Unformatted text preview: Physics 212
Lecture 8
Today's Concept:
Capacitors
Capacitors in a circuits, Dielectrics, Energy in capacitors Physics 212 Lecture 8, Slide 1 Music
Who is the Artist?
BB A)
B)
C)
D)
E) Michael McDonald
Van Morrison
Glenn Frey
Robert Palmer
David Bowie My favorite Van the Man album… Many of
Many
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??
does
Did you know he wrote “Gloria”.. He did!
Did From Last time:
Really.. Incredible
“Send in the Clowns”
By Van the Man A Classic, Of Course ! Physics 212 Lecture 8, Slide 2 Your Comments
“The last parts of this preflight, and if you could post my comment it would be awesome!
nt
Shout out to Sam!!!!!
Shout “Problem 8, 10, and 12 from the prelecture. ”
Problem
prelecture Will Do.. They were the hardest “I am confused about what things change when
am
dielectrics are added and what things stay the same.”
dielectrics “Most concepts, but specifically, why capacitance and potential energy are inversely
nergy
proportional. That seems counterintuitive to me. ”
Careful.. There are Three Variables
U = ½ Q2/C = ½ CV2
/C
“DO MORE HOMEWORK LIKE PROBLEMS! “
DO 35 “Dielectrics! especially when they do not cover the
Dielectrics! 30 whole space between capacitor plates! you're
blowing my mind! “ 25 WILL DO
See Calculation at End 20
15
10
5
0 05 Confused Confident Physics 212 Lecture 8, Slide 3 Some Exam Stuff
• Exam next Wednesday at 7:00
–
–
–
– Covers material through lecture 8
Bring your ID
Conflict exam at 5:15 – sign up in your gradebook if you need to
If you have conflicts with both of these contact us immediately https://my.physics.illinois.edu/undergrad/examprep/index.asp
Physics 212 Lecture 8, Slide 4 Simple Capacitor Circuit
Q V C +Q
Q V C Q=VC Q
This “Q” really means that the battery has
This
really
moved charge Q from one plate to the other,
moved
so that one plate holds +Q and the other Q.
so 8 Physics 212 Lecture 8, Slide 5 Dielectrics V C0
Q0=VC0 V C1=κC0
Q1=VC1 By adding a dielectric you are just making a
By
new capacitor with larger capacitance (factor of κ)
new 11 Physics 212 Lecture 8, Slide 6 Qtotal V Parallel Capacitor Circuit
C2 C1
Q1 = C1V Q2 = C2V Qtotal
Key point: V is the same for both capacitors
Key Point: Qtotal = Q1 + Q2 = VC1 + VC2 = V(C1 + C2)
Ctotal = C1 + C2
14 Physics 212 Lecture 8, Slide 7 Series Capacitor Circuit
Q Q=VCtotal
+Q
Q V V1 Q V +Q
Q V2 C1
C2 Q
Q Q
Key point: Q is the same for both capacitors
Key point: Q = VCtotal = V1C1 = V2C2
VC
Also: V = V1 + V2 17 Q/Ctotal = Q/C1 + Q/C2 1
1
1
=
+
C1
C2
Ctotal Physics 212 Lecture 8, Slide 8 Preflight 2
Which has lowest total capacitance:
C
C C C
C Ctotal = C 1/Ctotal = 1/C + 1/C
= 2/C
2/C
Ctotal = C/2 Ctotal = 2C 70
60
50
40
30
20
10 18 0 Physics 212 Lecture 8, Slide 9 Preflight 4
Which has lowest total capacitance: C
C C C
C Cleft = C/2 Cright = C/2 Ctotal = C
Ctotal = Cleft + Cright
70 Ctotal = C 50
40
30
20 Same 60 10
0 20 Physics 212 Lecture 8, Slide 10
10 Similar to Preflight 6
Q2
C2 V0
V1 C1 BB V2
Q1 V3 C3 Q3 Ctotal
Which of the following is NOT necessarily true:
A)
B)
C)
D)
E)
24 V0 = V1
Ctotal > C1
V2 = V3
Q2 = Q3
V1 = V2 + V3
Physics 212 Lecture 8, Slide 11
11 Preflight 6
BB To simplify,
To
Assume C1 = C2 = C3
Assume
NO
YES
NO
YES
NO
YES Q1 = Q2
V1 < V2
25 (A) V1 = V2 + V3 V1 > V2 Q2 = Q3 Q1 Q2 Q2
=
+
C1 C2 C3 Q2 = C2C3
Q1
C1 (C2 + C3 ) Q1 = Q2
V1 < V2 Q1 = Q2
V1 < V2 Q1 = Q2
V1 < V2 (B) (C) (D) Physics 212 Lecture 8, Slide 12
12 Energy in a Capacitor
In Prelecture 7 we calculated the work done to move charge Q from
In Prelecture we
one plate to another:
one C +Q V
Q U = 1/2QV
= 1/2CV2
=1/2Q2/C Since Q = VC This is potential energy waiting to be used… 26 Physics 212 Lecture 8, Slide 13
13 Messing w/ Capacitors
• If connected to a battery V stays constant
V1 = V V κ C1 = κ C Q1 = C1V1
= κ CV = κQ • If isolated then total Q stays constant κ Q1 = Q
C1 = κ C V1 = Q1/C1
= Q/κC = V /κ
Physics 212 Lecture 8, Slide 14
14 Preflight 8 BB 60 “When a dielectric is added to a capacitor, the
capacitance will increase. Because C=Q/V and Q is
constant, this means that V has to decrease. “ 50 “C=Q/V; since C increases and Q increases
proportionally with C, V is constant ” 20 “Capacitance lowers in case 2, meaning V increases in
case 2. ” 33 40
30 10
0 Physics 212 Lecture 8, Slide 15
15 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. C0 V A) U1 < U0 V B) U0 = U1 C1 BB
BB κ=2 C) U1 > U0 Compare using U = 1/2CV2 U1/U0 = κ
35 Potential Energy goes UP
Potential
UP Physics 212 Lecture 8, Slide 16
16 Preflight 10 BB A B C “U=(1/2)QV. The V decreases and the Q stays the
U=(1/2)QV.
same, since it has nowhere to go. Therefore, the
potential energy decreases. ”
potential
“Potential energy depends on the charge and the radius,
Potential
since neither has changed, it remains the same. “
since
“the addition of a dielectric increases the
the
capacitance, the charge, and the potential energy”
capacitance,
33 40
30
20
10
0 Physics 212 Lecture 8, Slide 17
17 Preflight 12
BB V must be the same ! 50
40 Q: Q1 Q2
=
C1 C2 U1 = 1 C1V 2
2
U:
U 2 = 1 C2V 2
2 C
Q1 = 1 Q2
C2 U1 = C1
U2
C2 30
20
10
0 Physics 212 Lecture 8, Slide 18
18 Calculation
C0 V x0 An airgap capacitor, V κ
x0/4 BB having capacitance C
0 and width x0 is
connected to a battery
of voltage V.
A dielectric (κ) of
width x0/4 is inserted
into the gap as shown. What is Qf, the final
• Conceptual Analysis:
charge on the
Q
capacitor?
C≡
V
What changes when the dielectric added? (A) Only C (B) only Q
(B) (C) only V
(C) (D) C and Q Adding dielectric changes the physical capacitor
V does not change and C changes
38 (E) V and Q
C changes
Q changes Physics 212 Lecture 8, Slide 19
19 Calculation
C0 V V x0 κ BB An airgap capacitor, x0/4 • Strategic Analysis:
–
– Calculate new capacitance C
Apply definition of capacitance to determine Q To calculate C, let’s first look at: Vleft (A) Vleft < Vright
(A) κ A dielectric (κ) of
width x0/4 is inserted
into the gap as shown.
What is Qf, the final
charge on the
capacitor? Vright (B) Vleft = Vright
(B) (C) Vleft > Vright
(C) The conducting plate is an equipotential !!
40 having capacitance C0
and width x0 is
connected to a battery
of voltage V. Physics 212 Lecture 8, Slide 20
20 An airgap capacitor,
having capacitance C0
and width x0 is
connected to a battery
of voltage V. Calculation
C0 V V x0 BB κ
x0/4 A dielectric (κ) of
width x0/4 is inserted
into the gap as shown.
What is Qf, the final
charge on the
capacitor? Can consider capacitor to be two capacitances, C1 and C2, in parallel κ = C1 κ C2 What is C1 ? (A) C1 = C0 (B) C1 = 3/4C0
(A)
(B) (C) C1 = 4/3C0
(C) In general. For parallel plate capacitor: C = ε0A/d
In
A = 3/4A0
C1 = 3/4 (ε0A0/d0)
d = d0 43 (D) C1 = 1/4C0
(D) C1 = 3/4C0
Physics 212 Lecture 8, Slide 21
21 Calculation
C0 V x0 V An airgap capacitor,
having capacitance C0
and width x0 is
connected to a battery
of voltage V. κ
x0/4 κ = C1 κ C2
C1 = 3/4C0 BB A dielectric (κ) of
width x0/4 is inserted
into the gap as shown.
What is Qf, the final
charge on the
capacitor? What is C2 ? (A)C2 = κC0 (B) C2 = 3/4 κC0
(B) (C) C2 = 4/3 κC0
(C) (D) C2 = 1/4 κC0
(D) In general. For parallel plate capacitor filled with dielectric: C = κε0A/d
A = 1/4A0
d = d0
45 C = ¼(κε0A0/d0) C2 = 1/4 κC0
Physics 212 Lecture 8, Slide 22
22 An airgap capacitor,
having capacitance C0
and width x0 is
connected to a battery
of voltage V. Calculation
C0 V x0 V κ BB A dielectric (κ) of
width x0/4 is inserted
into the gap as shown. x0/4 κ C = C1 κ What is Qf, the final
charge on the
capacitor? C2 C2 = 1/4 κC0 C1 = 3/4C0 What is C?
What (A) C = C1 + C2 (B) C = C1 + κ C2 (C) C = 1 + 1 (B)
C C 1
2
C = parallel combination of C1 and C2: −1 C = C1 + C2 C = C0 (3/4 + 1/4 κ)
46 Physics 212 Lecture 8, Slide 23
23 An airgap capacitor,
having capacitance C0
and width x0 is
connected to a battery
of voltage V. Calculation
C0 V V x0 κ
x0/4 κ C C1 = κ A dielectric (κ) of
width x0/4 is inserted
into the gap as shown.
What is Qf, the final
charge on the
capacitor? C2
C1 = 3/4C0 C2 = 1/4 κC0 C = C0 (3/4 + 1/4 κ)
What is Q? C≡ Q
V Q = VC 3 1 Q f = VC0 + κ 4 4 50 Physics 212 Lecture 8, Slide 24
24 Different Problem
V Q0 C0
x0 V κ BB
BB 1/4x0 (A) Vf < V (B) Vf = V
(B) Q stays same: no way to add or subtract
stays
We know C: (property of capacitor)
We (C) Vf > V
(C) An airgap capacitor,
having capacitance C0
and width x0 is
connected to a battery
of voltage V and then
battery is
disconnected.
A dielectric (κ) of
width 1/4x0 is inserted
into the gap as shown.
What is Vf, the final
voltage on the
capacitor? Q = Q0 = C0V C = C0 (3/4 + 1/4 κ)
Vf = Q/C = V/(3/4 + 1/4 κ) Physics 212 Lecture 8, Slide 25
25 Different Problem
V Q0 C0
x0 BB V κ
1/4x0 An airgap capacitor,
having capacitance C0
and width x0 is
connected to a battery
of voltage V and then
battery is disconnected.
A dielectric (κ) of width
1/4x0 is inserted into the
gap as shown.
What is Vf, the final
voltage on the capacitor? Vf = Q/C = V/(3/4 + 1/4 κ)
How did energy stored in capacitor
How
change when dielectric inserted?
change (A) U increased (B) U stayed same (C) U decreased
(B)
(C) U = ½ Q2/C
Q remained same
C increased U decreased
Physics 212 Lecture 8, Slide 26
26 ...
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 Spring '11
 MESTRE
 Physics, Energy, Ctotal

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