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Ch.26 - Capacitors and Dielectrics.
LNK2LRN 2009/10 AP Physics C January 29 to February 5.
Plans for the Week and Assignments:
1. Friday(01/29): Ch.26 - Capacitance. HW: Read and Study pages
795-802, then solve problems 1, 5, 7, 13, and 15 on pages 822-3.
2. Monday(02/01): Combinations of Capacitors. HW: Read and Study
pages 802-06, then solve problems 16, 18, 21, 27, and 30 on pages
823-5.
3. Tuesday(02/02): Energy Stored in a Capacitor. Capacitors with
Dielectrics. HW: Read and Study pages 807-14, then solve
problems 31, 33, 34, 43, and 44 on pages 825-6.
4. Wednesday(02/03): Electric Dipole in an External Electric
Field. An Atomic Description of Dielectrics. HW: Read and Study pages
815-21, then solve problems 50 and 52 on page 826.
5. Thursday(02/04): REVIEW Ch.26. HW: Complete All Review
Handouts.
6. Friday(02/05): TEST on Ch.26 - Capacitance and Dielectrics.
HW: Go to website and study notes for Ch.27 - Current and Resistance.
Very Important: If you have any questions or miss a class, see
me before school (8:00 - 8:30 AM), during Lunch, or after school.
Best to send an email to rpersin@fau.edu.
Website Notes on Ch.26 - Capacitance and Dielectrics.
1. A capacitor is a device that stores charge. Capacitors are formed by a pair of
conductors separated by an insulator. They are found in computer keyboards,
automobile ignition systems, and flash cameras, for example.
2. The type of capacitor we are most interested in will have a charge Q and -Q
on each conductor. There will also be a resultant voltage, V, between the two
conductors.
3. This voltage is linearly dependent on the charge. If we triple the charge, we
triple the voltage. Because of this relationship, the ratio of Q / V is a constant
for that capacitor.
4. The value of Q/V for a given capacitor is known as its capacitance. This gives
the simple equation, C = Q / V .
5. The unit of capacitance is the Farad, after Michael Faraday (1791-1867).
It is equivalent to one coulomb per volt.
6. One Farad is an extremely large capacitance; most capacitors come in units of
micro (μ), nano (n), or pico (p) farads.
7. The capacitance of a capacitor is determined by two factors: (i) the geometry
of the capacitor, and (ii) the material between the conductors. This material is
known as a dielectric.
8. In a parallel plate capacitor, capacitance can be calculated by using the
equation, C = εoA / d , where C is capacitance, εo is the permittivity of free space,
A is the area of a plate, and d is the distance between the plates.
9. When one has several capacitors in a circuit, they can be combined in many
ways. There are equations which show how to calculate the equivalent capacitance,
Ceq for any type of combination.
10. For example, to find the equivalent capacitance of two capacitors in series, you
would add the inverse of their values and then take the inverse of their sum.
11. The equation for two capacitors connected in series is given by the following:
1 / Ceq = 1 / C1 + 1 / C2 .
12. To find the equivalent capacitance of 3 capacitors in parallel, you would add
their capacitances. Ceq = C1 + C2 + C3 .
13. In circuit applications, the capacitor can be subjected to numerous electrical,
mechanical, and environmental stresses.
14. One of the most noticeable effects of these stresses is the phenomena of
capacitance variation. The insertion of a non-conducting material between the
plates is an easy way to increase capacitance.
15. This increase is based on the value of κ, "kappa" , the dielectric constant.
"C" varies directly with "A" and "κ" and inversely with "d" or C = κεoA / d .
16. Any change in "C" must come as a result of some change or combination of
changes in "A", "κ", or "d".
17. The value of "A" is set by design and, once a capacitor is made, it is almost
impossible for "C" to change due to a change in "A". This is not a normal factor
in capacitance variation.
18. The value of "d" is also set by design. Some small changes in "d" can occur
on completed units due to external or internal pressure changes resulting in
mechanical movement of the electrodes. This is not usually critical nor does it
result in any large variations.
19. The value "κ" is also initially set by design in the choice of dielectric material
used to make the capacitor. Many factors will cause the "κ" to change, and this
change in "κ" will vary for different materials.
20. The "κ" in the basic formula is the effective dielectric constant of the total
"space" between the electrodes.
21. This "space" will consist of the dielectric material (or materials if a multiple
dielectric design), air, impregnant (if an impregnated unit), and even moisture
(if present).
22. The phenomena of capacitance is a type of electrical energy storage in the
form of a field in an enclosed space. The energy stored between the plates is
E = ˝ CV2.
And still, we need these steps to solve any problem in Physics:
(i) read the problem and identify the given variables
(ii) determine what you are asked to solve for
(iii) find the correct equation to use
(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown
(v) substitute-in the given information and simplify.
View the Powerpoint™: Click HERE.
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Scrambled Answers to Homework |
| 15.5 pF | 5.96 μF | 256 kV | 6 μC | 1.83 C |
| 11.1 kV/m | 48 μC | 2.00 μC | 9.00 V | 3.74 pF |
| 74.7 pC | 108 μC | 45.0 μC | 5.00 μC | 63.2 μC |
| 89.5 μC | 98.3 nC/m2 | 89.9 kV | 7.08x10-4 F | 17.0 μF |
| 26.3 μC | 54.0 μJ | 216 μJ | C0(√3 - 1)/2 | 6.04 μF |
| 2.40 kV | .150 J | 13.3 nC | Energy Doubles | 272 nC |
| (-9.1 i - 8.4 j)x10-12 C·m | 579 V | 81.3 pF | Half the Energy | 268 V |
| -2.09x10-8 Nm k | 489 pC | 112 nJ | 77.7 nV | 228 nJ |
THE
AP PHYSICS C ARCHIVES
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And Always Remember... "From Newtonian Mechanics, Through Quantum Theory, Without Physics, Life Would Be Dreary." |
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