Capacitance: Formulas, Capacitors in Series, Examples - PDF

CAPACITANCE General Physics 2 1/2 Science, Technology, Engineering, and Mathematics  Objectives At the end of the lesson, students should be able to: 1.deduce the effects of simple capacitors on the capacitance, charge, and potential difference when the size, potential diff...

CAPACITANCE General Physics 2 1/2 Science, Technology, Engineering, and Mathematics  Objectives At the end of the lesson, students should be able to: 1.deduce the effects of simple capacitors on the capacitance, charge, and potential difference when the size, potential difference, or charge is changed. 2.calculate the equivalent capacitance of a network of capacitors connected in series 3.participate actively in class through problem solving. EXAMPLES  WHAT IS CAPACITOR a device used to store an electric charge, consisting of one or more pairs of conductors separated by an insulator. Positive terminal of the battery removes electrons from the plate connected to it and transfers them to the other plate. Thus, the two plates are equally but oppositely charged.  CAPACITANCE It is the ability of a capacitor to store charges. The capacitance C of a capacitor is mathematically defined as the ratio of the amount of charge q in one plate to the potential difference V between the plates. In symbol, 𝑞 𝐶= 𝑉 Where: C= capacitance in Farad (F) q= charge in Coulomb (C) V= potential difference in Volts (V) Capacitance of a parallel plate is affected by the following factors: 1. The area of the plates - the bigger the area, the greater the capacitance. 2. The distance between plates - the closer the plates to each other, the greater the capacitance. 3. The insulating material or dielectric between them. - capacitance is determined in terms of material’s permittivity constant ϵ- the higher the ϵ, the greater the capacitance. The dependence of the capacitance of a parallel plate capacitor on the factor cited is mathematically expressed as, 𝑨 𝑪 =∈ 𝒅 Where: A= area of one plate in square meter (𝑚2 ) d= distance between the plates in meter (𝑚) ∈= permittivity of insulating material in 𝐶 2 /𝑁𝑚2  Example A capacitance consists of two square metal plates, each measuring 5.00𝑥10−2 𝑚 on a side. In between the plates us a sheet of mica measuring 1.00𝑥10−4 𝑚 thick. (a) What is the capacitance of the capacitor if the charge in one plate is 2.00𝑥10−8 𝐶? (b) What is the potential difference? (c) What is the electric field of between the plates?  Solution A capacitance consists of two square metal plates, each measuring 5.00𝑥10−2 𝑚 on a side. In between the plates us a sheet of mica measuring 1.00𝑥10−4 𝑚 thick. (a) What is the capacitance of the capacitor if the charge in one plate is 2.00𝑥10−8 𝐶? Given: 𝐴 𝐶= ϵ 5.00𝑥10−2 𝑚- side 𝑑 −2 𝑚 2 1.00𝑥10−4 𝑚- distance 5.00𝑥10 𝐶 = 4.8𝑥10−11 𝑞 = 2.00𝑥10−8 𝐶 1.00𝑥10−4 𝑚 ϵ= 4.8𝑥10−11 𝐶 2 /𝑁𝑚2 𝑪 = 𝟏. 𝟐𝒙𝟏𝟎−𝟗 𝑭  Example A capacitance consists of two square metal plates, each measuring 5.00𝑥10−2 𝑚 on a side. In between the plates us a sheet of mica measuring 1.00𝑥10−4 𝑚 thick. (b) What is the potential difference? Given: 𝑞 5.00𝑥10−2 𝑚- side 𝑉= 1.00𝑥10−4 𝑚- distance 𝐶 4.8𝑥10−11 𝐶 2 2.00𝑥10−8 𝐶 ϵ= 𝑉= 𝑁𝑚2 1.2𝑥10−9 𝐹 𝑞 = 2.00𝑥10−8 𝐶 𝑽 = 𝟏𝟔. 𝟕𝑽 ≈17 V 𝐶 = 1.2𝑥10−9 𝐹  Solution A capacitance consists of two square metal plates, each measuring 5.00𝑥10−2 𝑚 on a side. In between the plates us a sheet of mica measuring 1.00𝑥10−4 𝑚 thick. (c)What is the electric field of between the plates? Given: 𝑉 E= (from equation, V = Ed) 𝑑 5.00𝑥10−2 𝑚- side 16.7𝑉 1.00𝑥10−4 𝑚- distance 𝐸= 1.00𝑥10−4 𝑚 𝑞 = 2.00𝑥10−8 𝐶 ϵ= 4.8𝑥10−11 𝐶 2 /𝑁𝑚2 𝑬 = 𝟏𝟔. 𝟕𝒙𝟏𝟎𝟓 𝑽/𝒎 ≈ 𝟏. 𝟕𝒙𝟏𝟎𝟓 𝑽/𝒎 𝑉 = 16.7 𝑉  CAPACITANCE OF CAPACITORS IN SERIES Multiple capacitors can be replaced with a single capacitor called the equivalent capacitor.  Capacitance of Capacitors in Series 1 1 1 1 = + + +⋯ 𝐶𝑇𝑜𝑡𝑎𝑙 𝐶1 𝐶2 𝐶3 The reciprocal of total capacitance is equal to the sum of the reciprocals of the individual capacitance. It should be noted that adding the capacitor in series decreases the total capacitance of the combination.  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹.  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹. Solution: 1 1 1 1 = + + 𝐶𝑇 𝐶1 𝐶2 𝐶3 1 1 1 1 = + + 𝐶𝑇 10.0𝐹 5.0𝐹 4.0𝐹 1 11 = 𝐶𝑇 20𝐹 20𝐹 𝐶𝑇 = = 1.8 𝐹 11  INSTRUCTION Find a partner. Each of you must select either red or blue as your chosen color Once chosen, you'll answer questions corresponding to your selected color. All answers must be written in a ½ crosswise for 5 minutes only. After answering, pairs will stand to form a circle ensuring that each pair faces one another. Those who chose red will serve as the inner circle, while blue will form the outer circle. Each will share their responses with their partner. Once done, those with the outer blue color will rotate to find another partner to exchange answers. This process will repeat five times. THE COLORED QUESTION  ASSESSMENT In a ½ Crosswise, answer the following by showing your solution and final answer. 1. A parallel plate capacitor is made up of two plates, each having an area of 8.0𝑥10−4 𝑚2 and separated from each other by 5.0 mm. Half of the space between the plates is filled with a glass and the other with mica. Find the capacitance of this capacitor. Note: ∈𝑚𝑖𝑐𝑎 = 4.8𝑥10−11 𝐶 2 /𝑁𝑚2 ∈𝑔𝑙𝑎𝑠𝑠 = 7𝑥10−11 𝐶 2 /𝑁𝑚2  ASSESSMENT In a ½ Crosswise, answer the following by showing your solution and final answer. 2. Two capacitors with 2.0F and 3.0F capacitance, respectively, are connected in series and subjected to a total potential difference of 100V. Find the total capacitance. Lesson 4.2 Capacitors in Series Connection General Physics 2 1/2 Science, Technology, Engineering, and Mathematics Among the most widely used electrical components are capacitors. Almost all circuit boards employ these materials to function. 2 These variations sometimes result in difficulties in standardization, a limitation that may be resolved through equivalent capacitance. 3 How do capacitors behave in series connections? 4  Learning Competencies At the end of the lesson, you should be able to do the following: 1. calculate the equivalent capacitance of a network of capacitors connected in series 2. appreciate the use of capacitors in series by citing examples. 3. participate actively in class through problem solving. 5  Solution A capacitance consists of two square metal plates, each measuring 5.00𝑥10−2 𝑚 on a side. In between the plates us a sheet of mica measuring 1.00𝑥10−4 𝑚 thick. (a) What is the capacitance of the capacitor if the charge in one plate is 2.00𝑥10−8 𝐶? Given: 𝐴 𝐶= ϵ 5.00𝑥10−2 𝑚- side 𝑑 1.00𝑥10−4 𝑚- distance 5.00𝑥10−2 𝑚 2 𝐶 = 4.8𝑥10−11 𝑞 = 2.00𝑥10−8 𝐶 1.00𝑥10−4 𝑚 ϵ= 4.8𝑥10−11 𝐶 2 /𝑁𝑚2 𝑪 = 𝟏𝒙𝟏𝟎−𝟗 𝑭  Example A capacitance consists of two square metal plates, each measuring 5.00𝑥10−2 𝑚 on a side. In between the plates us a sheet of mica measuring 1.00𝑥10−4 𝑚 thick. (b) What is the potential difference? Given: 𝑞 5.00𝑥10−2 𝑚- side 𝑉= 1.00𝑥10−4 𝑚- distance 𝐶 4.8𝑥10−11 𝐶 2 2.00𝑥10−8 𝐶 ϵ= 𝑉= 𝑁𝑚2 1.2𝑥10−9 𝐹 𝑞 = 2.00𝑥10−8 𝐶 𝑽 = 𝟏𝟔. 𝟕𝑽 = 𝟐𝐱𝟏𝟎𝟏 𝐕 𝐶 = 1.2𝑥10−9 𝐹  Solution A capacitance consists of two square metal plates, each measuring 5.00𝑥10−2 𝑚 on a side. In between the plates us a sheet of mica measuring 1.00𝑥10−4 𝑚 thick. (c)What is the electric field of between the plates? Given: 𝑉 E= (from equation, V = Ed) 𝑑 5.00𝑥10−2 𝑚- side 16.7𝑉 1.00𝑥10−4 𝑚- distance 𝐸= 1.00𝑥10−4 𝑚 𝑞 = 2.00𝑥10−8 𝐶 ϵ= 4.8𝑥10−11 𝐶 2 /𝑁𝑚2 𝑬 = 𝟏𝟔. 𝟕𝒙𝟏𝟎𝟓 𝑽/𝒎 ≈ 𝟐𝒙𝟏𝟎𝟓 𝑽/𝒎 𝑉 = 16.7 𝑉 Types of capacitors vary according to their uses—some examples include electrolytic, ceramic, silver mica, and tantalum, to name a few. 9  Capacitance This may be solved by using what is called an equivalent capacitor, which is a capacitor that contains the same amount of capacitance as the combination of capacitors in a given system. ○ Series ○ Parallel 10 CAPACITORS IN SERIES CONNECTION 11  Capacitors in Series The image shows a series connection with two uncharged capacitors connected by wires from point a to b. 12  Capacitors in Series These capacitors will then begin to be “charged” as soon as a constant voltage between the two points (a and b) has been applied. 13  Capacitors in Series Recall that capacitors consist of two parallel conductors. 14  Capacitors in Series The top conductor of C1 gets a positive charge, Q, which results in the negative charge being dragged down the bottom conductor of C1. 15  Capacitors in Series These negative charges came from the top conductor of C2 as it had been charged positively. 16  Capacitors in Series The net charge on the bottom conductor of C1 and the upper conductor of C2 is equivalent to zero. 17  Capacitors in Series The image shows how an equivalent single capacitor may be used to substitute the two capacitors in the series connection. 18  Capacitors in Series This equivalent capacitance, Ceq, of the series connection refers to a single capacitance in which the charge is similar throughout the combination, and the voltage is the same. 19  Capacitors in Series For capacitors in series, the voltages can be calculated as: The variables can be represented as V1, V2, and V3. 20  Capacitors in Series For capacitors in series, the magnitude of the charge must be similar throughout all the plates of the capacitors in the series connection. 21  Capacitors in Series For capacitors in series, the magnitude of the charge must be similar throughout all the plates of the capacitors in the series connection. The voltages of the capacitors are not of the same value unless their corresponding capacitances are. 22  CAPACITANCE OF CAPACITORS IN SERIES Multiple capacitors can be replaced with a single capacitor called the equivalent capacitor.  Capacitance of Capacitors in Series 1 1 1 1 = + + +⋯ 𝐶𝑇𝑜𝑡𝑎𝑙 𝐶1 𝐶2 𝐶3 The reciprocal of total capacitance is equal to the sum of the reciprocals of the individual capacitance. It should be noted that adding the capacitor in series decreases the total capacitance of the combination.  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹.  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹. Solution: 1 1 1 1 = + + 𝐶𝑇 𝐶1 𝐶2 𝐶3 1 1 1 1 = + + 𝐶𝑇 10.0𝐹 5.0𝐹 4.0𝐹 1 11 = 𝐶𝑇 20𝐹 20𝐹 𝐶𝑇 = = 1.8 𝐹 11 Under what conditions may a combination of capacitors in a series be replaced by an equivalent capacitor? 28 Remember The reciprocal of the equivalent capacitance of a series combination is equivalent to the summation of the reciprocal values of each capacitance in the system. Remember that the equivalent capacitance Ceq always has a lesser value than any of the capacitances in the connection. 29  Let’s Practice! Assign the following values to the variables of the schematic diagram below: C1 = 5.5 μF, C2 = 1.3 μF. Determine the equivalent capacitance of the system. 30  Let’s Practice! Assign the following values to the variables of the schematic diagram below: C1 = 5.5 μF, C2 = 1.3 μF. Determine the equivalent capacitance of the system. The equivalent capacitance in the series connection is 1.05 μF. 31 Try It! Using the same diagram, let C1 and C2 be 2 𝜇F and 0.56 𝜇F, respectively. Determine the equivalent capacitance. 32  Let’s Practice! Let C1 = 12.13 μF, C2 = 10.20 μF, and Vab = 20 V. Determine the equivalent capacitance of the system. 33  Let’s Practice! Let C1 = 12.13 μF, C2 = 10.20 μF, and Vab = 20 V. Determine the equivalent capacitance of the system, as well as the charge on each capacitor. The equivalent capacitance in the series connection is 5.6 𝜇F. 34 Try It! INDEPENDENT LEARNING PERIOD (1/2 Crosswise by pair) 35 Try It! Using the diagram, let C1 = 3.99 𝜇F, C2 = 1.45 𝜇F, and Vab = 20 V. Calculate the equivalent capacitance of the system, as well as the charge on each capacitor. 36 PAIR ACTIVITY 10 seconds only to answer each item.  Concept Check (Pair Activity) Instruction: Choose the word from the box that will complete the statement. Write the letter of the answer in a ¼ paper. A. Greater D. Permittivity B. Less E. Capacitance C. Farad F. Field 1. The SI unit of capacitance is _________.  Concept Check (Pair Activity) Instruction: Choose the word from the box that will complete the statement. Write the letter of the answer in a ½ crosswise. A. Greater D. Permittivity B. Less E. Capacitance C. Farad F. Field 2. The farther the plates are from one another, the _________ the capacitance.  Concept Check (Pair Activity) Instruction: Choose the word from the box that will complete the statement. Write the letter of the answer in a ½ crosswise. A. Greater D. Permittivity B. Less E. Capacitance C. Farad F. Field 3. The bigger the area of the plate, the _________ the capacitance.  Concept Check (Pair Activity) Instruction: Choose the word from the box that will complete the statement. Write the letter of the answer in a ½ crosswise. A. Greater D. Permittivity B. Less E. Capacitance C. Farad F. Field 4. _________ is the ability of the capacitor to store charges.  Concept Check (Pair Activity) Instruction: Choose the word from the box that will complete the statement. Write the letter of the answer in a ½ crosswise. A. Greater D. Permittivity B. Less E. Capacitance C. Farad F. Field 5. Capacitance is determined by its _________.  ANSWER KEY 1. C 2. B 3. A 4. E 5. D CAPACITORS IN PARALLEL CONNECTION 44  Learning Competencies At the end of the lesson, you should be able to do the following: 1. calculate the equivalent capacitance of a network of capacitors connected in parallel. 2. appreciate the use of capacitors in parallel by citing examples. 3. participate actively in class through problem solving. 45  Capacitors in Parallel What can you say about the voltage in C1 and C2 here? 46 Capacitors in Parallel What can you say about the charges Q1 and Q2 here? 47  Capacitors in Parallel The net charge Q can be represented by: With respect to the capacitances: 48  Capacitors in Parallel The equivalent capacitance of a parallel combination is expressed as: 49  Capacitors in Parallel For capacitors in parallel, the voltages are similar throughout all the capacitors. The charges on the capacitors are not of the same value unless they have similar individual capacitances. 50 Under what conditions may a combination of capacitors in a parallel be replaced by an equivalent capacitor? 51 Remember The equivalent capacitance of a parallel combination is equivalent to the summation of each of the capacitances in the system. The equivalent capacitance Ceq is greater than any of the individual capacitance at all times. 52  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹.  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹. Identify the formula 𝐶𝑇 = 𝐶1 + 𝐶2 + 𝐶3 Substitute the given 𝐶𝑇 = 10.0 𝐹 + 5.0𝐹 + 4.0𝐹 Solve for the unknown 𝐶𝑇 = 19𝐹  Let’s Practice! Assign the following values to the variables of the schematic diagram: C1 = 8.0 μF, C2 = 4.0 μF, and Vab = 22 V. Solve the equivalent capacitance of the system, the charge on each capacitor, and the potential difference for each capacitor. 55  Let’s Practice! Assign the following values to the variables of the schematic diagram: C1 = 8.0 μF, C2 = 4.0 μF, and Vab = 22 V. Solve the equivalent capacitance of the system. The equivalent capacitance in the parallel connection is 12 𝜇F. 56 Try It! Using the same diagram, let C1 = 9.76 𝜇F, C2 = 5.44 𝜇F, and Vab = 22 V. Solve the equivalent capacitance of the system. 57 ACTIVITY Answer the following items with your pair Write your answer in a ½ crosswise 3 minutes only to answer each item. 1. Identify the following: (a)connection (b)formula (c)Substitute the given (d)the unknown and formulate your conclusion - + - + - + 2. Identify the following: (a) connection (b) formula (c) Substitute the given (d) the unknown and formulate your conclusion + - + - + - 3. Identify the following: (a)connection (b)formula (c)Substitute the given (d)the unknown and formulate your conclusion - + - + - + 4. Identify the following: (a) connection (b) formula (c) Substitute the given (d) the unknown and formulate your conclusion Try this! Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹. (a) Identify the formula (b) Substitute the given (c) Solve for the unknown and formulate your conclusion  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹. Solution: First, get the total capacitance of 𝐶1 and 𝐶2 in series. 1 1 1 = + 𝐶1𝑎𝑛𝑑2 𝐶1 𝐶2 1 1 1 = + 𝐶1𝑎𝑛𝑑2 10.0𝐹 5.0𝐹 𝐶1𝑎𝑛𝑑2 = 3.3 𝐹  Example Find the total capacitance if 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹. Solution: The combination of 𝐶1𝑎𝑛𝑑2 is parallel to 𝐶3. 𝐶𝑡𝑜𝑡𝑎𝑙 = 3.3 𝐹 + 4.0 𝐹  Check Your Understanding Identify whether each of the following statements is true or false. 1. For capacitors in series, the magnitude of the charge must be similar throughout all the plates of the capacitors in the series connection. 2. The equivalent capacitance Ceq of a series combination always has a higher value than any of the capacitances in the connection. 66  Check Your Understanding Identify whether each of the following statements is true or false. 3. An equivalent capacitor contains the same amount of capacitance as the combination of capacitors in a given system. 67  Let’s Sum It Up! An equivalent capacitor is a capacitor which contains the same amount of capacitance as the combination of capacitors in a given system. 68  Let’s Sum It Up! The reciprocal of the equivalent capacitance of a series combination is equivalent to the summation of the reciprocal values of each capacitance in the system. The equivalent capacitance Ceq always has a lesser value than any of the capacitances in the connection. 69  Let’s Sum It Up! The equivalent capacitance of a parallel combination is equivalent to the summation of each of the capacitances in the system. The equivalent capacitance Ceq is greater than any of the individual capacitance at all times. 70  Key Formulas Concept Formula Description Use this formula to Equivalent solve the equivalent Capacitance of a where capacitance of a Series Combination Ceq is the equivalent series combination. capacitance of a series combination, and C1 and C2 are the individual capacitances. 71  Key Formulas Concept Formula Description Use this formula to Equivalent solve the equivalent Capacitance of a where capacitance of a Parallel Combination Ceq is the equivalent parallel combination. capacitance of charge of parallel combination, and C1 and C2 are the individual capacitances. 72 Challenge Yourself Contrast the potential differences of capacitors in a series connection and in a parallel connection. 73 Bibliography Hewitt, Paul G. 2010. Conceptual Physics (11th ed). New York: Pearson Education. Holt, R., Serway, R., & Faugn, J. (2006). Physics. Holt McDougald. Austin, TX. Macalalad, E. P. and Vergara, R. L. 2011. Exploring the Realms of Science: Physics. Valenzuela City: JO-ES Publishing House, Inc. Vincent P. Coletta. Physics Fundamentals. Physics Curriculum & Instruction, Inc.: 2010. Walker, J., Halliday, D., & Resnick, R. (2011). Fundamentals of physics. Hoboken, NJ: Wiley. 74  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Charge and Potential Difference across Capacitors in Series Connection  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Recall: CAPACITANCE OF CAPACITORS IN SERIES: 1 1 1 1 = + + +⋯ 𝐶𝑇𝑜𝑡𝑎𝑙 𝐶1 𝐶2 𝐶3 The reciprocal of total capacitance is equal to the sum of the reciprocals of the individual capacitance. It should be noted that adding the capacitor in series decreases the total capacitance of the combination.  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Recall: Capacitance is the ratio of the amount of charge in one plate to the potential difference between the plates, 𝒒 𝑪= 𝑽 Derive the formula to solve for (a) charge (b) Voltage or potential difference  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Charge of Capacitors in Series The total charge is equal to the individual charge of each capacitor. 𝒒𝒕𝒐𝒕𝒂𝒍 = 𝒒𝟏 = 𝒒𝟐 = 𝒒𝟑 = 𝒒𝒏  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Example: Find the individual charge of each capacitors.  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Solution Applying the rule, Given: C1 = 4F, C2 = 12F, C3 = 6F, Vtotal = 9V 𝑞𝑡𝑜𝑡𝑎𝑙 = 𝑞1 = 𝑞2 = 𝑞3 Formula: q = CV 𝑞𝑡𝑜𝑡𝑎𝑙 = 18 𝐶 𝑞1 = 18𝐶 qtotal = Ctotal Vtotal 𝑞2 = 18 𝐶 qtotal = (2F)(9V) 𝑞3 = 18 𝐶 qtotal = 18C  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Potential Difference of Capacitors in Series The total potential difference or total voltage, is the sum of the potential differences across each capacitors. 𝑽𝒕𝒐𝒕𝒂𝒍 = 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟑 + … 𝑽𝒏  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Example: Find the individual potential difference across each capacitor.  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Solution Given: C1 = 4F, C2 = 12F, C3 = 6F, Vtotal = 9V, 𝑞𝑡𝑜𝑡𝑎𝑙 = 18𝐶, 𝑞1 = 18𝐶, 𝑞2 = 18𝐶, 𝑞3 = 18𝐶 𝑞 Formula: 𝑉 = 𝐶 𝑞1 𝑞2 𝑞3 𝑉1 = 𝑉2 = 𝑉3 = 𝐶1 𝐶2 𝐶3 18𝐶 18𝐶 18𝐶 𝑉1 = 𝑉2 = 𝑉3 = 4𝐹 12𝐹 6𝐹 𝑉1 = 4.5𝑉 𝑉2 = 1.5𝑉 𝑉3 = 3𝑉  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Solution Applying the rule, 𝑉𝑡𝑜𝑡𝑎𝑙 = 𝑉1 + 𝑉2 + 𝑉3 + … 𝑉𝑛 9𝑉 = 4.5𝑉 + 1.5𝑉 + 3𝑉 9𝑉 = 9𝑉 ASSESSMENT TRY THIS! TRY THIS! With the given capacitors, 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹 Find the following: 100 V (a)Individual charge of the capacitors (b)Potential difference across the capacitors.  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Charge and Potential difference across Capacitors in Parallel Connection  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Recall: CAPACITANCE OF CAPACITORS IN PARALLEL: 𝐶𝑇𝑂𝑇𝐴𝐿 = 𝐶1 + 𝐶2 + 𝐶3 + ⋯ The total capacitance is equal to the sum of the individual capacitance.  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Recall: q C V  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Potential Difference of Capacitors in Parallel The total potential difference or total voltage, across all capacitors is equal to the voltage across each capacitors. 𝑽𝒕𝒐𝒕𝒂𝒍 = 𝑽𝟏 = 𝑽𝟐 = 𝑽𝟑 = … 𝑽𝒏  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Example: Find the individual potential difference across each capacitor.  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Solution Given: C1 = 6F, C2 = 3F, Ctotal = 9F, Vtotal = 8V 𝑞 Formula: 𝑉 = 𝐶 Rule: 𝑉𝑡𝑜𝑡𝑎𝑙 = 𝑉1 = 𝑉2 𝑉𝑡𝑜𝑡𝑎𝑙 = 8𝑉 𝑉1 = 8𝑉 𝑉2 = 8𝑉  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Charge of Capacitors in Parallel The total charge is equal to the sum of the individual charge of each capacitor. 𝒒𝒕𝒐𝒕𝒂𝒍 = 𝒒𝟏 + 𝒒𝟐 + 𝒒𝟑 +𝒒𝒏  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Example: Find the individual charge of each capacitors.  NOTRE DAME OF DADIANGAS UNIVERSITY Integrated Basic Education Department Senior High School Solution 𝑞1 = 𝐶1 𝑉1 Given: C1 = 6F, C2 = 𝑞1 = (6𝐹)(8𝑉) 3F, Ctotal = 9F, Vtotal = 8V 𝑞1 = 48𝐶 Formula: q = CV 𝑞2 = 𝐶2 𝑉2 𝑞2 = (3𝐹)(8𝑉) Applying the rule, 𝑞2 = 24𝐶 𝑞𝑡𝑜𝑡𝑎𝑙 = 𝑞1 + 𝑞2 𝑞𝑡𝑜𝑡𝑎𝑙 = 48𝐶 + 24𝐶 𝑞𝑡𝑜𝑡𝑎𝑙 = 𝐶𝑡𝑜𝑡𝑎𝑙 𝑉𝑡𝑜𝑡𝑎𝑙 𝒒𝒕𝒐𝒕𝒂𝒍 = 𝟕𝟐𝑪 𝑞𝑡𝑜𝑡𝑎𝑙 = (9𝐹)(8𝑉) 𝑞𝑡𝑜𝑡𝑎𝑙 = 72𝐶 ASSESSMENT TRY THIS! With the given capacitors, 𝐶1 = 10.0 𝐹, 𝐶2 = 5.0 𝐹, 𝐶3 = 4. 0𝐹 and 𝑉𝑡𝑜𝑡𝑎𝑙 = 100𝑉 Find the following: (a)Individual charge of the capacitors (b)Potential difference across the capacitors.