Capacitors and Dielectrics With Calculations: For GENERAL PHYSICS 2/ Grade 12/ Quarter 3/ Week 3
Capacitors and Dielectrics With Calculations: For GENERAL PHYSICS 2/ Grade 12/ Quarter 3/ Week 3
Capacitors and Dielectrics With Calculations: For GENERAL PHYSICS 2/ Grade 12/ Quarter 3/ Week 3
WITH CALCULATIONS
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FOREWORD
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OBJECTIVES
At the end of this Self‒Learning Kit, you should be able to:
K: discuss about capacitors and its types, the total charge, the
charge on, and the potential difference across each capacitor
in the network given the capacitors connected in series/parallel;
: define potential energy and determine the potential energy
stored inside and across a capacitor;
LEARNING COMPETENCIES
Deduce the effects of simple capacitors (e.g., parallel-plate, spherical,
cylindrical) on the capacitance, charge, and potential difference when
the size, potential difference, or charge is changed (STEM_GP12EMIIId-
23).
Determine the total charge, the charge on, and the potential difference
across each capacitor in the network given the capacitors connected
in series/parallel (STEM_GP12EMIIId-25).
Determine the potential energy stored inside the capacitor given the
geometry and the potential difference across the capacitor
(STEM_GP12EMIIId-26).
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I. WHAT HAPPENED
Source: https://bit.ly/3mBqPtf
1. Everyone in the STEM class knows how to operate appliances but some
only knew what a capacitor looks like. To make her project, Anna
needs to know what a capacitor looks like. Let us help her recognize a
capacitor and draw it for her on her notebook.
A. B. C.
2. Anna is trying to put the capacitor for her series circuit project. Which
of the following she should follow? Why?
𝐶1
𝐶1 𝐶2 𝐶3 𝐶1 𝐶2 𝐶3
A. B. C.
𝐶2
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5. Is there a means of deducing a capacitor on the capacitance,
charge, and potential difference when the size, potential difference, or
charge is changed?
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II. WHAT I NEED TO KNOW
DISCUSSION:
CAPACITORS
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one cylinder to the other, therefore increasing the voltage across the
capacitor.
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DIFFERENT TYPES OF CAPACITORS
Electrolytic Capacitor
This is used when the large capacitor values are
required. The thin metal layer is used for one electrode
and for the second electrode (cathode) a semi-liquid
electrolyte solution which is in jelly or paste is used. The
dielectric plate is a thin layer of oxide, it is developed
electrochemically in production with thickness of the film.
It is possible to make capacitors with a large value of
capacitance for a physical size, which is in small and the
Source: https://bit.ly/3t6uWSd
Mica Capacitor
These capacitors are low loss capacitors, used at high frequencies and
is very stable chemically, electrically, and mechanically due to its specific
crystalline structure binding and typical layered structure.
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Paper Capacitor
The construction of this capacitor is between the two
tin foil sheets and they are separated from the paper or oiled
paper and thin waxed. The sandwiched foils and papers are
rolled in a cylindrical shape then it is enclosed in a plastic
capsule. The two foils of this paper capacitor attach to the
external load. The capacitance range of this capacitor is
Source: https://bit.ly/3t6uWSd
Film Capacitor
This capacitor used a thin plastic as a dielectric. The
film capacitor is prepared extremely thin using the
sophisticated film drawing process. There are different
types of film capacitors available like polyester film,
metalized film, polypropylene film, PTE film and polystyrene
film. The main difference between these film capacitors is
the material used as a dielectric and is chosen properly
Source: https://bit.ly/3t6uWSd
Non-Polarized Capacitor
The non-polarized capacitors are classified in to
two, the plastic foil capacitor and the electrolytic non-
polarized capacitor. The non-polarized capacitor requires
the Ac applications in a series or parallel with a signal or
power supply. The examples are the speaker crossover
Source: https://bit.ly/3t6uWSd
filters and power factor correction network. In these two
applications, a large AC voltage signal is applied across
the capacitor.
Ceramic Capacitor
This capacitor uses ceramic material as
dielectric. The ceramics are one of the first materials
used in the production of capacitors as an insulator.
The two common types of ceramic capacitors are
multilayer ceramic capacitor (MLCC) and ceramic
disc capacitor. The multilayer ceramic capacitors
are prepared by using the surface mounted
Source: https://bit.ly/3t6uWSd
(SMD)technology and they are smaller in size,
therefore, it used widely. While the ceramic disc capacitor is manufactured
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by coating a ceramic disc with silver contacts on both sides and to achieve
larger capacitance, these devices are made from multiple layers.
CAPACITANCE
In symbols,
The SI unit of capacitance is the farad, symbolized by letter F and was named
after Michael Faraday. It follows that one farad equals 1 coulomb per volt.
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This means increasing the area of the capacitor plates will also
increase the capacitance of a capacitor and vice versa.
C=
where, A is the area of one plate in square meters, d is the distance between
plates in meters, and is the permittivity of the insulating material or
dielectric.
DIELECTRICS
Dielectrics are insulators that serve three purposes:
1. To keep the conducting plates from coming in contact, allowing for
smaller plate separations and therefore higher capacitances;
2. To increase the effective capacitance by reducing the electric field
strength, which means you get the same charge at a lower voltage;
and
3. To reduce the possibility of shorting out by sparking (dielectric
breakdown) during operation at high voltage
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with a dielectric store the same charge as one without a dielectric, but a
lower voltage. Therefore, a capacitor with a dielectric in it is more effective.
POTENTIAL DIFFERENCE
If point A refers to the ground or infinity, the work done in bringing a unit
positive charge from ground or infinity to another point B is called the electric
potential at point B. Electric potential is designated by letter V.
Electric potential has the unit of volts. This unit is named after
Alessandro Volta who devised one of the first electric cells. It can be shown
that 1 volt= 1 joule/ coulomb (J/C).
On the other hand, if point A is not the ground nor the infinity, then the
work done in moving a unit positive test charge from point A to point B is
called the potential difference between points A and B.
= -
Sample Problem 1:
A charge of 6x 7
C is transferred from infinity to point A. If the work
done to do this is 1.2 x 5
J, what is the potential at point A?
Solution:
Given: W= 1.2 x 5
J
Q= 6x 7
C
Using the formula: V=
12 1
V=
6 1
= 20V
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Sample Problem 2:
Base on sample problem 1, what is the potential difference of point A
to B if point B is 37 V?
Solution:
= 37 V – 20 V
= 17 V
where, ⍺ means “proportional to”. We know that the voltage applied across
parallel plate is V= Ed where, V ⍺ E and V ⍺ Q and so is Q ⍺ V.
This is true in general that the greater the voltage applied to any capacitor,
the greater the charge stored in it.
Different capacitors will store different amounts of charge for the same
applied voltage, depending on their physical characteristics. We define their
capacitance (C) to be such that the charge (Q) stored in capacitor is
proportional to (C). The charge stored in capacitor is given by Q= CV. And
this equation expresses the two major factors affecting the amount of charge
stored. I we will rearrange it we will come up with C= .
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COMBINATION OF CAPACITORS
Capacitors may be connected in series or in parallel as shown in Figure
5. (a)&(b).
𝐶1 𝐶2 𝐶3 There are three important rules for capacitors in
series. These are:
1) The reciprocal of the total capacitance is
equal to the sum of the reciprocals of the
individual capacitance. It should be noted
that adding a capacitor in series decreases
Figure 5. (a) Capacitors in
series
the total capacitance of the combination.
1 2 3
Formulas to ponder!
Capacitors may be connected in series or in
parallel.
Series Capacitors Parallel Capacitors
𝐶𝑇 =𝐶1 𝐶2 𝐶3
𝐶𝑇 𝐶1 𝐶2 𝐶3
𝑉𝑇 =𝑉 𝑉 𝑉 𝑉𝑇 =𝑉1 𝑉2 𝑉3
𝑄𝑇 =𝑄1 𝑄2 𝑄3 𝑄𝑇 =𝑄1 𝑄2 𝑄3
𝐶1 𝐶2 𝐶3
a)
𝐶1
c) 𝐶3
𝐶1 𝐶2 𝐶3 𝐶2
b)
Solution:
Given: 1= 10.0F, 2= 5.0F, and 3= 4.0F
a) 1 2 3 are in series
1 1 1 1
1 5 4
2 4 5 11
= (where 20 is the least common denominator of the 3
2 2
capacitors)
11
= 1.8 F (the reciprocal of )
2
b) 1 2 3 are
in parallel
=10.0F + 5.0 F +4.0 F
= 19 F
c) Combination of series-parallel. First get the total capacitance of
1 2 .
1 1 1 1 2 3
1 5 1 1
3
C= 3.3 F (the reciprocal of )
1
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Performance Task:
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4) What are the two major factors affecting the amount of charge a
capacitor can store?
a. Voltage applied & capacitor’s physical characteristics
b. Dielectric & voltage applied
c. Capacitance & dielectric
d. Charge and voltage applied
Question: Infer what will happen to the capacitance, charge, and potential
difference in the respective capacitors when their size, potential difference,
or charge is changed.
Capacitance Potential Charge
Difference
Increase
Size
Decrease
Increase
Potential
Difference Decrease
Increase
Charge
Decrease
C. PROBLEM SOLVING
Directions: Read each problem very carefully. Solve the problems
and show your solutions on your notebook.
1) A 2.0 F and a 3.0 F are connected in series and subjected to a total
potential difference of 100 V. Find (a) their equivalent capacitance,
(b)charge stored in each capacitor, and (c) potential difference across
each capacitor.
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2) The capacitors in problem 1 are connected in parallel instead of being in
series. The combination is connected to 100 V line. Find (a) total
capacitance, (b) potential difference across each capacitor, and (c)
charge stored in each capacitor.
3) Suppose you have five 10.0 F capacitors. Show all possible connections of
all five capacitors to produce an equivalent capacitance of (a) 50.0 F, (b)
2.0 F, and (c) 35.0 F.
4) Solve the potential difference of point A and point B. If point A is 46 V and
point B is 100 V.
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REFERENCES
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DEPARTMENT OF EDUCATION
SCHOOLS DIVISION OF NEGROS ORIENTAL
ROSELA R. ABIERA
Education Program Supervisor – (LRMDS)
ARNOLD R. JUNGCO
PSDS-Division Science Coordinator
MARICEL S. RASID
Librarian II (LRMDS)
ELMAR L. CABRERA
PDO II (LRMDS)
STEPHEN C. BALDADO
Lay-out Artist
_________________________________________
ALPHA QA TEAM
JOSE MARI B. ACABAL
ROWENA R. DINOKOT
GENEVA FAYE L. MENDOZA
BETA QA TEAM
ZENAIDA A. ACADEMIA
ALLAN Z. ALBERTO
EUFRATES G. ANSOK JR.
ROWENA R. DINOKOT
LESTER C. PABALINAS
DISCLAIMER
The information, activities and assessments used in this material are designed to provide
accessible learning modality to the teachers and learners of the Division of Negros Oriental. The
contents of this module are carefully researched, chosen, and evaluated to comply with the set
learning competencies. The writers and evaluator were clearly instructed to give credits to
information and illustrations used to substantiate this material. All content is subject to copyright
and may not be reproduced in any form without expressed written consent from the division.
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SYNOPSIS
This self-learning kit contains interactive approach in describing
Capacitors and in deducing the effects of different physical
characteristics of capacitors on determining its capacitance, charge and
potential difference. It also contains problem solving that shows how to
calculate the equivalent capacitance and dielectrics of a network of
capacitors connected in series/parallel. The module is made simple, fun,
easy and interactive to help facilitate independent learning while learners
are at home.
ANSWER KEY
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