallel and series
work the way they do... Especially with V.
Can we go over again what the point of capacitors
are? We're spending some time on them, so they
must have a real world application that is
relevant to something, but capacitors aren't
everyday objects that I recognize or understand
the purpose.
the idea of inverse capacitance in series
capacitors, and what it actually means.
Nothing really.. thank goodness! This is going to
be good to have on the exam (
Potential energy of capacitors and MULTIPLE
CAPACITOR SYSTEMS please.
Why people have ridiculously long answers to this
question
I get this, it will just be good to go over the
info again. Thank you for taking the time to get
these online learning tools working. They really
make lecture easier to understand.
5
Simple Capacitor Circuit
V
C
8
6
Dielectrics
I want to learn more about dialectrics.
what is the exact role of Kappa,,??
By adding a dielectric you are just making a new
capacitor with larger capacitance (factor of k)
11
7
Parallel Capacitor Circuit
The explanation for the series and parallel
laws.
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
14
8
Series Capacitor Circuit
Why is the charge on each capacitor of a series
combination equal?
V
Key point Q is the same for both capacitors
Key point Q VCtotal V1C1 V2C2
Also V V1 V2
17
9
Preflight 2
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
18
10
Preflight 4
Which has lowest total capacitance
C
C
C
C
C
Ctotal C
Ctotal Cleft Cright
Same
20
11
Similar to Preflight 6
Looking at complex circuits to understand
interplay of series and parallel capacitors
CD
Ctotal

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

24
12
Preflight 6
25
13
Energy in a Capacitor
Why is U1/2QVc? half?
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
26
14
Messing w/ Capacitors

• If connected to a battery V stays constant
• If isolated then total Q stays constant

V1 V0
C1 k C0
k
Why (preferably without using math) does
inserting a dielectric decrease voltage of the
plates?
Q1 Q0
k
C1 k C0
15
Preflight 8
33
16
Messing w/ Capacitors ACT
Two identical parallel plate capacitors are
connected to identical batteries. Then a
dielectric is inserted between the plates of
capacitor C1. Compare the energy stored in the
two capacitors.
C1
V
k2
A) U0 lt U1 B) U0 U1 C) U0 gt U1
35
17
Messing w/ Capacitors ACT
Two identical parallel plate capacitors are
connected to identical batteries. Then a
dielectric is inserted between the plates of
capacitor C1. Compare the energy stored in the
two capacitors.
C1
V
k2
A) Battery B) Inserting Dielectric
Dielectrics. I don't see how adding one to a
system can increase the potential energy if it is
reducing the strength of the field. Is this
happening since the battery itself is providing
more charge? Or is work being done inserting the
dielectric in the first place?
35
18
Preflight 10
C
A
B
U decreases. According to the equation .5Q2/C, Q
remains constant as C increases, so U will
decrease.
if U is 1/2 Q V, and I just decided that V was
less for the second capacitor, and I know that
the charge stored Q can't change, since it is
isolated, then I would have to say that U1gtU2.
33
19
Calculation
I would like to see a complicated work problem
involving the dielectric.

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width x0/4 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
x0/4
38
20
Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width x0/4 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
x0/4

• 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 !!
40
21
Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width x0/4 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
x0/4
Can consider capacitor to be two capacitances,
C1 and C2, in parallel
In general. For parallel plate capacitor C
e0A/d
43
22
Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width x0/4 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
x0/4
C2
C1

C1 3/4C0
In general. For parallel plate capacitor filled
with dielectric C ke0A/d
45
23
Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width x0/4 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
x0/4
C2
C
C1

C2 1/4 kC0
C1 3/4C0
C parallel combination of C1 and C2 C C1
C2
46
24
Calculation

• An air-gap capacitor, having capacitance C0 and
  width x0 is connected to a battery of voltage V.
  
• A dielectric (k) of width x0/4 is inserted into
  the gap as shown.
• What is Qf, the final charge on the capacitor?

V
x0/4
C2
C
C1

C2 1/4 kC0
C1 3/4C0
What is Q?
50
25
Have a GREAT Weekend!