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Senior High School, NOT, , General Physics 2, Quarter 3 – Module 3, Capacitance and Capacitors, , Department of Education ● Republic of the Philippines

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General Physics 2- Grade 12, Alternative Delivery Mode, Quarter 3 - Module 3: Capacitance and Capacitors, First Edition, 2020, Republic Act 8293, section 176 states that: No copyright shall subsist in any, work of the Government of the Philippines. However, prior approval of the government, agency or office wherein the work is created shall be necessary for exploitation of such, work for profit. Such agency or office may, among other things, impose as a condition, the payment of royalty., Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,, trademarks, etc.) included in this book are owned by their respective copyright holders., Every effort has been exerted to locate and seek permission to use these materials, from their respective copyright owners. The publisher and authors do not represent, nor claim ownership over them., Published by the Department of Education – Division of Cagayan de Oro, Schools Division Superintendent: Dr. Cherry Mae L. Limbaco, CESO V, Development Team of the Module, Author:, , Ariel V. Fabrigas, SPST-I, , Content Evaluator: Glenmark A. Dal, MT-I, Layout and Design: Arian M. Edullantes, Language Evaluator: Pinky Babiera Dela Calzada, Management Team, Chairperson:, Cherry Mae L. Limbaco, Ph.D., CESO V, Schools Division Superintendent, Co-Chairperson:, , Rowena H. Para-on, Ph.D., Asst. Schools Division Superintendent, , Members, , Lorebina C. Carrasco, OIC-CID Chief, Jean S. Macasero, EPS - Science, Joel D. Potane, LRMS Manager, Lanie O. Signo, Librarian II, Gemma Pajayon, PDO II, , Printed in the Philippines by, Department of Education – Division of Cagayan de Oro City, Office Address:, Fr. William F. Masterson Ave Upper Balulang Cagayan de Oro, Telefax:, (08822)855-0048, E-mail Address:, [email protected]

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Senior, High, School, Senior, High, School, , General Physics 2, Quarter 3 - Module 3, Capacitance and Capacitors, , This instructional material was collaboratively developed and reviewed, by educators from public schools. We encourage teachers and other education, stakeholders to email their feedback, comments, and recommendations to the, Department of Education at [email protected], We value your feedback and recommendations., , Department of Education ● Republic of the Philippines, , FAIR USE AND CONTENT DISCLAIMER: This SLM (Self Learning Module) is, for educational purposes only. Borrowed materials (i.e. songs, stories, poems,, pictures, photos, brand names, trademarks, etc.) included in these modules are, owned by their respective copyright holders. The publisher and authors do not, represent nor claim ownership over them.

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Table of Contents, What This Module is About………………………………………………………………………..i, What I Need to Know………………………………………………………………………………i, How to Learn from this Module…………………………………………………………………...ii, Icons of this Module………………………………………………………………………………..ii, What I Know………………………………………………………………………………………..iii, , Lesson 1: Capacitance and Capacitors, What I Need to Know...…………………………………………………………...1, What Is It…………………………….……………………………………………..1, What I Have Learned…………………………………………………………….3, What I Can Do…………………………………………………………………….3, , Lesson 2: Capacitors in Series and Parallel, What’s In………………………………………………………………………… 4, What I Need to Know……………………………………………………………..4, What’s More……………………………………………………………………….5, What I Have Learned…………………..………………………………………...5, , Lesson 3: Energy Stored and Electric Field Energy, in Capacitor, What’s In………………………………………………………………………… 6, What I Need to Know…………………………………………………………….6, What I Have Learned…………………………………………………………… 7, What’s More …………………………………………………………………….. 8, , Summary………………………………………………………………………………………….. 8, Assessment: (Post-Test) ……………………………………………...…………………………9, Key to Answers…………………………………………………………………………………… 11, References……………………………………………………………………………………… ..12

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Module 3, Capacitance and Capacitors, What This Module is About, This module showcases your knowledge in Capacitors and Capacitance and critical, problem-solving skills in analyzing capacitors in different network configuration. It also tackles, the fundamental principles of Dielectrics and Capacitor’s Electric Field Energy., , •, •, •, , This module has three (3) lessons:, Lesson 1: Capacitance and Capacitors, Lesson 2: Capacitors in Series and Parallel, Lesson 3: Energy Stored and Electric Field Energy in Capacitors, , What I Need to Know, After going through this module, you are expected to:, , _, , 1. 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_GP12EM-IIId-23), 2. Calculate the equivalent capacitance of a network of capacitors connected in, series/parallel (STEM_GP12EM-IIId-24), 3. 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_GP12EM-IIId-25), 4. Determine the potential energy stored inside the capacitor given the geometry and the, potential difference across the capacitor (STEM_GP12EM-IIId-26), 5. Describe the effects of inserting dielectric materials on the capacitance, charge, and, electric field of a capacitor (STEM_GP12EM-IIId-29), 6. Solve problems involving capacitors and dielectrics in contexts such as, but not limited, to, charged plates, batteries, and camera flashlamps. (STEM_GP12EM-IIId-30), , i

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How to Learn from this Module, To achieve the objectives cited above, you are to do the following:, •, , Take your time reading the lessons carefully., , •, , Follow the directions and/or instructions in the activities and exercises diligently., , •, , Answer all the given tests and exercises., , Icons of this Module, What I Need to, Know, , This part contains learning objectives that, are set for you to learn as you go along the, module., , What I know, , This is an assessment as to your level of, knowledge to the subject matter at hand,, meant specifically to gauge prior related, knowledge, This part connects previous lessons with that, , What’s In, , of the current one., , What’s New, , An introduction of the new lesson through, various activities, before it will be presented, to you, , What is It, , These are discussions of the activities as a, way to deepen your discovery and understanding of the concept., , What’s More, , These are follow-up activities that are intended for you to practice further in order to, master the competencies., , What I Have, , Activities designed to process what you, , Learned, , have learned from the lesson, , What I can do, , These are tasks that are designed to showcase your skills and knowledge gained, and, applied into real-life concerns and situations., , ii

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What I Know, PRE-TEST : MULTIPLE CHOICE., Directions: Read and understand each item and choose the letter of the best answer. Write, your answers on the space provide before the number., , ___ 1. It is the unit of capacitance., A) Coulomb, B) Volts, , C) Farad, , D) Ampere, , ___ 2. Which of the following refers to the function of a capacitor?, A) It dissipates voltage across the circuit., B) It absorbs and stores electrical charge., C) It acts as the main source of electric potential., D) It allows DC signals to pass through., ___ 3. Capacitor stores which type of energy?, A) kinetic energy, B) vibrational energy, C) potential energy, D) heat energy, ___ 4. 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., ___ 5. If a parallel plate capacitor of plate area 2 m2 and plate separation of 1 m, stores the charge of 1.77 x 10-11 C, what is the voltage across the capacitor?, A) 1V, B) 2V, C) 3V, D) 4V, ___ 6. Which of the following is a passive device?, A) Transistor, B) Rectifier C) Capacitor, , D) Vacuum Tubes, , ___ 7. What is the value of capacitance of a capacitor which has a voltage of 4V and, has 16C of charge?, A) 2F, B) 4F, C) 6F, D) 8F, ___ 8. Of which medium is capacitance high?, A) Air, B) Mica, C) Water, , D) Metal, , ___ 9. What is the voltage of a battery connected to a parallel plate capacitor with, a plate area of 2.0 cm2 and a plate separation of 2 mm if the charge stored on, the plates is 4.0 pC?, A) 4.4V, B) 4 V, C) 4.2V, D) 4.5V, ___ 10. A typical capacitor in a memory cell have a capacitance of 3 x 10-14 F. If the, voltage across the capacitor is 0.5 V, what is the number of electrons that, must move to the capacitor to charge it?, A) 93750, B) 94500, C) 92350, D) 96430, , 1

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Lesson, , 1, , Capacitance and Capacitors, , What I Need to Know, 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., , (a), Look at picture (a) shown above. What do you think is the use of batteries in our, devices? How important is energy storage in devices and modern electronics?, , What Is It, 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., , 1

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(b) Capacitor symbol in a circuit, , (a) Capacitors in different forms, , 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, , 𝐶=, , 𝑄, A, = 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, , A, surface area of plates, in meters squared (m2), , in coulomb, V, voltage across capacitors in volts, , d, distance between the, plates in meters, , 2

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What I Have Learned, Direction: Answer the following questions as directed. For the, calculations, show your solution and encircle the final answer., 1. What is a capacitor?, 2. Why do capacitors block DC currents?, 3. What is the unit of capacitance?, , 4. What is the relationship among C, Q, and V?, , What I Can Do, , Performance Task:, List down all the devices you own with capacitors in it., Note:, • Only the items found in your home should be listed., • You may enhance your work using different materials., • It is handwritten in an A4 bond paper., , Enrichment Activity:, Watch a video through YouTube link below entitled, “The basics how capacitors work working principle”,, https://www.youtube.com/watch?v=X4EUwTwZ110, , 3

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Lesson, , Capacitors in Series and, Parallel Connection, , 2, What’s In, In the previous lesson, you have learned about the definition of, capacitance and the functions of capacitors. You also learned about the basic, operations of capacitor in DC set-up and its mathematical definition., In this lesson, you are going to analyze and calculate capacitance in different, capacitor circuit configurations such as series and parallel connection., , What I Need to Know, 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, each capacitor gets the same total, 1, 1, 1, 1, charge Q such that Q1 = Q , Q2 = Q and 𝐶𝑡 = 𝐶1 + 𝐶2 + ⋯ + 𝐶𝑛., , Capacitors in Series, 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, , Capacitors in parallel, 4

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What’s More, Derive and Analyze., Direction. Follow the instruction and derive the formula given., 1. Using the definition C = Q/V, show that for a SERIES connection of capacitors:, 1/C = 1/C1 + 1/C2. What does this equation mean? What happens to C as more, and more capacitors are connected in series?, 2. Using the definition C = Q/V, show that for a PARALLEL connection of, capacitors: C = C1 + C2. What does this equation mean? What happens to C, as more and more capacitors are connected in parallel?, , What I Have Learned, Direction: Calculate the values asked in the following questions with the given circuit, diagram., 1. Determine the values of the following variables in Circuit A., a. V1, b. V2, c. V3, d. Q1, e. Q2, f. Q3, g. Total Capacitance, CT, h. Total Charge, QT, Circuit A, , 2. Determine the charge in each capacitor and, the voltage across each capacitor in Circuit B., Given:, V3 = 5V, , Circuit B, , Enrichment Activity:, Watch a video through YouTube link below entitled “How To Solve Any Circuit, Problem With Capacitors In Series and Parallel Combinations - Physics”,, https://www.youtube.com/watch?v=a-gPuw6JsxQ, , 5

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Lesson, , 3, , Energy Stored and Electric, Field Energy in Capacitors, , What’s In, In the previous lesson, you learned to analyze and calculate the values of, capacitance, charge, and voltages across the nodes in series and parallel connection., In this lesson, we will examine the energy stored in a capacitor as electrostatic, potential energy and its relationship to the charge and voltage., , What I Need to Know, 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:, , Electric field in a charged parallel-plate capacitor, , 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 UC = 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:, , 6

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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, 𝑉, 𝑄, A, plates is uniform so that 𝐸 = and 𝐶 = ϵ0 d .Because 𝐶 = we can express, 𝑑, , 𝑉, , this result in other equivalent forms:, , What Have I Learned, Direction. Explain the following., 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, 1, expression: U = 2 Q2/C, [Hint: The power P in the capacitor is given by P =, a simple exercise on integration.], , 𝑑𝑈, 𝑑𝑡, , = IV where I =, , 𝑑𝑄, 𝑑𝑡, , . This is, , 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=12.0μF,C2=2.0μF , and C3=4.0μF , respectively., , 7

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What’s More, 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., , Dielectric in a parallel-plate capacitor, , Summary, Capacitors play an important role in modern electronics. Its significance can, be observed with current development of technology. The mechanism of capacitor to, charge and discharge electrical energy enables modern devices to function, accordingly., We learned from this lesson the relationship of capacitance to charge and, voltage. Moreover, we were able to analyze the different behaviors of parameters in, series and parallel connections., , 8

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Assessment: (Post-Test), MULTIPLE CHOICE., Directions: 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, , 9

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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 singly-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, -11, C) 4.5 × 10 J, D) 3.9 × 10-11 J, , 10

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Key to Answers, Pretest, , Post-Test, , Lesson 1, What Have I Learned?, 1. What is a capacitor? ->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, 2., , Why do capacitors block DC currents? ->due to zero frequency of dc signal, , 3., , What is the unit of capacitance? ->Farad, , 4. What is the relationship among C, Q, and V? -> the capacitance C is equal to, the charge stored Q over the electric potential V, , Lesson 2, What’s more, 1. Using the definition C = Q/V, show that for a SERIES connection of, capacitors: 1/C = 1/C1 + 1/C2. What does this equation mean? What happens to, C as more and more capacitors are connected in series?, Capacitance decreases as the number of capacitors in series increases., 2. Using the definition C = Q/V, show that for a PARALLEL connection of, capacitors: C = C1 + C2. What does this equation mean? What happens to C as, more and more capacitors are connected in parallel?, Capacitance Increases as the number of capacitors in parallel increases., , 11