Download GP2-Q4-CAPACITANCE AND DIELECTRICS

Central Philippine Adventist College-Academy
Alegria, Murcia, Negros Occidental
Contact nos. 704-1800 (126)
E-mail Add: [email protected]
“Promoting Excellence in Service, Faith and Learning”
LEARNING MODULE
GENERAL PHYSICS 2 STEM 12 | Q4
1st – 6th week
NAME OF STUDENT:
TEACHER:
______________________________
_
Ms. Chrisma Jane C. Manalo
Connect with God
Week 1-3
Heart: Capacitor of God’s Words
I have hidden your word in my heart that I might not sin against you.
—PSALM 119:11
In Psalm 119:11, the writer reminded us of the importance of storing and treasuring God’s
Word in our hearts. He has made room and stored up the most valuable resource there is—God’s truth
and promises.
We hide God’s Word in our hearts as we read it, meditate on it, memorize it, cling to it, pray it,
and sing it. We store it in our hearts because it gives us strength. It protects us. Sustains us. Convicts us.
And it also is one of the primary ways God is making us better, more like Christ (Romans 12:2).
In the busyness and messiness of our daily lives, it’s easy to forget what is most important. We can let
daily tasks get in the way of feeding on our daily bread. What our hearts need most is to be filled with
what lasts. We need the power and truth of God’s Word to keep us going and to guard us from sin.
What will you fill your heart with today? What will you treasure? What will you make room to store up?
Whatever you do, make it a priority to hide God’s Word in your heart!
Prepare to Learn
MODULE 1: CAPACITANCE AND DIELECTRICS
CONTENT STANDARD
The learner demonstrates understanding of key
concepts of: Capacitance and capacitors: a.
Capacitors in series and parallel; b. Energy stored
and electric-field energy in capacitors; Dielectrics
PERFORMANCE STANDARD
The learner is able to use theoretical and
experimental approaches to solve multi-concept
and rich-context problems involving electricity
and magnetism.
LEARNING COMPETENCIES
After going through this lesson, you are expected to:
• 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.
• Calculate the equivalent capacitance of a network of capacitors connected in series/parallel.
• Determine the total charge, the charge on, and the potential difference across each capacitor in
the network given the capacitors connected in series/parallel.
• Determine the potential energy stored inside the capacitor given the geometry and the potential
difference across the capacitor.
• Describe the effects of inserting dielectric materials on the capacitance, charge, and electric field
of a capacitor.
• Solve problems involving capacitors and dielectrics in contexts such as, but not limited to,
charged plates, batteries, and camera flash lamps.
Look at your appliances at home. Can you imagine the complex circuitry that lies behind your
common household appliances? Do you know the underlying components that enables it to operate at
ease? These devices and appliances lessen our workloads in our daily life.
In this lesson, you will learn the use and function of capacitor and define capacitance.
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Look at picture (a) shown. What do you think is the use of
batteries in our devices? How important is energy storage in
devices and modern electronics?
Acquire New Skills
Every complex and modern gadget made today consists of different electronic components. One
of those is known as a capacitor. A Capacitor is a component which has the ability or “capacity” to store
energy in the form of an electrical charge producing a potential difference (Static Voltage) across its
plates, much like a small rechargeable battery.
There are many different kinds of capacitors which are available from very small capacitor beads used in
resonance circuits to large power factor correction capacitors, but they all do the same thing, they store
charge.
In its basic form, a capacitor consists of two or more parallel conductive (metal) plates which are
not connected or touching each other but are electrically separated either by air or by some form of a
good insulating material such as waxed paper, mica, ceramic, plastic, or some form of a liquid gel as used
in electrolytic capacitors. The insulating layer between a capacitors plates is commonly called the
Dielectric.
Due to this insulating layer, DC current cannot flow through the capacitor as it blocks it allowing
instead a voltage to be present across the plates in the form of an electrical charge.
Capacitance is the ability of an object (in this case a circuit element) to store an electric charge
Q. The circuit element that has this property is called a capacitor. When a capacitor is connected in series
to a power supply (in this case, a DC power supply of potential V), charges – Q and + Q are stored in the
plates of the capacitor when they are connected to the negative and positive terminals of the DC-power
supply, respectively. The potential across the plates of this capacitor is then equal to the potential V of
the power supply. Capacitance C is defined as the ratio of the charge Q = |±Q| stored in each plate to
the potential V between the plates. Mathematically, capacitance can be defined by
𝑄
𝐴
𝐶 = = 𝜀0
𝑉
𝑑
Where,
C, is the value of capacitance Farad unit
𝜀0, the permittivity of free space 8.854 x10-12
Q, the value of charge stored in coulomb
A, surface area of plates in meters squared (m 2)
V, voltage across capacitors in volts
d, distance between the plates in meters
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CAPACITORS IN SERIES AND PARALLEL CONNECTION
Capacitors can be installed in a circuit in two different configurations.
1. Series Connection
Electric charge Q is a conserved physical quantity. This means that the total charge in a circuit stays the
same. As a charge Q, therefore, passes through a SERIES (or a one-path system) connection of capacitors,
1
1
1
1
each capacitor gets the same total charge Q such that Q1 = Q , Q2 = Q and 𝐶𝑡 = 𝐶1 + 𝐶2 + ⋯ + 𝐶𝑛.
2. Parallel Connection
When Q passes through a PARALLEL (or a multi-path system) connection of capacitors, Q splits up
according to the number of paths present. In this case, Q = Q1 + Q2 and 𝐶𝑡 = 𝐶1 + 𝐶2 + 𝐶3 + ⋯ + 𝐶𝑛
ENERGY STORED AND ELECTRIC FIELD ENERGY IN CAPACITORS
In a charged parallel-plate capacitor, the stored charges ±Q in the plates give rise an electric field E
between the plates. This is illustrated in the figure below:
To gain insight into how this energy may be expressed (in terms of Q and V), consider a charged,
empty, parallel-plate capacitor; that is, a capacitor without a dielectric but with a vacuum between its
plates. The space between its plates has a volume Ad, and it is filled with a uniform electrostatic field E.
The total energy UC of the capacitor is contained within this space. The energy density UE in this space is
simply UC divided by the volume Ad. If we know the energy density, the energy can be found as U C = UE
(Ad). We will learn in Electromagnetic Waves (after completing the study of Maxwell’s equations) that
the energy density UE in a region of free space occupied by an electrical field E depends only on the
magnitude of the field and is:
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Multiplying the energy density by the volume between the plates, we obtain the amount of
energy stored between the plates of a parallel-plate capacitor.
In this derivation, we used the fact that the electrical field between the plates is uniform so that
𝑉
𝐴
𝐸 = 𝑑 and 𝐶 = 𝜖0 𝑑 .Because 𝐶 =
𝑄
𝑉
we can express this result in other equivalent forms:
Dielectric is an insulating material or a very poor conductor of electric current. When dielectrics
are placed in an electric field, practically no current flows in them because, unlike metals, they have no
loosely bound, or free, electrons that may drift through the material. Instead, electric polarization occurs.
The positive charges within the dielectric are displaced minutely in the direction of the electric field, and
the negative charges are displaced minutely in the direction opposite to the electric field. This slight
separation of charge, or polarization, reduces the electric field within the dielectric.
Challenge Yourself
ASSESSMENT: Read and understand each item and choose the letter of the best answer. Write your
answers on the space provide before the number.
1. Capacitor stores which type of energy?
A) kinetic energy
B) vibrational energy
C) potential energy D) heat energy
2. Why does capacitor block dc signal at steady state?
A) due to high frequency of dc signal
B) due to zero frequency of dc signal
C) capacitor does not pass any current at steady state
D) due to zero frequency of dc signal
3. What is the value of capacitance of a capacitor which has a voltage of 4V and has 16 C of charge?
A) 2F
B) 4F
C) 6F
D) 8F
4. Which of the following is a passive device?
A) Transistor
B) Rectifier
C) Capacitor
D) Vacuum Tubes
5. Evaluate the circuit shown at the right. What is the
charge of capacitor C3?
A) 30uC
B) 40uC
C) 50uC
D) 60uC
6. Refer to the diagram in item number 5. What is the
voltage across C4?
A) 5V
B) 10V
C) 15V
D) 20V
7. Evaluate the circuit shown below. What is the voltage
across C1?
A) 5V
B) 10V
C) 15V
D) 20V
GENPHYS2|SY 21-22
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8. Refer to the diagram in item number 7. What is the charge of C4?
A) 60uC
B) 80uC
C) 50uC
D) 70uC
9. A potential difference of 100 mV exists between the outer and inner surfaces of a cell membrane. The
inner surface is negative relative to the outer. How much work is required to move a sodium ion Na+
outside the cell from the interior? (Express your answer in electron volts. A single-charged ion has a
charge of A eV, 1 eV = 1.6 × 10−19 J.)
A) 0.1 eV
B) 0.2eV
C) -0.1eV
D) -0.2eV
10. A parallel-plate capacitor has 4.00 cm2 plates separated by 6.00 mm of air. If a 12.0V battery is
connected to this capacitor, how much energy does it store in Joules?
A) 4.25 × 10-11 J
B) 4 × 10-11 J
C) 4.5 × 10-11 J
D) 3.9 × 10-11 J
Apply Learned Skills
ACTIVITY 2: Explain the following
Write your explanation in your answer sheet.
1. What is the relationship between the electric field E and the electric potential V between the plates
of the capacitor? Explain.
2. Where is the energy stored in a parallel-plate capacitor? Explain.
3. Let the energy stored “in the capacitor” be U. Show that U is given by the expression: 𝑈 = ½
[Hint: The power P in the capacitor is given by 𝑃 =
𝑑𝑈
𝑑𝑡
= 𝐼𝑉 where 𝐼 =
𝑑𝑄
𝑑𝑡
𝑄2
𝐶
. This is a simple exercise on
integration.]
4. Calculate the energy stored in the capacitor network in the
figure below when the capacitors are fully charged and when the
capacitances are C1 = 12.0 μF, C2 = 2.0 μF, and C3 = 4.0 μF,
respective
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GENPHYS2|SY 21-22
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