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Senior High School, NOT, , General Physics 2, Quarter 3 - Module 4, Current, Resistivity, and Resistance, , Department of Education ● Republic of the Philippines

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General Physics 2 - Grade 12, Alternative Delivery Mode, Quarter 3 - Module 4: Current, Resistivity, and Resistance, 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, Authors:, , Allyn Y. Aclo, SPST-I & Shoji-an D. Daradal, SPST-I, , Content Evaluator: Glenmark A. Dal, Illustrator and Layout Artist:, , Shoji-an D. Daradal, SPST-I, Arian M. Edullantes, , Management Team, Chairperson:, Cherry Mae L. Limbaco, Ph.D., CESO V, Schools Division Superintendent, Co-Chairpersons:, , 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 4, Current, Resistivity, and Resistance, , 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, , Current, Resistivity, and Resistance ………………………………………..1, What I Need to Know .…………………………………………………………...1, What’s New…………...…………………………………………………………...2, What Is It…………..……………………………………………………………….3, What’s More…………………………..…………………………………………...8, Assessment…………………………………………………………………………………………11, Key to Answers…………………………………………………………………………………….12, References………………………………………………………………………………………….14, , i

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Module 4, Current, Resistivity, and Resistance, What This Module is About, This module talks about current and its relationship to other parameters such as, charge and time. It also talks about the resistivity of materials and how these are affected by, temperature. This module will be teaching you conductivity and how a material is able to, conduct current in terms of resistivity and conductivity., This module has one (1) lesson:, Current, Resistivity, and Resistance, , What I Need to Know, After going through this module, you are expected to:, 1. Distinguish between conventional current and electron flow STEM_GP12EM-IIId-32, 2. Apply the relationship charge = current x time to new situations or to solve related, problems STEM_GP12EM-IIIe-33, 3. Describe the effect of temperature increase on the resistance of a metallic conductor, STEM_GP12EM-IIIe-35, 4. Describe the ability of a material to conduct current in terms of resistivity and, conductivity STEM_GP12EM-IIIe-36, 5. Apply the relationship of the proportionality between resistance and the length and, cross-sectional area of a wire to solve problems STEM_GP12EM-IIIe-37, , 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, , This part contains learning objectives that, , Know, , 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 lesson 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, 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. Which refers to the motion of charges from one place to another?, a. Current, b. Electricity, c. Power, d. Voltage, __2. Which of the following is not a derivative of Ohm’s Law?, a. V = IR, b. R = V/I, c. I = V/R, d. I = R/V, __3. What is conductivity?, a. It is the ability of the material to mobilize charges, b. It is the ability of the material to move to places, c. It is the ability of the material to change form, d. It is the ability of the material to enhance its power, __4. Which of the following is true?, a. Resistivity decreases as temperature increases, b. Resistivity increases as temperature decreases., c. Resistivity increases as temperature increases, d. Resistivity does not change as temperature increases., __5. What is referred to as the interaction of charges in motion from one region to another?, a. Charge, b. Voltage, c. Resistance, d. Electric current, __6. Which of the following refers to the resistance offered by the material directly proportional, to the length of the conductor and inversely to its cross-sectional area?, a. Conductivity, b. Resistivity, c. Electricity, d. Elasticity, __7. Which of the following most likely has the largest resistivity?, a. Silver, b. Titanium, c. Plastic Bottle, d. Wood, __8. Which of the following most likely has the largest conductivity?, a. Mercury, b. Carbon steel, c. Copper, d. Glass, __9. Which of the following is not true?, a. I = Q/t, c. It = Q, b. I = t/Q, d. t = Q/I, __10. Which of the following represents the flow of current in an electric circuit?, a. Voltage, c. Conventional Current, b. Ohm’s Law, d. Flow of Elections, iii

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Current, Resistivity, and, Resistance, , What I Need to Know, It’s very common among us the word “electricity” in fact every month we receive, a monthly bill of electricity that we must pay. If you come to think about it, have you, ever wondered what’s the science behind electricity? What’s with electricity that helps, and provides us the convenience to watch movies and drama in our television set, and, able us to use wi-fi from our router or broadband that is plug-in into the socket, which, also connected with the main source of electricity., There is electricity because of electrons, so, the highlight for this lesson is you, are to distinguish between conventional current and electron flow, Apply the, relationship charge = current x time to new situations or to solve related problems,, describe the effect of temperature increase on the resistance of a metallic conductor,, describe the ability of the material to conduct current in terms of resistivity and, conductivity, and apply the relationship of the proportionality between resistance and, the length and cross-sectional area of a wire to solve problems., Behind the science of electricity is the current, resistivity, and resistance as well, as the Ohm’s Law., Take time to reflect on the picture shown below:, , What do you think is the importance of understanding electricity? Try to see it from, smaller to larger scale., , 1

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What’s New, , Word Search!, Direction: Search and encircle the word listed below. Use colored pens or, highlighter for emphasis., Current, Conductor, Resistance, , Temperature, Conductivity, Resistivity, , Electron flow, Ohm’s Law, Rho, Alpha, , N, , A, , T, , U, , R, , A, , L, , I, , S, , T, , I, , C, , A, , P, , P, , E, , E, , U, , R, , E, , S, , I, , S, , T, , I, , V, , I, , T, , Y, , W, , E, , R, , L, , L, , O, , B, , E, , D, , I, , E, , N, , T, , E, , R, , H, , R, , E, , O, , O, , E, , E, , C, , O, , N, , D, , U, , C, , T, , I, , V, , I, , T, , Y, , S, , P, , T, , P, , C, , O, , U, , C, , O, , V, , E, , R, , L, , O, , W, , H, , N, , O, , L, , O, , H, , T, , N, , N, , R, , O, , W, , L, , U, , L, , C, , A, , I, , O, , M, , E, , N, , A, , R, , F, , D, , I, , R, , E, , E, , L, , W, , E, , L, , N, , M, , E, , S, , R, , H, , O, , I, , E, , S, , W, , E, , L, , L, , E, , L, , S, , K, , O, , S, , E, , T, , N, , N, , D, , R, , I, , A, , I, , N, , Y, , M, , L, , M, , T, , R, , U, , R, , A, , T, , F, , E, , N, , S, , Y, , E, , L, , T, , E, , P, , H, , R, , E, , B, , U, , T, , O, , L, , N, , E, , T, , T, , R, , O, , R, , E, , H, , O, , U, , T, , J, , T, , R, , O, , O, , C, , A, , A, , O, , W, , E, , U, , T, , O, , N, , T, , H, , E, , A, , W, , E, , W, , E, , T, , N, , Y, , O, , U, , E, , C, , N, , O, , H, , A, , C, , R, , H, , O, , A, , I, , H, , C, , O, , L, , O, , U, , A, , W, , R, , F, , N, , T, , E, , L, , I, , T, , S, , E, , E, , U, , B, , D, , Y, , N, , H, , A, , U, , W, , C, , P, , I, , A, , T, , Y, , A, , L, , R, , N, , B, , O, , T, , A, , P, , L, , O, , H, , M, , A, , M, , A, , E, , R, , O, , O, , T, , P, , U, , R, , R, , L, , L, , R, , A, , E, , G, , G, , G, , S, , T, , C, , N, , O, , R, , R, , U, , P, , E, , Y, , A, , R, , T, , A, , M, , E, , 2

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What Is It, Electricity is a kind of energy that takes in many forms, and one of this is the, current electricity or electric current. Electric current refers to the interaction of charges, in motion from one region to another. These moving charges are called electrons,, which is one of the subatomic particles of atom, the smallest unit of matter. Electric, circuit, on the other hand, occur the moment when the charges in motion within a, conducting path forms a closed loop. The path refers to the electric circuit which serves, as a medium for transferring energy from one area to another., Prerequisite of analyzing electric circuits is to understand first the basic, properties of electric currents that explains the charges in motion or the flow of, electrons, and its conductivity, resistivity as well as the relationship of current, voltage, and resistance., Current, represented by capital (I) refers to the motion of charges from one, place to another. It is the rate at which charges flow through a circuit element or over, a cross-sectional unit of an area per unit time., Current represents the flow of electrons, however it flows from the positive, terminal of the battery towards the negative terminal, and it is the common way of, representing the flow of current in an electric circuit, that is how it perceive, thus it is, called conventional current, the choice or preferred current flow, so the moving, charges are considered positive, so it is assume that it is moving in the same direction, with current. On the other hand, the opposite direction is the actual flow of electrons,, from the negative terminal to the positive terminal. Look at the illustration below to, distinguish even better the difference between conventional current and electron flow., Flow of Conventional, Current (I), , Actual Electron Flow, , 3

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The electric current flows from the circuit shows the flow of electricity. Given the, equation below current can also be described in terms of the rate of charges flow over, time. It represents how many electrons per seconds are flowing at any given point., Ampere (A), the SI unit of current is defined as one coulomb per second (1 A = 1 C/s)., Keep in mind that 1 electron has a charge of 1.6 x10-19 C., , I=Q, t, Where:, I = current in Ampere, , Q = charge in coulomb, , t = time in seconds, , A current of 1 Ampere (A) means that you have 1 Coulomb of electric charge moving, in every second. Current is directly proportional to charges, so the higher the charges, the higher the current, and it is inversely proportional to time in seconds., Example:, A current of 5 A flows through a resistor for 30 minutes. How many electrons, flows through the resistor during the time given?, Given: I = 5 A;, Q?, t = 30 mins (convert to seconds; 1 min = 60 seconds), 30 min x 60 seconds = 1800 seconds, 1 min, 1 ampere is equal to 1 coulomb per second, therefore from the given question 5 ampere is, also equal to 5 coulomb per second, 1 A = 1 C/s, 5 A = 5 C/s, Rearrange the given equation to find the value of charge in coulomb, I = Q ; Q = It, t, Q=5C, s, , x 1800 s = 9000 C or 9 x103 C, , 9 x 103 C is not yet the final answer, since the question asked for the number of electrons, flowing through the resistor. Thus, use the value below for conversion., 1 e- = 1.6 x10-19 C, 9 x103 C x, , 1 electron, 1.6 x10-19 C, , =, , 5.63 x10-22 electron, -, , It means in 30 minutes 5.63 x10-22 electrons will have flowed through the resistor given, the current of 5 amperes. Therefore, the higher the current the greater the number of, electrons that will flow., , 4

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There are other factor and properties that affects the flow of electric charges, and one, of which is voltage and resistance aside from current. Its relationship is summarized, and explained by Ohm’s Law, which named after George Simon Ohm. It states that, the current is directly proportional to voltage and inversely proportional to resistance, as shown in the equation below., I= V, R, Where, (V) is denoted for voltage and has a unit of volts, it serves as a “force” that, pushes electrons through a certain component in an electric circuit, (I) for current is, the electron flow which is measured in ampere, and resistance (R) is measured in, ohms(Ω)., Ohm’s law is also comparable to an ideal gas equation, which is an idealized model, that describes and explain the behavior of some materials. This law links voltage and, current to the properties of the conductor, such as its resistance in a circuit that, opposes the flow of electric current. On the other hand, when talking about dimension, such as length and area relative to the flow or resistance of electric charge,, Conductivity and Resistivity is used., Conductivity is the ability of the material to mobilize charges. It is the opposite of, resistivity. Moreover, resistivity (p) is defined as the resistance offered by the material, directly proportional to the length of the conductor and inversely to its cross-sectional, area. The SI unit of resistivity is Ohmmeter (Ω.m)., Resistivity and Temperature, The resistivity of a metallic conductor nearly always increases with increasing, temperature. As temperature increases, the ions of the conductor vibrate with greater, amplitude, making it more likely that a moving electron will collide with an ion. This, impedes the drift of electrons through the conductor and hence reduces the current., Over a small temperature range (up to 100°C), the resistivity of a metal can be, represented approximately by the equation, PT=PO [ 1+ α (T-TO), where,, PO = the resistivity at reference temperature range TO (often taken as 0°C to 100°C), PT = the resistivity at temperature T, α = the temperature coefficient of resistivity in unit 1/°C, Temperature Coefficients of Resistivity, (Approximate values near room Temperature), , Material α [(°C)-1, Aluminum, 0.0039, Brass, 0.0020, Carbon (graphite), -0.0005, Constantan, 0.00001, Copper, 0.00393, Iron, 0.0050, , Material α [(°C)-1, Lead, Manganin, Mercury, Nichrome, Silver, Tungsten, , 5, , 0.0043, 0.00000, 0.00088, 0.0004, 0.0038, 0.0045

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To elaborate more the ability of the material to conduct current in terms of its, resistivity and conductivity, let’s define again the two common terms in physics. So,, resistivity is the ability of the material to resist the flow of the electric current or the, electric charges. The electrical resistivity of a conductor material is measured by how, strong the material opposes the flow of an electric current in a circuit path. The, resistivity factor enables the different types of conductor can be compared to one, another at different specific temperature relative to the physical properties of the, material. For example, the resistivity of a good conductor such as copper is on the, order of 1.72 x 10-8ohm meter (or 17.2 nΩm), whereas the resistivity of a poor, conductor (insulator) such as air can be well over 1.5 x 1014 or 150 trillion Ωm., Materials such as copper and aluminum are known for their low levels of, resistivity thus allowing electrical current to easily flow through them making these, materials ideal for making electrical wires and cables. Silver and gold have much low, resistivity values, but for obvious reasons are more expensive to turn into electrical, wires., The following are the factors that affect the resistance (R) of a conductor in, ohms., • The resistivity (ρ) of the material from which the conductor is made., • The total length (L) of the conductor., • The cross-sectional area (A) of the conductor, • The temperature of the conductor., Example:, Calculate the total DC resistance of a 100meter roll of 2.5mm2 copper wire if, the resistivity of copper at 20oC is 1.72 x 10-8 Ω meter., Data given: resistivity of copper at 20oC is 1.72 x 10-8, coil length L = 100m,, the cross-sectional area of the conductor is 2.5mm2 giving an area of: A = 2.5 x 10-6, metres2., 𝑳, 𝑹= 𝝆 𝛀, 𝑨, , 𝑹=, , (1.72 x 10−8 ) 𝟏𝟎𝟎, 2.5 x 10−6, , = 𝟔𝟖𝟖 𝐦𝛀, , That is 688 milli-ohms or 0.688 Ohms., Resistance (R) is directly proportional to the length of the conductor and inversely to, its cross-sectional area. The SI Unit is 1 Ω which is also equivalent to 1 Volt over 1, Ampere., Conductivity on the other hand, refers to the flow of electric current through a, material without any resistance. It is the total opposite of resistivity. So metals such, as copper, aluminum or silver have very large values of conductance meaning that, they are good conductors., Conductivity, σ (Greek letter sigma), is the reciprocal of the resistivity. That is 1/ρ, and is measured in siemens per meter (S/m). Since electrical conductivity σ = 1/ρ,, the previous expression for electrical resistance, R can be rewritten as:, 6

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𝑳, 𝟏, 𝑹 = 𝝆 𝛀 𝐚𝐧𝐝 𝛔 =, 𝑨, 𝝆, , , , 𝑹=, , 𝑳, 𝝈𝑨, , 𝛀, , Example:, A 20meter length of cable has a cross-sectional area of 1mm2 and a resistance, of 5 ohms. Calculate the conductivity of the cable., Data given: DC resistance, R = 5 ohms, cable length, L = 20m, and the cross-sectional, area of the conductor is 1mm2 giving an area of: A = 1 x 10-6 metres2., 𝑹=, 𝛔=, , 𝑳, 𝑳, 𝛀 ; 𝛔 =, 𝛔𝑨, 𝑹𝑨, , 𝑳, 𝟐𝟎 𝒎, 𝟏, =, = 𝟒 𝐱 𝟏𝟎𝟔, −6, 𝟐, 𝑹𝑨 5 Ω (1 x 10 𝒎 ), 𝛀. 𝒎, , Therefore, a material or a conductor with high conductivity will have a low resistivity,, and vice versa. As you observe from the previous discussion, Greek letter 𝝆 (rho), represents the electrical resistivity of a material, and electrical conductivity on the other, hand may be represented by the Greek letter 𝛔 (sigma), 𝜿 (kappa), or 𝜸 (gamma)., The table below are the electrical resistivity and electrical conductivity of some, materials., , Table of Resistivity and Conductivity at 20°C, , Material, Silver, Copper, Annealed copper, Gold, Aluminum, Calcium, Tungsten, Zinc, Nickel, Lithium, Iron, Platinum, Tin, Carbon steel, Lead, Titanium, , ρ (Ω•m) at 20 °C, Resistivity, 1.59×10−8, 1.68×10−8, 1.72×10−8, 2.44×10−8, 2.82×10−8, 3.36×10−8, 5.60×10−8, 5.90×10−8, 6.99×10−8, 9.28×10−8, 1.0×10−7, 1.06×10−7, 1.09×10−7, (1010), 2.2×10−7, 4.20×10−7, 7, , σ (S/m) at 20 °C, Conductivity, 6.30×107, 5.96×107, 5.80×107, 4.10×107, 3.5×107, 2.98×107, 1.79×107, 1.69×107, 1.43×107, 1.08×107, 1.00×107, 9.43×106, 9.17×106, 1.43×10−7, 4.55×106, 2.38×106

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Grain oriented electrical steel 4.60×10−7, 2.17×106, Manganin, 4.82×10−7, 2.07×106, Constantan, 4.9×10−7, 2.04×106, Stainless steel, 6.9×10−7, 1.45×106, Mercury, 9.8×10−7, 1.02×106, Nichrome, 1.10×10−6, 9.09×105, GaAs, 5×10−7 to 10×10−3, 5×10−8 to 103, −4, −4, Carbon (amorphous), 5×10 to 8×10, 1.25 to 2×103, Carbon (graphite), 2.5×10−6 to 5.0×10−6 //basal plane 2 to 3×105 //basal plane, 3.0×10−3 ⊥basal plane, 3.3×102 ⊥basal plane, Carbon (diamond), 1×1012, ~10−13, Germanium, 4.6×10−1, 2.17, −1, Sea water, 2×10, 4.8, 1, 3, Drinking water, 2×10 to 2×10, 5×10−4 to 5×10−2, Silicon, 6.40×102, 1.56×10−3, Wood (damp), 1×103 to 4, 10−4 to 10-3, Deionized water, 1.8×105, 5.5×10−6, Glass, 10×1010 to 10×1014, 10−11 to 10−15, Hard rubber, 1×1013, 10−14, 14, Wood (oven dry), 1×10 to 16, 10−16 to 10-14, Sulfur, 1×1015, 10−16, Air, 1.3×1016 to 3.3×1016, 3×10−15 to 8×10−15, Paraffin wax, 1×1017, 10−18, Fused quartz, 7.5×1017, 1.3×10−18, PET, 10×1020, 10−21, Teflon, 10×1022 to 10×1024, 10−25 to 1, , What’s More, , A. Explain and distinguish conventional current and electron flow. Provide a diagram, to elaborate your explanation., , 8

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B. Calculate the following Problems. Show your solution., 1. A charge of 12 C passes through the filament of a car headlamp bulb in 4 s., What is the current?, , 2. A current of 0,5 A flows for 20 s through a small electric motor. How much, charge has passed?, , 3. A current of 200 mA flows for 2 minutes. How much charge has passed?, , 4. Solve and complete the given table. Show your solution., , 1., 2., 3., 4., 5., , Charge, 60 C, 150C, 0.15 C, , Current, 2A, 10 A, 0.50 A, , Time, 3s, 2 minutes, 3s, 25 s, , C. Describe in a creative way the effect of temperature increases on the resistance of, a metallic conductor., Also, describe the ability of the material to conduct current in terms of its resistivity and, conductivity., Note: You may express your answer through a drawing, just by making a slogan or a, poster, or a “hugot”. It is all up to you as long as you can describe., , 9

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D. Solve the following problems relative to the resistivity and conductivity. Show yur, solution., 1. The resistance of a wire of length 10 m is 2 ohm. If the area of cross section of the, wire is 2 × 10–7 m2, determine its (a) resistivity, and (b) conductivity, , 2. Calculate the (a) resistivity and the (b) conductivity of a material that has a length, of 15 m and a cross-sectional area of 5 × 10–8 m2 and a resistance (R) of 5 Ω., , 10

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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. Which refers to the motion of charges from one place to another?, a. Current, b. Electricity, c. Power, d. Voltage, __2. Which of the following is not a derivative of Ohm’s Law?, a. V = IR, b. R = V/I, d. I = V/R, d. I = R/V, __3. What is conductivity?, a. It is the ability of the material to mobilize charges, b. It is the ability of the material to move to places, c. It is the ability of the material to change form, d. It is the ability of the material to enhance its power, __4. Which of the following is true?, a. Resistivity decreases as temperature increases, b. Resistivity increases as temperature decreases., c. Resistivity increases as temperature increases, d. Resistivity does not change as temperature increases., __5. What is referred to as the interaction of charges in motion from one region to another?, a. Charge, b. Voltage, c. Resistance, d. Electric current, __6. Which of the following refers to the resistance offered by the material directly proportional, to the length of the conductor and inversely to its cross-sectional area?, a. Conductivity, b. Resistivity, c. Electricity, d. Elasticity, __7. Which of the following most likely has the largest resistivity?, a. Silver, b. Titanium, c. Plastic Bottle, d. Wood, __8. Which of the following most likely has the largest conductivity?, a. Mercury, b. Carbon steel, c. Copper, d. Glass, __9. Which of the following is not true?, a. I = Q/t, c. It = Q, b. I = t/Q, d. t = Q/I, __10. Which of the following represents the flow of current in an electric circuit?, a. Voltage, c. Conventional Current, b. Ohm’s Law, d. Flow of Elections, , 11

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Key to Answers, Pretest, , Lesson 1, What’s New, , What’s More, , 12

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Post-test, , 13

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References, Arons, Arnold. 1996. Teaching Introductory Physics. Wiley., , Canva. Accessed December 24, 2020. https://www.canva.com/education, Giancoli. 2004. Physics. Prentice Hall., Khan, Sal. n.d. Khan Academy. Accessed July 30, 2020. khanacademy.org/science/highschool-physics/dc-circuits/electric-current-resistivity-and-ohms-law/a/resistance-andresistivity-ap1., Young, Hugh, and Roger Freedman. 2015. University Physics with Modern Physics., Pearson., , 14

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For inquiries and feedback, please write or call:, Department of Education – Bureau of Learning Resources (DepEd-BLR), DepEd Division of Cagayan de Oro City, Fr. William F. Masterson Ave Upper Balulang Cagayan de Oro, Telefax:, ((08822)855-0048, E-mail Address:, [email protected], , 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., , 15