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CHAPTER ONE CAPACITORS 1|P a g e  Chapter One Laws Parallel Combination Series combination 𝟏 𝟏 𝟏 1) 𝑪𝒆𝒒 = 𝑪𝟏 + 𝑪𝟐 1) = +...

CHAPTER ONE CAPACITORS 1|P a g e  Chapter One Laws Parallel Combination Series combination 𝟏 𝟏 𝟏 1) 𝑪𝒆𝒒 = 𝑪𝟏 + 𝑪𝟐 1) = + 𝑪𝒆𝒒 𝑪𝟏 𝑪𝟐 2) ∆𝑽𝒕 = ∆𝑽𝟏 = ∆𝑽𝟐 2) ∆𝑽𝒕 = ∆𝑽𝟏 + ∆𝑽𝟐 3) 𝑸𝒕 = 𝑸𝟏 + 𝑸𝟐 3) 𝑸𝒕 = 𝑸𝟏 = 𝑸𝟐 𝑸 𝝐° 𝑲𝑨 1 𝑪= 2 𝑪= ∆𝑽 𝒅 𝑷∙𝑬 ∆𝑽 3 𝑷= 4 𝑹= 𝒕 𝑰 ∆𝑽 5 𝑬= 6 𝑪𝑲 = 𝑲 ∙ 𝑪 𝒅 𝑬 ∆𝑽 7 𝑬𝑲 = 8 ∆𝑽𝑲 = 𝑲 𝑲 𝟏 𝟏 𝟏 𝑸𝟐 9 𝑷 ∙ 𝑬 = 𝑸 ∙ ∆𝑽 𝑷∙𝑬= 𝑪 ∙ ∆𝑽𝟐 𝑷∙𝑬= ∙ 𝟐 𝟐 𝟐 𝑪 2|P a g e ‫‪Chapter One Notes‬‬ ‫ﺛﺎﺑت اﻟﻌزل ﻟﻠﮭواء او اﻟﻔراغ )‪ (Dielectric constant for air or vacuum‬ﯾﺳﺎوي واﺣد )‪.(k=1‬‬ ‫ ‬ ‫𝑬‬ ‫𝑽∆‬ ‫ﻻ ﺗﺳﺗﺧدم ﻓﻲ اﻟﺣل اﻻ ﻓﻲ ﺣﺎﻟﺔ واﺣدة ﻓﻘط ان ﺗﻛون اﻟداﺋرة ﻋﺑﺎرة ﻋن‬ ‫= 𝒌𝑬‬ ‫𝑲‬ ‫وﻗﺎﻧون‬ ‫𝑲 = 𝑲𝑽∆‬ ‫اﻧﺗﺑﮫ ﻗﺎﻧون‬ ‫ ‬ ‫ﻣﺗﺳﻌﺔ واﺣدة وﻣﻔﺻوﻟﺔ ‪.‬‬ ‫داﺋﻣﺎ ً اﻟﻣﺟﺎل اﻟﻛﮭرﺑﺎﺋﻲ )‪ (the electric field‬ﯾﺗﺑﻊ ﻓرق اﻟﺟﮭد ))𝑽∆( ‪ (potential difference‬ﯾﻌﻧﻲ اذا ازداد ﻓرق‬ ‫ ‬ ‫اﻟﺟﮭد ﯾزداد اﻟﻣﺟﺎل اﻟﻛﮭرﺑﺎﺋﻲ‪ ،‬واذا ﺗﺿﺎﻋف ﻓرق اﻟﺟﮭد ﯾﺗﺿﺎﻋف اﻟﻣﺟﺎل اﻟﻛﮭرﺑﺎﺋﻲ ‪ ،‬واذا ازداد ﻓرق اﻟﺟﮭد ارﺑﻊ اﺿﻌﺎف ﻣﺎ ﻛﺎن‬ ‫ﻋﻠﯾﮫ ﯾزداد اﻟﻣﺟﺎل اﻟﻛﮭرﺑﺎﺋﻲ ﺗﺑﻌﺎ ً ﻟذﻟك اﻟﻰ ارﺑﻊ اﺿﻌﺎف ﻣﺎ ﻛﺎن ﻋﻠﯾﮫ وھﻛذا ‪....‬ﺑﺷرط ان ﯾﻛون اﻟﺑﻌد ﺑﯾن اﻟﺻﻔﯾﺣﺗﯾن ﺛﺎﺑت‪.‬‬ ‫𝑽∆‬ ‫=𝑬‬ ‫𝒅‬ ‫ﯾﻣﻛن ﺣل ﻣﺳﺎﺋل ھذا اﻟﻔﺻل ﺑدون ﺗﺣوﯾل ﻣﺎﻋدا ﻗواﻧﯾن اﻟطﺎﻗﺔ وﻗﺎﻧون اﻟﻣﺟﺎل اﻟﻛﮭرﺑﺎﺋﻲ وﻗﺎﻧون اﻟﺳﻌﺔ )أﺑو اﻻﺑﺳﻠون(‬ ‫ ‬ ‫𝟏‬ ‫𝟏‬ ‫𝟏‬ ‫𝟐𝑸‬ ‫𝑽∆ 𝑸 𝟐 = 𝑬 ∙ 𝑷‬ ‫𝟐𝑽∆ 𝑪 𝟐 = 𝑬 ∙ 𝑷‬ ‫×𝟐=𝑬∙𝑷‬ ‫𝑪‬ ‫𝑬∙𝑷‬ ‫𝑨𝑲 ‪𝝐°‬‬ ‫𝑽∆‬ ‫=𝑷‬ ‫=𝑪‬ ‫=𝑬‬ ‫𝒕‬ ‫𝒅‬ ‫𝒅‬ ‫ﻓﻲ ﻣﺳﺎﺋل ﺛﺎﺑت اﻟﻌزل ‪ Dielectric constant for air or vacuum‬ﯾﺟب ان ﺗﻧﺗﺑﮫ ‪..‬‬ ‫ ‬ ‫ﻋﻨﺪ ادﺧﺎل ﻣﺎدة ﻋﺎزﻟﺔ إذا ﻛﺎﻧﺖ اﻟﻤﺘﺴﻌﺔ‬ ‫ﻋﻨﺪ ادﺧﺎل ﻣﺎدة ﻋﺎزﻟﺔ إذا ﻛﺎﻧﺖ اﻟﻤﺘﺴﻌﺔ‬ ‫ﻣﻔﺼﻮﻟﺔ‬ ‫ﻣﺘﺼﻠﺔ‬ ‫‪disconnected‬‬ ‫‪Connected‬‬ ‫ﻛﻞ ﺷﻲء ﯾﺘﻐﯿﺮ ﻣﺎﻋﺪا‬ ‫ﻛﻞ ﺷﻲء ﯾﺘﻐﯿﺮ ﻣﺎﻋﺪا‬ ‫‪ 𝑄+‬ﯾﺒﻘﻲ ﺛﺎﺑﺖ‬ ‫‪ ∆𝑉+‬ﯾﺒﻘﻲ ﺛﺎﺑﺖ‬ ‫واﻟﺴﻌﺔ ‪ c‬اﻟﺘﻲ ﻟﻢ ﺗﻮﺿﻊ ﻓﯿﮭﺎ ﻣﺎدة ﻋﺎزﻟﺔ‬ ‫واﻟﺴﻌﺔ ‪ c‬اﻟﺘﻲ ﻟﻢ ﺗﻮﺿﻊ ﻓﯿﮭﺎ ﻣﺎدة ﻋﺎزﻟﺔ‬ ‫‪3|P a g e‬‬ 4|P a g e (1) ISOLATED CONDUCTOR AND CAPACITOR Q) What happens to an isolated spherical conductor if it is provided with an electrical charge (Q)? Is it possible to continue adding charges to it? Q) Why the isolated spherical conductor rarely used to store electrical charges? Single conductor can stores charges, but in limited quantities, and continuing to add charges will lead to an increase in the voltage difference between it and any other object, as in the relationship: 𝑲𝑸 𝑽= 𝒓 Thus, the amount of the electric field increases as in the relationship: ∆𝑽 𝑬= 𝒅 Which leads to an electrical discharge in the surrounding air. Where 𝑲: The proportionality constant and its value equal to 1 𝑁. 𝑚$ 𝐾= = 9 × 10# + $ 0 4𝜋𝜖° 𝐶 𝝐° : The vacuum permittivity and its value is equal to 𝐶$ = 8.85 × 10%&$ + 0 𝑁. 𝑚$ Q) What are the shapes of the capacitor? Capacitor Shapes: 1) two Parallel-plates capacitors. 2) two concentric - sphere capacitor. 3) two concentric - cylinders capacitor. 5|P a g e  Q) What is the Definition of the capacitor? Definition of Capacitor: It is a device used to store electrical charges and electrical energy, and it consists of a pair or more of conductive parallel plates separated by an insulator. Q) How can the capacitor with two parallel plates be charged? One of the two plates is connected to the positive terminal of the battery, so it shows a positive charge and the other is connected to the negative terminal of the battery so it shows a negative charge, and the capacitor is charged with two charges of equal in magnitude and different in type. Q) Why in a capacitor with two parallel plates both charges lie on the opposite surfaces of the two plates? Because of the attraction forces between the two charges. Q) What is the amount of the net charge on a charged capacitor plates? Why? Q) Why the net charge on the capacitor plates equals zero? Zero. Because it is charged with two charges of equal in magnitude and different in type. Q) Why are all points of one plate of the capacitor charged with equal voltage? Because the capacitor plates are made by conductor material, and both are insulated. Q) When is the electric field between the two plates of capacitor be a uniform? When the distance (d) between the plates is very small compared to the dimensions of plate. 6|P a g e  Q) Define the two-parallel plates capacitor? It consists of two identical, isolated and parallel conductive plates, the area of each of them (A) separated from each other by a distance (d) and charged with two charges of equal magnitude and of different types. Q) What does the electric potential difference depend on at the two ends of the capacitor? It depends on the amount of the charge, as it is directly proportional to it. 𝑸 ∝ ∆𝑽 Q) What is meant by capacitance of capacitor (electrical capacitance)? Electrical Capacitance: It is the ratio of charge (Q) stored in any of the plates to the the potential difference (ΔV) between the plates. It is measured in the Farad unit. 𝑸 𝑪= ∆𝑽 Q) What is the use of capacitance? The capacitance used as a measure of the charge that needs to be placed on each plates to generate a particular potential difference, and the capacitor with the larger capacitance that it stores larger charge. Ministerial Exams: ****Q.1) single spherical conductor is rarely used for storing electric charges or? **Q.2) The net charge on the charged plates of a capacitor is equal to zero? *Q3) The isolated single spherical conductor can store a limited amount of electric charges. the reason for that? 7|P a g e (2) DIELECTRICS Q) What are the types of the dielectrics? Polar dielectrics. Non-polar dielectrics. Q) Explain what is the effect of inserting a polar dielectric material between a charged capacitor plates on the electric field, and the electric potential difference between the capacitor plates? When the polar dielectric material is inserted between the two plates of the charged capacitor, the electric field between plates will affect these dipoles, and align parallel to the electric field of the capacitor, and they have permanent bipolar electric moments. As a result, an electric field is generated inside the dielectric. This field has opposite direction to the external field, and it has less amount. it is, so the amount of net electric field between the plates of the capacitor decreases. Where 𝑬𝑲 = 𝑬 − 𝑬𝒅 EK: The electric field obtained (after inserting the dielectric). E: The electric field of the capacitance (before inserting the dielectric). Ed: The electric field of the dielectric material. Where, it was found that the electric field decreases by the dielectric constant (K). 𝑬 𝑬𝑲 = 𝑲 Since the electric field is equal to: ∆𝑽 𝑬= 𝒅 That is, the potential difference is directly proportional to the field, so it is also reduces by the dielectric constant. ∆𝑽 Where ∆𝑽𝑲 = ΔVK: The electric potential difference in the presence of the dielectric. 𝑲 ΔV: The electric potential difference before inserting the dielectric. 8|P a g e  Q) Explain what is the effect of inserting a non-polar dielectric material between a charged capacitor plates on the electric field, and the electric potential difference between the capacitor plates? When the non-polar dielectric material is inserted between the capacitor plates, the electric field between the capacitor plates will minimally displace centers of the negative and positive charges in the molecule so, it will temporarily gain dipole electric moment by electric induction method. and the molecule turns into electric dipole that align in the opposite direction of effective electric field As a result, an electric field opposite the electric field between the capacitor plates is generated inside the dielectric, thus the resulting electric field decreases. Where EK: The electric field obtained (after inserting the dielectric). 𝑬𝑲 = 𝑬 − 𝑬𝒅 E: The electric field of the capacitance (before inserting the dielectric). Ed: The electric field of the dielectric material. Where, it was found that the electric field decreases by the dielectric constant (K). 𝑬 𝑬𝑲 = 𝑲 Since the electric field is equal to: ∆𝑽 𝑬= 𝒅 That is, the potential difference is directly proportional to the field, so it is also reduced by the dielectric constant. Where ∆𝑽 ΔVK: The electric potential difference in the presence of the dielectric. ∆𝑽𝑲 = ΔV: The electric potential difference before inserting the dielectric. 𝑲 9|P a g e  Q) What are meant by polar and nonpolar dielectrics? Polar Dielectrics: They are electrically insulating materials, as their particles have permanent bipolar electric moments. The distance between centers of their negative and positive charges is constant (this molecule is called dipole molecules have permanent bipolar). such as pure water. Non-polar Dielectrics: They are electrically insulating materials and the distance between the centers of their positive and negative charges is not constant, and when they are entered into an electric field it will temporarily gain dipole electric moment by electric induction method such as glass and polyethylene. Q) What are dielectric materials? and what are its types? They are electrically insulating materials that reduce the amount of electric field that they are placed in, in addition to being non-conductive under normal conditions, such as [wax paper, plastics, and glass]. and it has two types which are: 1) Polar dielectrics. 2) Non-polar dielectrics. Q) Compare between the polar and non-polar dielectrics? Polar Dielectrics Non-polar Dielectrics When placed in an electric field it will When placed in an electric field it will have temporarily gain dipole electric permanent bipolar electric moments moment by electric induction method. The distance between the centers of its The distance between the centers of its positive and negative charges is not positive and negative charges is constant. constant. such as pure water such as glass and polyethylene 10 | P a g e  Q) In what type of dielectrics a charges appear on both sides? Mentioning the mathematical relationship of the electric field generated from these charges. Non-polar Dielectrics 𝑬𝑲 = 𝑬 − 𝑬𝒅 Ministerial Exams: *Q.1) What is the effect of inserting a non-polar insulator between charged plates of a capacitor ? *Q.2) What is the effect of inserting a non-polar insulator between two separated charged capacitive plates on the electric field between the two plates? ***Q.3) What is the difference between polar and non-polar insulators? *Q.4) What is the effect of inserting a polar insulator between two separated charged capacitive plates on the electric field between the two plates? 11 | P a g e (3) FACTORS AFFECTING THE AMOUNT OF THE CAPACITOR Q) What factors does the capacitor of the two parallel plates depend on? 1. Surface area (A) of parallel plates, it is directly proportional with it (C ∝ A) ) 2. Distance (d) between the plates, it is inversely proportional with it (𝐶 ∝ *). 3. Type of dielectric medium between the plates According to the equation: 𝝐° 𝑲𝑨 Where 𝑪= The dielectric constant of air and vacuum equals (K=1) 𝒅 Q) Show how the capacitance (𝑪) of the capacitor changes as the opposite surface area (𝑨) of the two plates changes? We take a charged capacitor, disconnected from the voltage source, and connected to a voltmeter to measure the potential difference between the plates. Since the facing surface area of the capacitor is (A), the reading of the voltmeter will be at a certain degree, the potential difference between the plates will be (ΔV). ) Reducing the facing surface area of the plates to the half ( + 𝐴) by removing one of the plates aside (keeping the amount of charge constant). A double increase in the reading of the voltmeter is observed (2ΔV). , According to the relation (𝐶 = ∆-), Capacitance of capacitor decreases when there is increase in potential difference between the plates as the charge (Q) is kept constant. We can conclude that capacitance of capacitor decreases when the facing area of the plates decreases and vice versa: (C ∝ A) Capacitance (C) of parallel-plate capacitor is directly proportional with facing area (A) of the plates. 12 | P a g e  Q) Show how the capacitance (𝑪) of the capacitor changes as the distance (𝒅) between the two plates changes? We take a charged capacitor, disconnected from voltage source, and connected to ends of a voltmeter. The initial distance between them is (d).Note that the reading of the voltmeter points to a certain amount of potential difference (ΔV) between the charged plates (Q). ) When the plates are brought closer to each other (+ 𝑑) (while keeping the charge ) constant) the reading of the voltmeter drops to the half (+ ∆𝑉). , According to the relation, (𝐶 = ∆-) decrease in potential difference between plates of capacitor means increase capacitance of capacitor (when the charge is constant). We can conclude that capacitance of capacitor increases when there is a ) decrease in distance (d) between the plates and vice versa. 𝐶 ∝ * 13 | P a g e  Explain the effect of inserting a dielectric between the plates of a charged capacitor; which is disconnected from the battery in electric potential difference between them (Faraday's experiment), what effect would it make in capacitance of capacitor? Activity Tools: Parallel-plate Capacitor (air as dielectric) not charged. Battery. Voltmeter. wires. Dielectric plate (dielectric constant K). Activity Steps: 1) One terminal of the battery is connected to one plate and then the other terminal is connected to the second plate. One plate will be positively charged (+Q) and the other is negatively charged (-Q). 2) Disconnect battery from the plates. Then Connect the positive terminal of the voltmeter to the positive plate and the negative terminal of the voltmeter to the negative plate. Note the deviation of the voltmeter indicator at a specific reading. The electric potential difference (ΔV) between the plates of a charged capacitor is generated when air is the dielectric. 3) The dielectric plate is inserted between the plates of the charged capacitor, we notice a decrease in the voltmeter reading Conclusion: Inserting a dielectric with constant (k) between the plates of the charged capacitor would decrease electric potential difference by the rate of dielectric constant (k), then ∆𝑽 ∆𝑽𝑲 = 𝑲 Due to decrease in electric potential difference between the plates, the capacitance of the capacitor increases according to the equation 𝑸 𝑪= ∆𝑽 When the amount of charge is constant (Q)Capacitance of the capacitor increases by the factor (k) when the dielectric exists: 𝑪𝑲 = 𝑲 ∙ 𝑪 14 | P a g e  Q) What is the mean of dielectric constant if material? The ratio between capacitance of the capacitor after inserting the dielectric is (CK), 𝑪𝑲 and its capacitance in vacuum or air is (C), so; 𝑲 = 𝑪 Where CK: The capacitance of the capacitor (after inserting the dielectric). C: The capacitance of the capacitor (when the dielectric is air or vacuum). K: The dielectric constant (has no unit of measurement) Q) What does the dielectric constant depend on? Dielectric constant depends on the type of material. Q) It is noted on each capacitance a writing specifying the maximum potential difference in which the capacitor operates. Do you think that is necessary? Explain this. Answer: Yes, it's necessary because in case the potential difference on the plates kept increasing, this will greatly increase the electric field between plates, which will lead to an electric breakdown of the dielectric, as a result of the electric spark passing through it. This will discharge the capacitor (i.e., damage of the capacitor). Q) What is the dielectric strength? and in what unit is it measured? It is the maximum amount of electric field that a material can hold before its electrical breakdown, Dielectric strength is defined as a measurement of a material's ability to 𝑽𝒐𝒍𝒕 withstand electric field applied on it, and it is measured in units of ( ). 𝒎𝒆𝒕𝒆𝒓 Ministerial Exams: *Q.1) Explain practically how the magnitude of the capacitance of the capacitance changes with the change in the opposite surface area (A) of the two plates? **Q.2) Explain how the capacitance of a two-parallel plate capacitor changes in practice with the change in the distance between the two parallel plates ***Q.3) What are the factors affecting capacitance? Write a mathematical relationship that shows this ****Q.4) Explain, through an experiment, the effect of inserting an electrical insulator between two charged capacitor plates separated from the battery on the electric potential between them (Farady's experiment), and what is its effect on the capacitance of the capacitor? *****Q.5) what the meaning of (dielectric strength) ? 15 | P a g e *Q.6) what the meaning of (dielectric constant) ?. *Q.7) What physical quantities are measured in this unit / █ Example (1): A two-plate parallel capacitor with capacitance of (10PF) is charged by a battery with the potential difference between its poles (12V), so if the capacitor is disconnected from the battery and then insert- ed between its two plates a plate of dielectric material with a dielectric constant (6) fills the space be- tween them. What is the magnitude of: ❶ the stored charge in any of the capacitor plates. ❷ the capacitance of the capacitor in the presence of the dielectric. ❸ the potential difference between the two plates after inserting the dielectric. 16 | P a g e █ Q.2) A two-plate parallel capacitor with a capacitance of (4μF) is connected to the ends of (20V) battery. ❶ Find the magnitude of charge in any plates of the capacitor. ❷ If the capacitor is disconnected from the battery and a dielectric is inserted between its plates, the potential difference reduces to (10V). What is the dielectric constant of the dielectric and find the capacitance of capacitor after inserting dielectric in them. 17 | P a g e █ Example (2): A two-plate parallel capacitor with a distance between its plates of (0.5cm) and each of the two plates are square in shape and each side length is (10cm) and the plates are separated by vacuum (note that vacuum Permittivity ) What is the magnitude of: ❶ the capacitance of the capacitor. ❷ the stored charge in any of the capacitor plates after adding a potential difference of (10V) between them. 18 | P a g e 1 █ 2019 Round (1) Practical A two-plate parallel capacitor with a distance between its plates of (0.4 cm) and each of the two plates are square in shape and each side length is (10 cm) and the plates are disconnected by vacuum (note that vacuum permittivity ) What is the magnitude of: ❶ the capacitance of the capacitor. ❷ the stored charge in any of the capacitor plates after adding a potential difference of (10V) between them. ❸ If the capacitor is disconnected from the battery and a dielectric plate is inserted between its two plates, the potential difference between its two plates drops to (5V), what is the capacitance magnitude of the dielectric constant of the dielectric plate. and what is the capacitance magnitude of the capacitor in the case of a dielectric between its two plates. 19 | P a g e 2 █ 2021 Round (2) Biology A two-plate parallel capacitor with a capacitance of (4μF) is connected to the ends of (20V) battery. ❶ Find the magnitude of charge in any plates of the capacitor. ❷ If the capacitor is disconnected from the battery and a dielectric with a dielectric constant (K) is inserted between its plates, the stored energy in the electric field of the capacitor will be (4x10-4J). Calculate the capacitance of the capacitor after insertion of the dielectric and the dielectric constant of the dielectric material? 20 | P a g e 3 █ 2018 Biology Preliminary A two-plate parallel capacitor with a capacitance of (6μF) is connected to the ends of (30V) battery. ❶ Find the magnitude of charge in any plates of the capacitor. ❷ If the capacitor is disconnected from the battery and a dielectric is inserted between its plates, the potential difference reduces to (5V). What is the capacitance of capacitor after inserting dielectric in them. 21 | P a g e 4 █ 2021 practical Preliminary A two-plate parallel capacitor with a capacitance of (5μF) is connected to the ends of (40V) battery. ❶ Find the magnitude of charge in any plates of the capacitor. ❷ If the capacitor is disconnected from the battery and a dielectric is inserted between its plates, the potential difference reduces to (10V). What is the capacitance of capacitor after inserting dielectric in them. and the electric field between the two plates of the capacitor? 22 | P a g e 5 █ 2020 practical round (3) A two-plate parallel capacitor with a capacitance of (30μF) the air is insulating between its two plates, it was charge by a continuous voltage source with a charge of (600μC) then it was separated from it, so if an insulating material was inserted between its two plates the capacitance of the capacitor increased by (60μF) What is the magnitude of: ❶ the dielectric constant of the dielectric material ❷ the energy stored in the electric field between the two plates after inserting dielectric in them. 23 | P a g e 6 █ 2019 Round (1), Practical, Outside Country A capacitor with a capacitance of (5μF) is connected to a battery pole with a potential difference of (30V) ❶ Find the magnitude of charge in any plates of the capacitor. ❷ If the capacitor is disconnected from the battery and a dielectric with a dielectric constant (K) is inserted between its plates, the stored energy in the electric field of the capacitor will be (11.25x10-4J). Calculate the capacitance of the capacitor after insertion of the dielectric and the dielectric constant of the dielectric material? 24 | P a g e 7 █ 2018 Biology Preliminary Q.4) A two-plate parallel capacitor with capacitance of (20μF) is charged by a battery with the potential difference between its poles (6V), so if the capacitor is disconnected from the battery and then inserted between its two plates a plate of dielectric material with a dielectric constant (3) fills the space between them. What is the magnitude of: ❶ the stored charge in any of the capacitor plates. ❷ the capacitance of the capacitor in the presence of the dielectric. ❸ the potential difference between the two plates after inserting the dielectric. 25 | P a g e 8 █ 2016 Preliminary Q.2) A two-plate parallel capacitor with a capacitance of (8μF) is connected to the ends of (10V) battery. ❶ Find the magnitude of charge in any plates of the capacitor. ❷ If the capacitor is disconnected from the battery and a dielectric is inserted between its plates, dielectric constant of (2), find the potential difference between the capacitor two plates and the capacitance magnitude of the capacitor when the dielectric between its two plates. 26 | P a g e 9 █ 2015 Round (1) Outside Country A capacitor with a capacitance of (2μF) and the distance between its plates (0.1mm) is charged with a voltage source of (30V). ❶ Calculate the charge of the capacitor and the magnitude of the electric field between its two plates. ❷ If the capacitor is disconnected from the source and a dielectric is inserted between its two plates, the stored energy in the electric field of the capacitor will be (3x10-4J). Calculate the potential difference of the capacitor after insertion of the dielectric and the dielectric constant of the dielectric material? 27 | P a g e (4) COMBINATION OF CAPACITORS (PARALLEL AND SERIES) Q) Compare capacitors connected in parallel or series connections? Parallel Combination: 1) Equivalent capacitance is larger than the capacitance of any capacitor in the group. This is due to the increase in the surface area (𝑨) opposite to the capacitor plates, so the capacitance increases (𝑪 ∝ 𝑨). 𝑪𝒆𝒒 = 𝑪𝟏 + 𝑪𝟐 2) The charge is equal, and the potential difference is variable. 𝑸𝒕 = 𝑸𝟏 + 𝑸𝟐 ∆𝑽𝒕 = ∆𝑽𝟏 = ∆𝑽𝟐 3) This connection is used to increase the equivalent capacitance of the group and to store a large electrical charge with a low potential difference, and this not obtained by using a single capacitor. Series Combination: 1) Equivalent capacitance is smaller than the capacitance of any capacitor in the group. This is due to the increase in the distance between the equivalent capacitor 𝟏 plates, so the capacitance decreases (𝑪 ∝ ). 𝒅 𝟏 𝟏 𝟏 = + 𝑪𝒆𝒒 𝑪𝟏 𝑪𝟐 2) The charge is equal and the potential difference is variable. 𝑸𝒕 = 𝑸𝟏 = 𝑸𝟐 ∆𝑽𝒕 = ∆𝑽𝟏 + ∆𝑽𝟐 3) This connection is used to increase the potential difference between the two ends of the group, which may not be withstand by the single capacitor. 28 | P a g e  Q) What is the purpose of connecting capacitors in parallel? To increase the equivalent capacitance of the group, and thus store electrical charges in larger quantities. Q) What is the purpose of connecting capacitors in series? In order to be able to place a greater electric potential difference on the two ends of the group, which any capacitor of the group may not withstand if it is connected separately. Q) Connecting capacitors in parallel combination increases the equivalent capacitance of the group. (What is the physical explanation)? Connecting the capacitors in parallel combination leads to an increase in the opposite surface area (A), so the equivalent capacitance increases because: 𝝐° 𝑲𝑨 𝑪= 𝒅 Q) Connecting capacitors in series combination decreases the equivalent capacitance of the group. (What is the physical explanation)? Connecting the capacitors in series combination leads to an increase in the distance (d) between the capacitor plates, so the equivalent capacitance decreases because: 𝝐° 𝑲𝑨 𝑪= 𝒅 Q) Connecting capacitors in series combination to obtain high voltages. Give the reason. Because connecting the capacitors in series combination to an increase in the distance (d) between the capacitor plates, which leads to a decrease in the equivalent 𝝐° 𝑲𝑨 𝑸 capacitance because (𝑪 = ) and since (𝑪 = ∆𝑽) therefore the potential difference 𝒅 reactance increase. Q) When connecting the capacitors in series combination, the total charge (𝑸𝒕 ) of the source is equal to the amount of the charge of any of the two plates of each capacitor? the potential of the two middle plates is equal, they are two plates connected together by a wire, therefore, they can be considered as one conductor and its surface will be an equipotential surface. They will have equal charges yet different in type of charge (by means of induction), 29 | P a g e  What is the way to connect a group of capacitors? To obtain huge equivalent capacitance to store a huge electric charge and low potential difference, this can not be done by using only one capacitor. Parallel Combination. What is the way to connect a group of capacitors? In order to impose huge potential difference on the ends of the group that one capacitor cannot hold. Series Combination. Derive the formula for the equivalent capacitance of a group of capacitors connected in series Derive the formula for the equivalent capacitance of a group of capacitors connected in parallel Qt =Q1 +Q2 CeqΔVt= C1ΔV1+ C2ΔV2 CeqΔVt= C1ΔVt+ C2ΔVt CeqΔVt= (C1+C2) ΔVt Ceq= C1+C2 30 | P a g e  Q) How to calculate the amount of energy stored in the electric field of a charged capacitor? By drawing a graph between the amount of the stored charge (Q) and the potential difference (ΔV), and by calculating the area of the triangle: 𝟏 𝑷∙𝑬= 𝑸 ∆𝑽 𝟐 Science: 𝑸 𝑪= ∆𝑽 Either: 𝟏 𝑷∙𝑬= 𝑪 ∆𝑽𝟐 𝟐 Or: 𝟏 𝑸𝟐 𝑷∙𝑬= × 𝟐 𝑪 31 | P a g e Ministerial Exams: ****Q.1) Explain the decrease in the equivalent capacitance of a set of capacitors connected in series **Q.2) How do you explain? Increasing the amount of capacitance equivalent to a set of capacitors connected in parallel *Q.3) Answer: What is the purpose of connecting capacitors in parallel? *Q.4) What is the difference between the purpose of connecting capacitors in parallel and the purpose of connecting capacitors in series? **Q.5) What is the purpose (or what is the point of) of connecting a set of capacitors in series? █ Example (6) What is the magnitude of energy stored in the electric field of a capacitor with capacitance of (2μF) if charged to an electric potential difference of (5000V), and What is the magnitude of power do we get when discharging it at a time (10μS)? 32 | P a g e 10 █ 2016 round (3) Outside Country. █ 2019 round (3) Biology What is the magnitude of energy stored in the electric field of a capacitor with capacitance of (5μF) if charged to an electric potential difference of (4000V), and What is the magnitude of power do we get when discharging it at a time (10μS)? 33 | P a g e 11 █ 2022 practical Preliminary. What is the magnitude of energy stored in the electric field of a capacitor with capacitance of (20μF) if charged to an electric potential difference of (500V), and What is the magnitude of power do we get when discharging it at a time (10μS)? 34 | P a g e █ Example (3): Four capacitors with the capacitances of (6μF, 12μF, 8μF & 4μF) respectively, are connected to each other in a parallel combination, the group connected to two poles of a battery with a potential difference between its poles of (12V), calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total charge stored in the group. 35 | P a g e █ Example (4): Three two-parallel-plates capacitors with the capacitances of (18μF, 9μF & 6μF) respectively, are connected to each other in a series combination, the group charged with a total charge of (300μ coulomb), see figure (18) and calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total potential difference between the group ends. 36 | P a g e 12 █ 2021 Preliminary, Biology Four capacitors with the capacitances of (6μF, 12μF, 8μF & 4μF) respectively, are connected to each other in a parallel combination, the group connected to two poles of a battery with a potential difference between its poles of (12V), calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total charge stored in the group. 37 | P a g e 13 █ 2020 Round (3) Biology Two capacitors with two parallel plates (C1=3μF, C2=6μF) are connected to each other in parallel, and their group is connected to the electric potential difference table between their poles (24V): ❶ the potential difference between the two plates of each capacitor. ❷the energy stored in the electric field between the two plates of each capacitor. 38 | P a g e 14 █ 2020 Preliminary, Biology Four capacitors with the capacitances of (6μF, 12μF, 8μF & 4μF) respectively, are connected to each other in a parallel combination, the group connected to two poles of a battery with a potential difference between its poles of (12V), calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total charge stored in the group. 39 | P a g e 15 █ 2018 Round (3) Biology Capacitors with the capacitance of (4μF, 8μF, 12μF) are connected in parallel combination and then connected to the battery which potential difference is (24V). Calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total potential difference between the group ends. ❹ the energy stored in the electric field of the first capacitor only 40 | P a g e 16 █ 2019 Round (1) Practical Three capacitors with the capacitance of (6μF, 9μF, 18μF) are connected respectively in series combination and then the group of capacitors charged with a total charge of (300μC). Calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total potential difference between the group ends. 41 | P a g e 17 █ 2020 Preliminary, Practical Three capacitors with the capacitance of (6μF, 9μF, 18μF) are connected respectively in series combination and then the group of capacitors charged with a total charge of (300μC). Calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total potential difference between the group ends. 42 | P a g e 18 █ 2019 Round (3) Practical Two capacitors with two parallel plates (C1=9μF, C2=18μF) are connected to each other in parallel, and their group is connected to the electric potential difference table between their poles (12V): ❶ the equivalent capacitance of the group. ❷ the potential difference between the two plates of each capacitor. 43 | P a g e 19 █ 2019 Preliminary, Practical Q.9) Three capacitors with the capacitance of (12μF, 6μF, 4μF) are connected respectively in series combination and then the group of capacitors charged with a total charge of (240μC). Calculate the magnitude of: ❶ the equivalent capacitance of the group. ❷ the stored charge in any of the two plates of each capacitor. ❸ the total potential difference between the group ends. 44 | P a g e 20 █ 2015 Round (3) Q.7) Two capacitors with two parallel plates whose capacitance (C1=3μF, C2=6μF) are connected in series combination. The group is charged with a total charge of (72μC). Calculate the magnitude of: ❶ the total potential difference between the two ends of the group. ❷ the potential difference between the two plates of each capacitor. ❸ the energy stored in the electric field between the two plates of each capacitor. 45 | P a g e █ Q.6) You have three capacitors in which their capacitances (C1=6μF, C2=9μF, C3=18μF) and a (18V) battery is connected to them. Draw circuit diagram and explain how to connect these three capacitors to get. ❶ The Maximum amount of equivalent capacitance, then find stored charge in the each of the plates and stored charge in the group.? ❷ the smallest amount of equivalent capacitance, then find stored charge in the each of the plates and stored charge in the group.? 46 | P a g e 21 █ 2018 Round (2) Biology You have three capacitors in which their capacitances (C1=9μF, C2=12μF, C3=18μF) and a (25V) battery is connected to them. Draw circuit diagram and explain how to connect these three capacitors to get. ❶ The Maximum amount of equivalent capacitance, then find stored charge in the each of the plates and stored charge in the group.? ❷ the smallest amount of equivalent capacitance, then find stored charge in the each of the plates and stored charge in the group.? 47 | P a g e 22 █ 2016 Round (1) Outside Country Q.10) You have three capacitors in which their capacitances (C1=8μF, C2=12μF, C3=24μF) and a (6V) battery is connected to them. Draw circuit diagram and explain how to connect these three capacitors in order to get. ❶ The Maximum amount of equivalent capacitance, then find stored charge in the each of the plates and stored charge in the group.? ❷ the smallest amount of equivalent capacitance, then find stored charge in the each of the plates and stored charge in the group.? 48 | P a g e 23 █ 2017 Round (3) Practical You have three capacitors in which their capacitances (C1=6μF, C2=9μF, C3=18μF) and a (12V) battery is connected to them. Draw circuit diagram and explain how to connect these three capacitors in order to get. ❶the smallest magnitude of equivalent capacitance, ❷find stored charge in the each of the plates ❸ What is the magnitude of potential difference between plates of each capacitor? ❹ What is the magnitude of charge stored in in the electric field between the plates of the third capacitor? 49 | P a g e (5) TYPES OF CAPACITORS AND APPLICATIONS ­ Types of two-opposite-plates capacitors, with an explanation of each type: 1) Wax paper capacitors: This type is used in many electrical and electronic devices and is characterized by its small size and large plates area. 2) Rotary plate with variable capacitance of capacitor: it consists of two groups of plates as half disks, one group is fixed (unmovable), while the other rotate around a fixed axis. The two groups are connected between the terminals of battery while charging: therefore, this capacitor is equivalent to a group of capacitors in parallel combination. And it characterized by the capacitance of this capacitor changes during rotation due to change in surface area of the plates. Air is the dielectric between the plates. This type of capacitor is used in radio and wireless devices 3) Electrolyte Capacitor: It consists of two plates, one of them from aluminum and the other is an electrolytic paste, and the dielectric material is generated as a result of the chemical reaction between aluminum and the electrolyte, and the plates are wrapped in a cylindrical shape, and it characterized by This capacitor has of tolerating high potential difference; a mark is placed on the sides of the capacitor to indicate polarity, in order to be connected properly in the electric circuit. Q) What are the components of the electrolyte capacitor? It consists of two plates, one of them from aluminum and the other is an electrolytic paste, and the dielectric material between the two plates is formed as a result of the chemical reaction between the aluminum and the electrolytic paste. Q) What are the practical applications of capacitors? 1. The capacitor placed in the flash lamp system in the camera 2. The capacitor placed in microphone. 3. The capacitor placed in the device for stimulating and regulating the movement of heart muscles (the defibrillator), 4. Capacitor used in computer keyboard a capacitor is placed under each letter in the keyboard, 50 | P a g e ­ An illustration of how each application works: The capacitor placed in the flash lamp system in the camera: The capacitor is charged by the battery, and then suddenly discharged in the lamp to glow in a bright light. The capacitor placed in microphone: where one of its plates is solid fixed and the other is flexible and free movement, Sound waves cause vibration of the flexible moving plat it back and forth, so the amount of capacitance of the capacitor changes according to the change of distance between its two plates, and with same sound waves frequency, which means transformation of mechanical vibrations into electrical vibrations. The capacitors used in computer keyboard: Capacitor used in computer keyboard a capacitor is placed under each letter in the keyboard, each key is connected to a movable plate, which represents one plate of the capacitor, while the other plate is connected to the base of the key. When the key is pressed, the distance between the plates of the capacitor decreases, which in turn, increase the capacitance. This makes the external electronic circuits recognize the pressed keys. The capacitor used in the defibrillator (cardiac muscle stimulation and regulation system): The capacitor placed in the device for stimulating and regulating the movment of heart muscles (the defibrillator), This device is used to transfer different and specific amounts of electric energy to the patient, when his heart not able to pump blood, , which stimulate the heart and reorganizes its work. the capacitor is charged to a high voltage and then discharged for a very short period through the pole placed on the patient's chest, stimulating, restoring and regulating the work of the patient's heart. The amount of electric energy in charged capacitor it depends on the selector switch that located on the front of device with range between (10-360J). Q) What is the factor that changes in the capacitor used in microphone? Distance (d) between the two plates Q) What is the factor that changes in the capacitor used in computer keyboard? Distance (d) between the two plates Q) What is the use of the capacitor placed in the camera flash light? The capacitor is charged by the battery and then suddenly discharged in the lamp to glow in a bright light. Q) What is the use of the capacitor placed in the microphone? Converting mechanical vibrations into electrical signals with the same frequency. 51 | P a g e  Q) What is the use of the capacitor placed in the computer keyboard? the external electronic circuits, recognize the pressed keys. Q) What is the use of the capacitor placed in the defibrillator (cardiac muscle stimulation and regulation system)? The capacitor discharges the energy stored in its electric field in the patient's body (whose heart is unable to pump blood) in order to stimulate his heart and to restore the heart regular work. Q) What determines the amount of energy stored in the capacitor placed in the defibrillator (cardiac muscle stimulation and regulation system)? The amount of electric energy in charged capacitor it depends on the selector switch that located on the front of device. Ministerial Exams: ******Q.1) Mention three practical applications of the capacitor and explain the practical benefit of using the capacitor in each application ***Q.2) What does a variable capacity capacitor with rotating plates consist of? and Where it used? ****Q.3) What are the features of a waxed paper capacitor? **Q.4) Answer: Are the capacitors of a variable-capacity capacitor connected to each other in series or in parallel? Explain this ****Q.5) Answer: what does an electrolytic capacitor consist of and what is it characterized by? ***Q.6) What is the practical benefit of the capacitor placed in the audio recorder? *Q.7) Answer: the capacitance placed in the audio recorder, what does it consist of? **Q.8) Answer: What is the practical benefit of using a capacitor placed in a device to stimulate and regulate the movement of the heart muscles? *****Q.9) What is the practical use (or purpose) of the capacitor in the camera's flash-light *Q.10) what's will happen? With clarification when pressing a computer key *Q.11) What is the practical benefit of the capacitor placed in the computer keyboard? *Q.12) Answer: What is the factor that does not change in the capacitor placed in the computer keyboard during its use? 52 | P a g e (6) DC CIRCUIT WITH RESISTOR AND CAPACITOR Q) Show experimentally How to charge the capacitor? Activity Tools: Battery with suitable potential difference. Double electrical switch. Resistance. Lamp (L0 ). Galvanometer (where “zero” being in the middle of the scale). Capacitor with two parallel plates. Activity Steps: The circuit is connected as in figure, where by the switch(k) in position (1), This implies connecting the plates of the capacitor to the terminals of the battery, to be charged, so the pointer of the galvanometer (G) instantly moves to one side zero reading (to the right for example) and back quickly to zero reading, notice at the same time the lamp(L1) glows for a while, when the capacitor is charged completely, the potential of each plate is equal with battery terminals, so, the capacitor is fully charged, which means: Potential difference between plates of capacitor, equals potential difference between terminals of the battery. In this case, therefore, there is no potential difference between the sides of the resistor in the circuit, this makes the current in the circuit zero. (𝐼 = 0). Therefore, existence of charged capacitor in the direct current circuit is considered as open switch. Q) What does the capacitor do in a DC circuit containing resistance? Capacitor work as an open electrical switch. Where the moment the circuit is closed, a current is called the charging current, and after the charging process is completed, (∆𝑉1 ) becomes (∆𝑉1 = ∆𝑉23++456 ) and then the current becomes (𝐼 = 0). 53 | P a g e  Q) Why the capacitor, which placed in the DC circuit, is considered as an open electrical switch? Because the capacitor, when fully charged, the potential difference of each plate is equal to the potential difference of the electrode connected to the battery, and this means that the battery potential difference is equal to the potential difference of the capacitor, and then the current in the circuit equal zero. Q) Show experimentally how to discharge the capacitor Activity Tools: Capacitor charged and disconnected from the source. Lamp (L0 ). Galvanometer. Electrical switch. Steps of the activity: We connect the electric circuit, see figure, but the switch (K) is in position (2). This means connecting the plates of the capacitor by a wire, in this way, the capacitor will be discharged, i.e., neutralized charge of plates. So, the Galvanometer (G) instantly moves from zero (to the left) then back to zero quickly and the lamp glows (L2) at the same time, then goes off. We conclude that: An instantaneous current flow in the electric circuit, it is called discharge current, this discharge current fading (equals zero) when there is no potential difference between the plates of the capacitor (ΔVAB= 0 V). Q) What is the difference between a DC circuit containing resistance and a DC circuit containing resistance and capacitive? In a DC circuit containing resistance, the current is constant, and in a DC circuit containing resistance and capacitive, the current is variable with time. 54 | P a g e Ministerial Exams: ******Q.1) Explain an activity in which you explain how to charge the capacitor? ****Q.2) Answer: Draw a diagram of an electrical circuit (with markings on its parts) showing the process of discharging the capacitor of its charge ****Q.3) what the reason: A capacitor in a DC circuit consider an open switch ***Q.4) Answer: Draw a diagram of an electrical circuit (marking its parts) to show the process of charging the capacitor *Q.5) Answer: Draw a diagram of an electrical circuit (with markings on its parts) showing the process of charging and discharging the capacitor 55 | P a g e █ Q.1) From the information shown in the electrical circuit figure. Calculate. ❶ Maximum magnitude of the charging current at the moment of closing the switch. ❷ Potential difference between plates of capacitor after a closing the switch. ❸ Stored charge in any plate of the capacitor. ❹ the stored energy between plates of the capacitor 56 | P a g e █ Example (8): A series-connected circuit containing a light bulb with resistance of (r=10Ω) and a resistance with the magnitude (R=20Ω) and a battery with the magnitude of the potential difference between its poles (ΔV=6V) connected in the capacitor circuit of the two parallel plates with a capacitance of (5μF). What is the magnitude of charge stored in any of the two plates of the capacitor? and the electrical energy stored in its electric field, if the capacitor connected: ❶ in parallel combination with the lamp, note the figure, ❷ in series combination with the lamp, resistance, and battery in the same circuit, (after the disconnection of the capacitor from the first circuit and discharged from all its charge), note the figure. 57 | P a g e 24 █ 2013 Round (1) / 2017 Round (1) Displaced From the information shown in the electrical circuit in the figure, calculate: ❶ the maximum magnitude of charging current in the moment the switch is closed. ❷ the magnitude of potential difference between the two-capacitor plates after a period of shutting the switch (after the completion of the charging process). ❸ the charge is stored in any of the two-capacitor plates. ❹ the energy stored in the electric field between the two capacitor plates. 58 | P a g e 25 █ 2013 Round (3) A series-connected circuit containing a light bulb with its resistance (r=5Ω) and a resistance with magnitude of (R=10Ω) and a battery with the potential difference between its poles (ΔV=12V). A capacitor with two-plate with capacitance of (3μF) connected to the circuit. What is the magnitude of charge stored in any of the two-capacitor plates? and the magnitude of the energy stored in the electric field of the two plates if the capacitor connected with the lamp in parallel combination. 59 | P a g e 26 █ 2015 Preliminary A series-connected circuit that contains a light bulb whose resistance (r=5Ω) with a resistance with the magnitude of (R=10Ω) and a battery is the magnitude of potential difference between its poles (ΔV=4V), a capacitor with two parallel plates with a capacitance of (3μF) connected to the circuit, what is the magnitude of charge stored in any of the two capacitor plates? and the energy stored in the electric field between the capacitor two plates, if the capacitor connected: ❶ in parallel combination with the lamp. ❷ in series combination with the lamp, resistance, and battery in the same circuit, (after the disconnection of the capacitor from the first circuit and discharging all its charge). 60 | P a g e 27 █ 2016 Round (3) A series-connected circuit that contains a light lamp whose resistance (r=6Ω) with a resistance with the magnitude of (R=14Ω) and a battery is the magnitude of potential difference between its poles (4V), a capacitor with two parallel plates with a capacitance of (2μF) connected to the circuit. What is the magnitude of charge stored in any of the two capacitor plates? and the energy stored in its electric field if the capacitor connected: ❶ in parallel combination with the light lamp. ❷ in series combination with the light lamp, resistance, and battery in the same circuit (after disconnection of the capacitor from the first circuit and discharging all its charge). 61 | P a g e 28 █ 2018 Preliminary, Practical / 2018 Round (1), Practical A series-connected circuit that contains a light lamp whose resistance (r=4Ω) with a resistance with the magnitude of (R=16Ω) and a battery is the magnitude of potential difference between its poles (ΔV=60V), a capacitor with two parallel plates with a capacitance of (20μF) connected to the circuit, ❶ What is the magnitude of charge stored in any of the two capacitor plates? and the energy stored in its electric field if the capacitor connected with the light lamp in parallel combination. 62 | P a g e 29 █ 2021 Round (2) supplementary practical A series-connected circuit containing a light bulb with its resistance (r=5Ω) and a resistance with magnitude of (R=10Ω) and a battery with the potential difference between its poles (ΔV=12V). A capacitor with two-plate with capacitance of (3μF) connected to the circuit. What is the magnitude of charge stored in any of the two-capacitor plates? and the magnitude of the energy stored in the electric field of the two plates if the capacitor connected with the lamp in parallel combination. 63 | P a g e 30 █ 2017 Round (1), Biology A series-connected circuit containing a light bulb whose resistance (r=20Ω) with a resistance with the magnitude of (R=40Ω) and a battery with the potential difference between its poles (12V), were a capacitor with two parallel plates connected to the circuit in a series combination with a light bulb, so the magnitude of charge stored in any of the capacitor plate was (20μC), find the magnitude of: ❶ the capacitance of the capacitor. ❷ the electrical energy stored in its electric field. 64 | P a g e Chapter One Questions Q1 Choose the correct statement for each of the following: 1) Parallel-plate capacitor charged and disconnected from battery, air fills the space between its two plates, then a dielectric constant is (k =2) inserted between plates. The amount of electric field (Ek) between the plates with the dielectric compared with the amount of (E) in the case of air will be: a) E/4 b) 2E c) E d) E/2 2) (Farad) unit is used to measure capacitance of capacitor, it is not equal to one of the following units: a) Coulomb2/j b) Coulomb/V c) CoulombxV2 d) j/V2 3) Parallel-plate capacitor its capacitance (C), brought its two plate closer together until the distance between them became (1/3) what it was, so the amount of its new capacitance equals: a) 1/3C b) 1/9C c) 3C d) 9C 4) (20μF) capacitor, in order to store (2.5 J) energy in its electric field, it needs to be connected to a direct potential difference that equals: a) 150V b) 350V c) 500V d) 250kV 5) The capacitance of parallel-plate capacitor (50μF), air is the dielectric between plates, if a dielectric is inserted between plates to increase the capacitance by (60μF); dielectric constant of that material is: a) 0.45 b) 0.55 c) 1.1 d) 2.2 6) While you are in the laboratory, you needed (10µF) capacitor, you have a set of identical capacitors, with a capacitance (15µF) then the number of capacitors are used and combination method is: a) (4 capacitors), all connected in series combination. b) (6 capacitors), all connected to parallel combination. c) (3 capacitors), 2 connected in series combination, the group is connected to the third in parallel combination. d) (3 capacitors), two connected in parallel combination, the group is connected to the third in series combination. 65 | P a g e 7) Parallel-plate capacitor, its two plates are connected between terminals of a battery with constant potential difference, if the plates are separated from each other a little while the battery is still connected to them, the electric field between the two plates: a) Increases, stored charge in either of its plates increase. b) Decreases, stored energy in either of its plates decrease. c) Remains constant, the stored charge in any of the plates remain constant. d) Remains constant, stored charge in its plates increases. 66 | P a g e 8) To obtain maximum equivalent capacitance of group of capacitors in figure below, we choose one of the circuits below: Answer: In Figure (A) In Figure (B) 67 | P a g e In Figure (C) In Figure (D) 9) Two capacitors (C1, C2) connected in series combination, the group is connected to the terminals of the battery, capacitance of the first was larger than the second, when comparing potential difference between the plates of capacitor one (ΔV1) with that of capacitor two (ΔV2), we find that: a) ΔV1 greater than ΔV2 b) ΔV1 less than ΔV2 c) ΔV1 equals ΔV2 d) All above, it depends on the charge of each. 68 | P a g e  10) Three capacitors, (C1.C2. C3) connected in parallel combination, this group is connected to a battery, if the capacitances are (C1> C2> C3), compare charges (Q1.Q2. Q3) stored in any of the plates of each capacitor, we find that: a) (Q3>Q2> Q1) b) (Q1>Q3> Q2) c) (Q1>Q2> Q3) d) (Q3=Q2= Q1) Q.2) When doubling the electric potential difference between the two plates of the capacitor with a constant capacitance, what happens to the amount of each of the following: a) Stored charge (Q) in each of the plates. b) Stored energy in the electric field between the plates. a) The charge stored in any of its plates doubles when the potential difference is doubled. b) The energy stored in the electric field increases to four times what it was: 69 | P a g e Q.3) A charged capacitor, potential difference between the two plates is very high (Disconnected from voltage source), such capacitor is dangerous for a long-time if plates are touched by hand directly. What is your explanation for that? The danger lies in the fact that the amount of the charge in any of its plate is very large because its potential difference is very large (Q = C.∆V ) and when touched by the hand the capacitance is discharged from its charge, and in order to safely touch this capacitor by hand, it must be discharged from its charge by a wire of conductive material coated with an insulating material that connects between its two plates or we use the electric discharger or screwdriver. Q.4) Parallel-plate capacitor (air is the insulator between plates) explain how the amount of its capacitance changes when the following factors change (mention mathematical relation in your answer): a. Surface area of the two plates. b. Distance between the two plates. c. Type of dielectric between the two plates. a) The surface area (A) opposite to each of the two plates is directly proportional to it. 𝑸∝𝑨 b) The distance (d) is between two plates of the capacitor inversely proportional to it. 𝟏 𝑪∝ 𝒅 c) The type of dielectric between the two plates {dielectric constant amount (K) between the two plates}. 𝝐° 𝑲𝑨 According to the equation: 𝑪= 𝒅 {where dielectric constant of air (K=1)} Q.5) Draw a diagram of an electric circuit (with marking its parts) and illustrate the following: a. The charging process of the capacitor. b. The process of discharging the capacitor from its charge. Answer: a) Capacitor Charging b) Capacitor Discharging 70 | P a g e Q.6) You have three identical capacitors, each with a capacitance (C) and a continuous voltage source with constant potential difference between the terminals. Draw a diagram of an electric circuit, illustrate proper way to connect the three capacitors in the circuit to obtain maximum amount of electrical energy that can be stored in the group. Then prove that the arrangement you chose is the best. The three capacitors are connected in parallel combination with each other between the two poles of the battery, so the equivalent capacitance of the group increases, and the energy increases to three times what it was. 𝑪𝒆𝒒 = 𝑪 + 𝑪 + 𝑪 ⟹ 𝑪𝒆𝒒 = 𝟑𝑪 𝟏 𝟏 𝟏 𝑷𝑬𝒕 = 𝟐 𝑪𝒆𝒒 ∙ ∆𝑽𝟐 ⟹ 𝑷𝑬𝒕 = 𝟐 × 𝟑𝑪 ∙ ∆𝑽𝟐 ⟹ 𝑷𝑬𝒕 = 𝟑 × 𝟐 𝑪 ∙ ∆𝑽𝟐 ⟹ 𝑷𝑬𝒕 = 𝟑𝑷𝑬 Q.7) Are the capacitors (variable) capacitance of rotating plates, connected in series combination or in parallel combination? Explain this? The capacitors are connected in parallel combination and consist of two groups, one of them fixed and the other moving around a fixed axis, and each group to be charged is connected to one of the battery poles (e.g., positive) and the other group is connected to the other pole (e.g., negative), so one of the two groups become with positive voltage and the other with negative voltage, and this is the advantage of the parallel combination. 71 | P a g e Q.8) The capacitor (C1) is connected to a battery terminal. Explain what happens? to the potential difference between the plates of (C1) and the stored charge in it, if another capacitor (C2) not charged is connected to (C1) (while the battery is still connected to the circuit), the connection method was: a) In parallel combination with (C1) b) In series combination with (C1) a) On connecting the capacitor (C2) to (C1) by parallel connection without disconnecting the battery from the circuit, the potential difference (ΔV) will be constant as: ∆𝑽𝟏 = ∆𝑽𝟐 = ∆𝑽𝒕 The stored charge (Q) in the capacitor (C1) also will be constant when (C1 & V1) be constant as: 𝑸𝟏 = 𝑪𝟏 ∙ ∆𝑽𝟏 b) On connecting the capacitor (C2) to (C1) by series connection without disconnecting the battery from the circuit, the potential difference (ΔV1) will be constant as: ∆𝑽𝒕 = ∆𝑽𝟏 + ∆𝑽𝟐 ∆𝑽𝟏 = ∆𝑽𝒕 − ∆𝑽𝟐 ∴ ∆𝑽𝟏 < ∆𝑽𝒕 The stored charge (Q) will decrease due to the potential difference decrease according to the following equation: 𝑸 = 𝑪∆𝑽 72 | P a g e Q.9) In figure; three identical capacitors each have capacitance (C). Arrange the four figures in descending from the largest amount of the equivalent capacitance of the group to the smallest amount: Answer: In figure (a), all capacitors are connected in series combination. 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏.𝟏.𝟏 𝟑 = + + ⟹ = = 𝑪𝒆𝒒 𝑪 𝑪 𝑪 𝑪𝒆𝒒 𝑪 𝑪 𝑪 𝑪𝒆𝒒 = 𝟑 ⟹ 𝑪𝒆𝒒 = 𝟎. 𝟑𝟑𝑪 In figure (b), the first and second capacitors are connected in series combination and are they are connected to the third one in parallel combination. 𝟏 𝟏 𝟏 𝟏 𝟐 𝑪 = + ⟹ = ⟹ 𝑪𝟏,𝟐 = 𝑪𝟏,𝟐 𝑪 𝑪 𝑪𝟏,𝟐 𝑪 𝟐 𝑪𝟏,𝟐 = 𝟎. 𝟓𝑪 ⟹ 𝑪𝒆𝒒 = 𝑪𝟏,𝟐 + 𝑪 𝑪𝒆𝒒 = 𝟎. 𝟓𝑪 + 𝑪 ⟹ 𝑪𝒆𝒒 = 𝟏. 𝟓𝑪 In figure (c), the first and second capacitors are connected in parallel combination, and the third one is connected with them in series combination. 𝑪𝟏,𝟐 = 𝑪 + 𝑪 ⟹ 𝑪𝟏,𝟐 = 𝟐𝑪 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏 = + ⟹ = + 𝑪𝒆𝒒 𝑪𝟏,𝟐 𝑪 𝑪𝒆𝒒 𝟐𝑪 𝑪 𝟏 𝟏C𝟐 𝟐𝑪 = ⟹ 𝑪𝒆𝒒 = ⟹ 𝑪𝒆𝒒 = 𝟎. 𝟔𝑪 𝑪𝒆𝒒 𝟐𝑪 𝟑 In figure (d), all the capacitors are connected in parallel combination. 𝑪𝒆𝒒 = 𝑪 + 𝑪 + 𝑪 = 𝟑𝑪 So the capacitance in the figure (d) is greater than (b) greater than (c) greater than (a). 73 | P a g e Q.10) A) Mention three practical applications of the capacitors and explain practical benefit of using this capacitor in each application. The capacitor placed in the camera flash light. Benefit: Providing the lamp with sufficient energy to glow suddenly with a bright light. The capacitor placed in the microphone. Benefit: The mechanical vibrations are converted into electrical signals of the same frequency. The capacitor placed in the defibrillator (cardiac muscle stimulation and regulation system). Benefit: Discharging its stored energy in the patient’s body in a very short time period, to stimulate his heart and restore its regular work. B) Explain benefit of inserting dielectric instead of air between plates of capacitor. 1) Increase the capacitance of the capacitor. (𝑪𝑲 = 𝑲. 𝑪 ) 2) Preventing premature collapse of the dielectric between its plates when a large potential difference is applied between its plates. C) What is the factor which changes capacitance of capacitor in a keyboard which is being used? The distance changes between the two plates (when the key is pressed, the distance decreases). D) What is the source of applied electrical energy of medical instrument (defibrillator) which is used to produce electric shock for purpose of stimulating and restoring regularity of the work of patient’s heart. The energy stored in the electric field between the two capacitor plates placed in the device. E) What is the physical explanation of the followings? a) Increase of equivalent capacitance of group when they are connected in parallel. b) Decrease of equivalent capacitance of group when they are connected in series. a) Because of the increase in the surface area of the capacitors in parallel combination. 𝑸∝𝑨 b) Because of the increase in the distance between the two plates of capacitors in series 𝟏 combination. 𝑪 ∝ 𝒅 𝝐° 𝑲𝑨 And according to the following equation: 𝑪= 𝒅 74 | P a g e Q.11) State the reason of the followings; a) A charged capacitor in DC circuit behaves like an open switch. Because the capacitor, when fully charged, the voltage of each plate is equal to the voltage of the electrode connected to the battery, and this means that the potential difference of the battery is equal to the potential difference of the capacitor, and then the current in the circuit is equal to zero. b) The amount of electric field between the plates of the capacitor decreases when a dielectric material is placed in it. Because an electric field is generated inside the dielectric (𝑬𝒅 ), it opposes in the direction the electric field (𝑬 )between the two plates of the capacitor, so the resulting field is: 𝑬𝑲 = 𝑬 − 𝑬𝒅 And decreases by the amount of the dielectric constant 𝑬 𝑬𝑲 = 𝑲 c) The maximum amount of electric potential difference can be determined, is specified and written on the capacitor. To prevent premature electrical breakdown of the dielectric between the two plates as a result of the electric spark passing through it, so the capacitor discharges its charge and damages at that time. d) A parallel plate capacitor is charged and disconnected from battery. When pure water is inserted instead of air between plates of capacitor, potential difference between plates decreases. Explain how. Since the capacitor is disconnected from the source, inserting the dielectric causes a decrease in the amount of the electric field between the two plates by the amount of the dielectric constant. 𝑬 𝑬𝑲 = 𝑲 Since: ∆𝑽 𝑬= 𝒅 And the potential difference decreases by the amount of the dielectric constant (𝑲) ∆𝑽 ∆𝑽𝑲 = 𝑲 75 | P a g e Q.12) A capacitor with parallel plates (the air is insulator between plates) is charged by a battery then disconnected from it, when a dielectric which dielectric constant (𝒌 = 𝟐) is placed between plates of the capacitor. What happens for the followings? a) Stored charge in any of its plates. Remains constant, where the capacitor disconnected from the battery. b) Capacitance. Increases to the double according to the equation of (𝑪𝑲 = 𝑲 ∙ 𝑪 = 𝟐𝑪) c) Potential difference between plates of the capacitor. Decreases to the half according to the equation of: ∆𝑽 ∆𝑽 ∆𝑽𝑲 = = 𝑲 𝟐 d) Electric field. Decreases to the half according to the equation of: 𝑬 𝑬 𝑬𝑲 = = 𝑲 𝟐 e) Stored energy in capacitor. Decreases to the half according to the equation of: 76 | P a g e Q.13) A parallel plates capacitor, the air is an insulator between the plates and the capacitor is connected to the battery. When a dielectric material which dielectric constant (k = 6) is inserted in capacitor, the battery is still connected. What happens for the followings quantities of the capacitor mention the reason? a) Potential difference between plates of the capacitor. Still constant because it connected to the battery b) Capacitance. It increases to six times its initial amount according to the equation of (𝑪𝑲 = 𝑲 ∙ 𝑪 = 𝟔𝑪) c) Stored charge in any of its plates. It increases to six times its initial amount 𝑸 = 𝑪∆𝑽 𝑸𝑲 = 𝑪𝑲 ∆𝑽 By dividing equation (1) by (2) 𝑸 𝑪∆𝑽 = 𝑸𝑲 𝑪𝑲 ∆𝑽 𝑸 𝑪 = 𝑸𝑲 𝟔𝑪 𝑸𝑲 = 𝟔𝑸 d) Electric field. Still constant as (ΔV) and (d) according to the equation of ∆𝑽 𝑬= 𝒅 e) Stored energy in capacitor. It increases to six times its initial amount 𝟏 𝑷𝑬 = 𝟐 𝑸 ∙ ∆𝑽 𝟏 𝑷𝑬 = 𝟐 𝑸𝑲 ∙ ∆𝑽 By dividing equation (1) by (2) 𝟏 𝑷𝑬 𝑸∆𝑽 𝑷𝑬 𝟏 = 𝟏 𝟐 ⟹ =𝟔 𝑷𝑬𝑲 𝑸 ∆𝑽 𝑷𝑬𝑲 𝟐 𝑲 𝐏𝐄𝐊 = 𝟔 𝐏𝐄 77 | P a g e Ministerial Exams: *******Q.1) what the reason: Determines the maximum amount of electrical potential difference at which the capacitor can operate ****Q.2) Choose the correct answer: A capacitor with two parallel plates has a capacity) c) moved it plates away from each other until the distance between them became (3) times what it was, what is the amount of its new capacitance (9C , 3C , 1/9C , 1/3C) *****Q.3) what the reason: the magnitude of the electric field decreases between the charged capacitor plates separated from the source when we insert an insulating material between its two plates? **Q.4) Answer: A capacitor with two parallel plates charged and separated from the battery. If the space between its two plates was filled with pure water instead of air, what would happen to the potential difference between its two plates? What is the explanation for that? *Q.5) Choose the correct answer: capacitor has a capacitance of (40µƒ) in order to store energy in its electric field of (7.2J), it requires connecting it to a continuous voltage source of: 600V , 150V , 160V , 120V *Q.6) Choose the correct answer: capacitor has a capacitance of (20µƒ) and in order to store energy in its electric field of (256 × 10=> ) it requires connecting it to a continuous voltage source equal to 500v. , 150v , 16v. , 12v. *Q.7) Choose the correct answer: capacitor with two parallel plates, its capacity (40µf ) when air as an insulator between its two plates. If an insulating material is inserted between its two plates, its capacity increases by an amount(70µf) , what the dielectric constant of that material is equal to: (1.4 , 0.71 , 2.75 , 2.2) *Q.8) Choose the correct answer: A capacitor with two parallel plates has its capacity(30µf) , the air fills the space between its two plates if inserted an insulating material between its two plates increases in capacity by an amount(60µf) , what the dielectric constant of that material is equal to: (2 , 3 , 4 , 5) **Q.9) Answer: Mention two practical benefits achieved from the inserting of an electrical insulating material that fills the space between two plates of a capacitor instead of air *Q.10) what's happen for? the amount of electric field and the charge stored between two parallel plates of a capacitor , its plates are connected to a battery that provides a constant voltage difference if the two plates are slightly apart while the battery remains connected to them 78 | P a g e ****Q.11) what will happen? And why? to the energy stored in the electric field between two capacitive plates of constant capacitance when the magnitude of the electric potential difference between the two plates of each capacitor is doubled *Q.12) what will happen? With a mention of the reason: for the stored charge (Q) in any of the two capacitance plates with a constant capacitance when doubling the electric potential difference between the two plates *Q.13) what is the effect of? Inserting an electrical insulator between two capacitive plates charged and isolated from the battery on each of the following: 1- The electric potential difference between its two plates, 2- The capacitance of the capacitor *Q.14) what the effect of? Inserting an electrically insulating material whose dielectric constant is (6) between two plates of a capacitor connected to a battery instead of air (voltage difference between its two plates, capacity) *Q.15) A capacitor with two parallel plates, the air is an insulator between its two plates, it connected to a battery when insulator is inserted its dielectric constant (6) and the capacitor is still connected to the battery, what happens to the energy stored in the electric field between its two plates? (With a reason) *Q.16) what will happen to? the energy stored in the electric field between two plates of a capacitor charged and separated from the source when an electrical insulator whose dielectric constant (2) is inserted between its plates *Q.17) what will happen? And why? A capacitor with two parallel plates. The air has an insulator between its two plates. It connects to a battery. Insert an electrical insulator between its two plates. Its dielectric constant (4), and the capacitor is still connected to the battery. What happens to each of the following quantities of a capacitor, with mentioning the reason: 1- Voltage difference between its two plates 2- Its capacity *Q.18) Explain the effect: inserting an electrically insulating material its dielectric constant (2) between two plates of capacitor charged and separated from the battery instead of air in: (the potential difference between its two plates, the energy stored in the electric field between its two plates) *Q.19) You have three capacitors, each with a capacity of C, and a source of continuous voltage. The potential difference between its poles is of a fixed amount. Draw a circuit diagram showing the appropriate way to connect all three capacitors in the circuit to obtain the largest amount of electrical energy that can be stored in the group? Then prove that the arrangement you choose is the best *Q.20) Choose the correct answer: When the electric potential difference between two capacitive plates of constant capacitance is doubled, the amount of charge stored (Q) in any of its plates becomes: 0 ? 𝑄 , 2Q , 4Q , Q 79 | P a g e *Q.21) What is the meaning of an electrical insulator? and mention two practical benefits as a result of the inserting of an electrical insulating material that fills the space between two wide plates with two parallel plates instead of air. **Q.22) Choose the correct answer: Two capacitors are (𝐶0 , 𝐶? )connected to each other in series , and their group is connected to a battery, The amount of capacitance of first capacitor is smaller than The amount of capacitance of the second one after comparing the amount of voltage difference of the first capacitor ∆𝑉0 with the amount of voltage difference of the second capacitor ∆𝑉? ∆𝑉? ‫𝑉∆ اﻛﺒﺮ ﻣﻦ‬0 , ∆𝑉0 ‫ ?𝑉∆ ﯾﺴﺎوي‬, ∆𝑉0 ‫?𝑉∆ اﺻﻐﺮ ﻣﻦ‬ *****Q.23) what will happen? And why? For the amount of potential difference between two capacitive plates 𝐶0 connected to a battery and the charge stored in it if another uncharged capacitor 𝐶? was connected to the first capacitor 𝐶0 (with the battery remaining connected in the circuit) and the connection method was in series *Q.24) Answer: A charged capacitor, the potential difference between its two plates is very high (and it is separated from the voltage source), such a capacitor for a long time is dangerous when touched directly with the hand, what is the explanation for that? 80 | P a g e █ Example (7): Two capacitors of parallel plates (C1=3μF & C2=6μF) are connected to each other in series combination. Their group connected between battery poles with a potential difference between them (24V) and the air was as dielectric between the two plates of each of them. If a dielectric plate inserted between two plates of each of them with a dielectric constant (2) to fills the space between the plates (and the group is still connected to the battery), what is the magnitude of the potential difference between the two plates of each capacitor, and the energy stored in the electric field between the two plates of each capacitor in two cases: ❶ Before inserting the dielectric ❷ After inserting the dielectric 81 | P a g e 82 | P a g e █ Q.3) Two capacitors (C1=9μF & C2=18μF) are connected in series combination and then connected to the battery which potential difference is (12V). ❶ Calculate the potential difference between plates of each capacitor and electric energy stored in it. ❷ A dielectric which dielectric constant (4) is placed between plates of first capacitor (the battery is still connected to the circuit). What is the magnitude of potential difference between plates of each capacitor and the stored energy in them after inserting dielectric? 83 | P a g e 84 | P a g e █ Q.4) Two parallel plate capacitors (C1=16μF & C2=24μF) are connected in parallel combination and they are connected to (48V) battery. When a dielectric material with dielectric constant (k) is placed between plates of first capacitor (C1) and the group is still connected to the battery, total magnitude of charge of the group is (3456μC). Calculate: ❶ Dielectric constant (k). ❷ Stored charge in any plate of each capacitor before and after inserting dielectric. 85 | P a g e 86 | P a g e █ Q.5) Two parallel plate capacitors (C1=4μF & C2=8μF) are connected in parallel combination. If the total stored charge of the group is (600μC) when they are charged by a continuous voltage source, then they are disconnected. ❶ Calculate the magnitude of stored charge and stored energy in each capacitor. ❷ If a dielectric material with a dielectric constant (2) is placed between plates of second capacitor (C2), find the capacitance, stored charge, potential difference, and the stored energy in each capacitor. 87 | P a g e 88 | P a g e 31 █ 2013 Round (2) Two capacitors (C1=12μF & C2=6μF) are connected in parallel combination, if their group charged with a total charge of (180μC) by a continuous voltage source and then disconnected from it. ❶ Calculate the magnitude of charge stored in any of the two plates of each capacitor and the energy stored in the electric field between their plates. ❷ A dielectric with a dielectric constant (4) is placed between plates of the second capacitor. What is the magnitude of the charge stored in any of the two plates of each capacitor? and the magnitude of potential difference between plates of each capacitor? 89 | P a g e 32 █ 2014 Preliminary Two capacitors (C1=12μF, C2=6μF) are connected in series combination and then connected to the battery which potential difference is (24V). A dielectric which dielectric constant (2) is placed between the plates of each capacitor (the battery is still connected to the circuit). What is the magnitude of potential difference between plates of each capacitor after inserting dielectric? 90 | P a g e 33 █ 2015 Round (1) Two capacitors (C1=4μF, C2=8μF) are connected in parallel, so if their group is charged with a total charge of (600μC) with a constant voltage source and then separated from it, calculate: ❶ the charge stored in any of the two plates of each capacitor. ❷ A dielectric plate with dielectric constant (K) Inserted between the second capacitor plates, and its charge became (480μC), what is the magnitude of the dielectric constant (K)? 91 | P a g e 34 █ 2015 Round (2) Two capacitors with parallel plates (C1=6μF, C2=12μF) are connected in series combination and then connected to the battery which potential difference is (12V). A dielectric with dielectric constant (3) is placed between plates of capacitors (the battery is still connected to the circuit), calculate: ❶ the potential difference between plates of each capacitor after inserting dielectric. ❷ the stored charge in any plate of each capacitor after inserting dielectric. 92 | P a g e 35 █ 2015 Round (2) Outside Country A capacitor with a capacitance of (15μF) is charged with a potential difference (300V) connected in parallel with another non-charged capacitor, so the potential difference becomes (100V) on both sides of the group. Calculate: ❶ the capacitance of the second capacitor. ❷ the charge of each capacitor after connection. ❸ If a dielectric material is inserted between the first capacitor plates, the group's potential difference becomes (75V), what is the dielectric constant of this material? 93 | P a g e 36 █ 2016 Round (1) Two capacitors with parallel plates (C1=120μF, C2=30μF) are connected in series combination and then connected to the battery which potential difference is (20V), the group disconnected from the battery and a dielectric with dielectric constant (2) is placed between plates of the second capacitor. Calculate the magnitude of the potential difference and the sored energy of the electric field between plates of each capacitor after inserting dielectric. 94 | P a g e 37 █ 2016 Round (2) Two capacitors (C1=6μF & C2=12μF) are connected in parallel combination, if their group charged with a total charge of (180μC) by a continuous voltage source and then disconnected from it. A dielectric with a dielectric constant (4) is placed between plates of the first capacitor. ❶ What is the magnitude of the charge stored in any of the two plates of each capacitor? and the magnitude of potential difference between plates of each capacitor before and after inserting dielectric 95 | P a g e 38 █ 2016 Round (2) Outside Country Two capacitors (C1=8μF & C2=12μF) are connected in parallel combination, if their group charged with a total charge of (60μC) by a continuous voltage source and then disconnected from it. A dielectric with a dielectric constant (2) is placed between plates of the second capacitor. ❶ What is the magnitude of the charge stored in any of the two plates of each capacitor? and the magnitude of potential difference between plates of each capacitor before and after inserting dielectric 96 | P a g e 39 █ 2017 Preliminary, Practical Two capacitors (C1=6μF, C2=3μF) are connected in series combination and then connected to the battery which potential difference is (12V). ❶ Calculate the potential difference between plates of each capacitor. ❷ A dielectric which dielectric constant (2) is placed between plates of the second capacitor (the battery is still connected to the circuit). What is the magnitude of potential difference between plates of each capacitor after inserting dielectric? 97 | P a g e 40 █ 2018 Round (2) Practical Two capacitors (C1=2μF, C2=6μF) are connected in parallel combination, if their group charged with a total charge of (400μC) by a continuous voltage source and then disconnected from it. ❶ Calculate the magnitude of charge stored in any of the two plates of each capacitor. ❷ A dielectric with a dielectric constant (2) is placed between plates of first capacitor. What is the magnitude of charge stored in any of the two plates of each capacitor after inserting dielectric? 98 | P a g e 41 █ 2018 Round (1) Practical Outside Country Two capacitors ( 𝑪𝟏 = 𝟓µ𝒇 , 𝑪𝟐 = 𝟏𝟎µ𝒇) connected together in parallel connected to a battery, so the charge was on the first capacitor (200µC). Calculate: 1- The charge stored on either of the second and total capacitors plates 2- If the group is separated from the battery and an insulating plate is inserted between the two plates of the first capacitor, the dielectric constant of its material (4), what is the amount of charge stored on any of the two plates of each capacitor after inserting the insulator? 99 | P a g e 42 █ 2018 Round (2) Practical Outside Country Two capacitors ( 𝑪𝟏 = 𝟏𝟐µ𝒇 , 𝑪𝟐 = 𝟒µ𝒇)connected in series with the potential difference source between its poles (8V) Calculate: 1- The charge of each capacitor and the electric energy stored in the electric field between the two plates of the first capacitor 2- The charge of each capacitor, after separating it from the source and from each other, and connecting them in parallel, so that the plates of similar charge are bound together. 100 | P a g e 43 █ 2019 Round (1) Practical Two capacitors (C1=9μF & C2=18μF) are connected in series combination, if their group charged by a continuous voltage source and then the energy stored in the electric field between the plates of the first capacitor is (288x10-6J). ❶ Calculate the magnitude of the potential difference between the plates of each capacitor. ❷ A dielectric with a dielectric constant (4) is placed between plates of first capacitor (The battery is still connected to the circuit). What is the magnitude of potential difference between plates of each capacitor after inserting dielectric? 101 | P a g e 44 █ 2020 Round (1) Practical Two parallel plate capacitors (C1=16μF & C2=24μF) are connected in parallel combination and they are connected to (48V) battery. When a dielectric material with dielectric constant (k) is placed between plates of first capacitor (C1) and the group is still connected to the battery, total magnitude of charge of the group is (3456μC). Calculate: ❶ Dielectric constant (k). ❷ Stored charge in any plate of each capacitor before and after inserting dielectric. 102 | P a g e 45 █ 2021 Round (2) Practical capacitor with two parallel plates. The air is an insulator between its two plates. It was charged by means of a battery and then separated from it. When a fixed electrical insulating plate (k = 3) was inserted between its two plates, what happens to each of the electric field and the energy stored between its two plates after inserting the insulator? (With a reason) 103 | P a g e 46 █ 2017 Preliminary, Biology Two capacitors (C1=3μF, C2=6μF) are connected in series combination and then connected to the battery which potential difference is (12V). ❶ Calculate the potential difference between plates of each capacitor. ❷ A dielectric which dielectric constant (2) is placed between plates of each capacitor (the battery is still connected to the circuit). What is the magnitude of potential difference between plates of each capacitor after inserting dielectric? 104 | P a g e 47 █ 2017 Round (2) Biology Two capacitors (C1=3μF, C2=6μF) are connected in series combination, if their group charged with a total charge of (900μC) by a continuous voltage source and then disconnected from it. ❶ Calculate the magnitude of charge stored in any of the two plates of each capacitor and the energy stored in the electric field between their plates. ❷ A dielectric with a dielectric constant (3) is placed between plates of first capacitor. What is the magnitude of charge stored in any of the two plates of each capacitor and the potential difference between plates of each capacitor and the stored energy in them after inserting dielectric? 105 | P a g e 48 █ 2017 Round (3) Biology Q.26) Two capacitors (C1=3μF, C2=6μF) are connected in series combination and then connected to the battery which potential difference is (12V). ❶ Calculate the potential difference and the stored energy between plates of each capacitor. ❷ A dielectric which dielectric constant (4) is placed between plates of the first capacitor (the battery is still connected to the circuit). What is the magnitude of potential difference between plates of each capacitor after inserting dielectric? 106 | P a g e 49 █ 2018 Round (1) Biology Two parallel plate capacitors (C1=9μF, C2=18μF) are connected in series combination and they are connected to (24V) battery. When a dielectric material with dielectric constant (k) is placed between plates of first capacitor (C1) and the group is still connected to the battery, total magnitude of charge of the group is (288μC). Calculate: ❶ Dielectric constant (k). ❷ Stored charge in any plate of each capacitor after inserting dielectric. 107 | P a g e 50 █ 201