Character analysis Essay Example | Topics and Well Written Essays - 1500 words

Character analysis - Essay Example â€Å"Never forget what you are. The rest of the world will not. Wear it like armor and it can never be used to hurt you† (Martin, 56). The dialogue is from George R.R Martin’s series, A ‘Song of Ice and Fire’, spoken by Tyrion Lannister, one of the most fascinating characters who carry a remarkable astuteness and intricate personality in the book. Apparently, his words indicate the great hopes and strong self-esteem that he possessed despite being a dwarf and believed that his physical disability does not imply his inability to deliver in life. Through his moving and treasured way of speaking, Tyrion shows outstanding ability of prudence and intuition. â€Å"As the most grandest creation† of the author Tyrion’s ambitions vitalizes on his unique perspective and open the new page of history on the great performance of a dwarf in media. Commendably, Tyrion sojourns on to attest that indeed the adversaries linked to his dwarfism can be overcome ( Ben, 01). Moreover, to fully comprehend the complexity and uniqueness of the characteristics of Tyrion, one must discern his childhood background. As a â€Å"high born dwarf† in an extremely dignified and arrogant family who had controlled their governance over seven kingdoms, Tyrion was not a son with interminable elegance and fondness. On the contrary, he has been depicted as a â€Å"midget† or â€Å"imp† who has been made an outcast by other characters in his family (Abraham et al., 116). Among different reasons behind people’s hatred towards Tyrion includes the death of his mother while she was giving birth to him. Tyrion Lannister does not share a strong bond with his only sister named Cersei Lannister. Nevertheless, his brother Jamie Lannister has a lot of compassion for Tyrion for which he has helped him throughout the novel. Additionally, the community of the Lannisters immensely ostracized Tyrion because he was expected to be

Writing Class Essay Example | Topics and Well Written Essays - 750 words

Writing Class - Essay Example I learnt a number of aspects about writing this semester. In the initial weeks, I kept using additional sources were they were not necessary. In the second week for example, I used different outside sources instead of sticking to the video that I was to describe. In the third week, I still used other sources, where I was expected to use my own ideas. In the fourth week however, I managed to use correct sources and I cited most of the statements I gave well. However, there were still a few ideas that lacked proper citations The biggest challenge I faced as a writer is that of creating paragraphs with a clear focus. This is majorly because I could create specific topic sentences that would guide me. A single paragraph should elaborate on one idea but mine were generally most often (Connelly 208). In my first two write-ups onto the third one, my paragraphs were still not clear since they did not seem to lead to one point. This is probably because I did not outline the work properly prior. The professor advised that I should stick to one idea in every single paragraph instead of mixing them all up in one paragraph because it will not only confuse the reader but also affect the flow of work. In the fourth week however, I had learnt how to create topic sentences since only a few paragraphs lacked the topic sentences. Moreover, in the third week, I also had problems with my choice of word. Generally, the language and grammar was not to the level expected. This is evident in the instance where I used the term cleavage as a synonym to differences. Growth was evident when it came to the creation of a clear thesis as well as strong introductions. In my early consecutive papers, the introduction could not interest a reader. Towards the third week, I still had problems producing good introductions that would capture the interest of the reader. It had however improved since I incorporated better choices of words.  

Electric Filed Strength And Electric Flux Density

Electric Filed Strength And Electric Flux Density All bodies are made up of atoms, which consist of a nucleus containing protons (+ve) and neutrons (neutral) and surrounding the nucleus are orbiting electrons (-ve). When a body is uncharged it is electrically neutral, it has the same negative charge as positive charge. If a conductor had a deficit of electrons it would exhibit a net positive charge and if it was to have a surplus of electrons it would exhibit a net negative charge (remember the previous study of the atom reference +ve/-ve ions). An imbalance in charge can be produced by friction (removing or depositing electrons using materials such as silk and fur, respectively) or induction (by attracting or repelling electrons using a second body which is, respectively, positively or negatively charged). Coulombs Law states that if charged bodies exist at two points, the force of attraction (if the charges are of opposite polarity) or repulsion (if the charges have the same polarity) will be proportional to the product of the magnitude of the charges divided by the square of their distance apart. Thus: + + + Direct Inverse Proportionality Maths Q1 and Q2 are the charges present at the two points (in Coulombs), d is the distance separating the two points (in metres), F is the force (in Newtons), and k is a mathematical constant depending upon the medium in which the charges exist. In a vacuum or free space, ÃŽÂ µ0 is the permittivity of free space (8.854 x 10-12 F/m Farad per meter). The force exerted on a charged particle is a manifestation of the existence of an electric field. The electric field defines the direction and magnitude of a force on a charged object. The field itself is invisible to the human eye but can be drawn by constructing lines which indicate the motion of a free positive charge within the field; the number of field lines in a particular region being used to indicate the relative strength of the field at the point in question. The figure above shows the electric fields between charges of the same and opposite polarity. The figure below shows the field which exists between two charged parallel plates. B A As illustrated above, plates A and B are doped and charged to different potentials. If an electron that has a negative charge is placed between the plates, a force will act on the electron tending to push it away from the negative plate B and towards the positive plate A. Similarly, a positive charge would be acted on by a force tending to move it toward the negative plate. The region between the plates in which an electric charge experiences a force, is called an electrostatic field. The direction of the field is defined by the force acting on a positive charge placed in the field, i.e. the direction of the force is from the positive plate to the negative plate. Such a field may be represented in magnitude and direction by lines of electric force drawn between the charged surfaces. The closeness of the lines is an indication of the field strength. Whenever a p.d. is established between two points, an electric field will always exist. The figure above shows two parallel conducting plates separated from each other by air, and are connected to opposite terminals of a battery of voltage V volts. There is therefore an electric field in the space between the plates. If the plates are close together, the electric lines of force will be straight and parallel and equally spaced, except near the edge where fringing will occur (see previous figure). Over the area in which there is negligible fringing, E is the electric field strength (V/m), V is the applied potential difference across the parallel plates (V) and d is the distance (m). **Note: Electric Field Strength is also called Potential/Voltage Gradient. A unit electric flux is defined as emanating from a positive charge of 1 coulomb. Thus electric flux à Ã‹â€  is measured in coulombs, and for a charge of Q coulombs, the electric flux à Ã‹â€  is equal to Q coulombs. Electric flux density D is the amount of flux passing through a defined area A that is perpendicular to the direction of the flux: à Ã‹â€  is the electric flux measured in coulombs, Q is the electric charge also measured in coulombs, and A is the area in m2 over which the flux is distributed. Problem 1: Two parallel rectangular plates measuring 20cm by 40cm carry an electric charge of 0.2  µC. (a) Calculate the electric  ¬Ã¢â‚¬Å¡ux density. (b) If the plates are spaced 5mm apart and the voltage between them is 0.25 kV determine the electric field strength. Solution 1: PERMITTIVITY At any point in an electric field, the electric field strength E maintains the electric flux and produces a particular value of electric flux density D at that point. For a field established in vacuum (or for practical purposes in air), the ratio D/E is a constant ÃŽÂ µ0, i.e. ÃŽÂ µ0 is called the permittivity of free space or the free space constant. The value of ÃŽÂ µ0 is 8.854 x 10-12 F/m Farad per meter. When a dielectric (i.e. insulating medium separating charged surfaces), such as mica, paper, plastic or ceramic is introduced into the region of an electric field, the ratio of D/E is modified. ÃŽÂ µr is called the relative permittivity of the insulating material and indicates its insulating power compared with that of vacuum. ÃŽÂ µr has no units and typical properties of some common insulating dielectric materials are shown below. The product of ÃŽÂ µ0 ÃŽÂ µr is called the absolute permittivity, ÃŽÂ µ, i.e. As discussed earlier, the dielectric is an insulating medium separating charged surfaces and has the property of very high resistivity. They are therefore used to separate conductors at different potentials, such as capacitor plates or electric power lines. The dielectric strength of an insulating dielectric is the maximum electric field strength that can safely be applied to it before breakdown (conduction) occurs. The amount of charge produced for a given applied voltage on the two parallel plates shown earlier will depend not only on the physical dimensions but also on the insulating dielectric material that appears between the plates. Such materials need to have a very high value of resistivity (i.e. they must not conduct charge) coupled with an ability to withstand high voltages without breaking down. A more practical arrangement of parallel plates with an insulating dielectric material is shown. In this arrangement the ratio of charge, Q, to the potential difference, V, is given by the following relationship. A = area of one on the plates, in m2 D = thickness of the dielectric in m ÃŽÂ µ = absolute permittivity of the dielectric material *Later learning, i.e. the parallel plate capacitor/capacitance and physical dimensions. à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦ single pair of plates à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦ arrangement of n plates Problem 1: The  ¬Ã¢â‚¬Å¡ux density between two plates separated by mica of relative permittivity 5 is 2 µC/m2. Find the voltage gradient between the plates. Solution 1: Problem 2: Two parallel plates having a p.d. of 200V between them are spaced 0.8mm apart. What is the electric  ¬Ã‚ eld strength? Find also the electric  ¬Ã¢â‚¬Å¡ux density when the dielectric between the plates is (a) air, and (b) polythene of relative permittivity 2.3 Solution 2: SELF ASSESSMENT (1-2) NOTE: Where appropriate take ÃŽÂ µ0 as 8.85 x 10-12 F/m A capacitor uses a dielectric 0.04mm thick and operates at 30V. What is the electric field strength across the dielectric at this voltage? [Answer: 750kV/m] A two-plate capacitor has a charge of 25C. If the effective area of each plate is 5cm2 determine the electric  ¬Ã¢â‚¬Å¡ux density of the electric field. [Answer: 50 kC/m2] A charge of 1.5 µC is carried on two parallel rectangular plates each measuring 60mm by 80mm. (a) Calculate the electric  ¬Ã¢â‚¬Å¡ux density. (b) If the plates are spaced 10mm apart and the voltage between them is 0.5kV determine the electric  ¬Ã‚ eld strength. [Answer: (a) 312.5 µC/m2, (b) 50kV/m] Two parallel plates are separated by a dielectric and charged with 10 µC. Given that the area of each plate is 50cm2, calculate the electric  ¬Ã¢â‚¬Å¡ux density in the dielectric separating the plates. [Answer: 2mC/m2] The electric  ¬Ã¢â‚¬Å¡ux density between two plates separated by polystyrene of relative permittivity 2.5 is 5 µC/m2. Find the voltage gradient between the plates. [Answer: 226kV/m] Two parallel plates having a p.d. of 250V between them are spaced 1mm apart. (a) Determine the electric  ¬Ã‚ eld strength. (b) Find also the electric  ¬Ã¢â‚¬Å¡ux density when the dielectric between the plates is (i) air and (ii) mica of relative permittivity 5. [Answer: (a) 250kV/m (bi) 2.213 µC/m2 (bii) 11.063 µC/m2] CAPACITORS CAPACITANCE A capacitor is a device for storing electric charge. In effect, it is a reservoir into which charge can be deposited and then later extracted. In its simplest form a capacitor consists of two parallel metal plates which are separated by an insulating material known as a dielectric. C:Documents and SettingsHarveyMy DocumentsMy PicturesPicturePicture 028.jpg Because of the dielectric, current cannot flow from one plate to the other. When the capacitor is connected to a dc source, electrons accumulate on the plate connected to the negative supply terminal. The negative charge repels electrons from the atoms of the other plate. These electrons flow away to the positive terminal of the dc source; this leaves the plate positively charged. C:Documents and SettingsHarveyMy DocumentsMy PicturesPicturePicture 032.jpg If the capacitor is disconnected from the supply, the charges remain. The capacitor stores the electric charge indefinitely. The symbols for a fixed capacitor and a variable capacitor used in electrical circuit diagrams are shown below. Typical applications include reservoir and smoothing capacitors for use in power supplies, coupling a.c. signals between the stages of amplifiers, and decoupling supply rails (i.e. effectively grounding the supply rails as far as a.c. signals are concerned). The following figures illustrate what happens to a capacitor when it is charging and discharging. If the switch is left open (position A), no charge will appear on the plates and in this condition there will be no electric field in the space between the plates nor will there be any charge stored in the capacitor. When the switch is moved to position B, electrons will be attracted from the positive plate to the positive terminal of the battery. At the same time, a similar number of electrons will move from the negative terminal of the battery to the negative plate. This sudden movement of electrons will manifest itself in a momentary surge of current (conventional current will flow from the positive terminal of the battery towards the positive terminal of the capacitor). Eventually, enough electrons will have moved to make the e.m.f. between the plates the same as that of the battery. In this state, the capacitor is said to be fully charged and an electric field will be present in the space between the two plates. If, at some later time the switch is moved back to position A, the positive plate will be left with a deficiency of electrons whilst the negative plate will be left with a surplus of electrons. Furthermore, since there is no path for current to flow between the two plates the capacitor will remain charged and a potential difference will be maintained between the plates. Now assume that the switch is moved to position C. The excess electrons on the negative plate will flow through the resistor to the positive plate until a neutral state once again exists (i.e. until there is no excess charge on either plate). In this state the capacitor is said to be fully discharged and the electric field between the plates will rapidly collapse. The movement of electrons during the discharging of the capacitor will again result in a momentary surge of current (current will flow from the positive terminal of the capacitor and into the resistor). The figure below shows the direction of current flow during charging (i.e. the switch in position B) and discharging (i.e. the switch in position C). It should be noted that current flows momentarily in both circuits even though you may think that the circuit is broken by the gap between the capacitor plates! The charge Q (in coulombs) stored in a capacitor is given by: I is the current in amperes and t is the time in seconds. Charge Q on a capacitor is proportional to the applied voltage V, i.e. Q V. Direct Inverse Proportionality Maths Q = CV The constant of proportionality C is the capacitance. The unit of capacitance C is the farad F (or more usually  µF =10-6F or pF =10-12F), and is defined as the capacitance when a p.d. of one volt appears across the plates when charged with one coulomb. Capacitance is the ability of a circuit or object (i.e. in this case a capacitor) to store electric charge. Problem 1: (a) Determine the p.d. across a 4  µF capacitor when charged with 5 mC (b) Find the charge on a 50 pF capacitor when the voltage applied to it is 2 kV. Solution 1: Problem 2: A direct current of 4A flows into a previously uncharged 20  µF capacitor for 3 ms. Determine the p.d. between the plates. Solution 2: Problem 3: A 5 µF capacitor is charged so that the p.d. between its plates is 800V. Calculate how long the capacitor can provide an average discharge current of 2 mA. Solution 3: SELF ASSESSMENT (3) Find the charge on a 10  µF capacitor when the applied voltage is 250 V. (Answer: 2.5 mC) Determine the voltage across a 1000à Ã‚ F capacitor to charge it with 2  µC. (Answer: 2 kV) The charge on the plates of a capacitor is 6 mC when the potential between them is 2.4 kV. Determine the capacitance of the capacitor. (Answer: 2.5  µF) For how long must a charging current of 2 A be fed to a 5  µF capacitor to raise the p.d. between its plates by 500V. (Answer: 1.25 ms) A direct current of 10 A flows into a previously uncharged 5  µF capacitor for 1 ms. Determine the p.d. between the plates. (Answer: 2 kV) A 16  µF capacitor is charged at a constant current of 4  µA for 2 minutes. Determine the final p.d. across the capacitor and the corresponding charge in coulombs. (Answer: 30V, 480  µC) A steady current of 10 A flows into a previously uncharged capacitor for 1.5 ms when the p.d. between the plates is 2 kV. Find the capacitance of the capacitor. (Answer: 7.5 µF) CAPACITANCE AND PHYSICAL DIMENSIONS (Conventional Parallel Plate Capacitor) The capacitance of a capacitor depends upon the physical dimensions of the capacitor (i.e. the size of the plates and the separation between them) and the dielectric material between the plates. The capacitance of a conventional parallel plate capacitor is given by: Where, C = Capacitance, unit of measure farads (F) ÃŽÂ µ0 = Permittivity of free space or the free space constant (8.85 x 10-12 F/m) ÃŽÂ µr = Relative permittivity of the dielectric medium between the plates (ÃŽÂ µr has no units as it is a ratio of density material/vacuum) A = Area of one of the plates (m2) d = Thickness of the dielectric or separation between the plates (m) In order to increase the capacitance of a capacitor, many practical components employ multiple plates as shown. Ten plates are shown, forming nine capacitors with a capacitance nine times that of one pair of plates. Such an arrangement has n plates then capacitance C à ¢Ã‹â€ Ã‚  (n -1). Thus capacitance is then given by: Problem 1: A ceramic capacitor has an effective plate area of 4cm2 and separated by 0.1 mm of ceramic of relative permittivity 100. Calculate the capacitance of the capacitor in picofarads (à Ã‚ F). If the capacitor in part (a) is given a charge of 1.2 µC what will be the p.d. between the plates? Solution 1: Problem 2: A waxed paper capacitor has two parallel plates, each of effective area 800 cm2. If the capacitance of the capacitor is 4425 pF determine the effective thickness of the paper if its relative permittivity is 2.5. Solution 2: Problem 3: A parallel plate capacitor has nineteen interleaved plates each 75 mm by 75 mm and separated by mica sheets 0.2 mm thick. Assuming that the relative permittivity of the mica is 5, calculate the capacitance of the capacitor. Solution 3: n = 19, thus (n 1) = 18 A = 75 x 75 = 5625mm2 ÃŽÂ µr = 5, ÃŽÂ µ0 = 8.85 x 10-12 F/m d = 0.2mm = 0.2 x 10-3m SELF ASSESSMENT (4) ** Where appropriate take ÃŽÂ µ0 as 8.85 x 10-12 F/m. A capacitor consists of two parallel plates each of area 0.01 m2, spaced 0.1 mm in air. Calculate the capacitance in picofarads (pF). [Answer: 885 pF] A waxed paper capacitor has two parallel plates, each of effective area 0.2m2. If the capacitance is 4000 pF determine the effective thickness of the paper if its relative permittivity is 2. [Answer: 0.885 mm] Calculate the capacitance of a parallel plate capacitor having 5 plates, each 30 mm by 20 mm and separated by a dielectric 0.75 mm thick having a relative permittivity of 2.3. [Answer: 65.14 pF] How many plates does a parallel plate capacitor have if its capacitance is 5nF, each plate is 40mm by 40mm and each dielectric is 0.102mm thick with a relative permittivity of 6? [Answer: 7] A parallel plate capacitor is made from 25 plates, each 70mm by 120mm interleaved with mica of relative permittivity 5. If the capacitance of the capacitor is 3000pF determine the thickness of the mica sheet. [Answer: 2.97mm] The capacitance of a parallel plate capacitor is 1000pF. It has 19 plates, each 50mm by 30mm separated by a dielectric of thickness 0.40mm. Determine the relative permittivity of the dielectric. [Answer: 1.67] CAPACITORS CONNECTED IN PARALLEL AND SERIES CAPACITORS CONNECTED IN PARALLEL The figure above shows three capacitors, C1, C2 and C3 connected in parallel with a supply voltage V applied across the arrangement. (Note: just like resistors in parallel, the supply voltage V is the same across each parallel capacitor) V = V1 = V2 = V3 When the charging current I reaches point A it divides, some flowing into C1, some flowing into C2 and some into C3. Hence the total charge QT (i.e. QT= I x t) is divided between the three capacitors. The capacitors each store a charge and these are shown as Q1, Q2 and Q3 respectively. Hence, But, QT=CV (where C is the total equivalent circuit capacitance) And, Q1=C1V Q2=C2V Q3=C3V Therefore, CV = C1V + C2V + C3V (where C is the total equivalent circuit capacitance) Dividing throughout by the common V giving, C = C1 + C2 + C3 à ¢Ã¢â€š ¬Ã‚ ¦Ãƒ ¢Ã¢â€š ¬Ã‚ ¦. + Cn The equivalent capacitance of a group of parallel connected capacitors is the sum of the capacitances of the individual capacitors. CAPACITORS CONNECTED IN SERIES The figure above shows three capacitors, C1, C2 and C3 connected in series across a supply voltage V. Let the p.d. across the individual capacitors be V1, V2 and V3 respectively as shown. Let the charge on the plate a of the capacitor C1 be +Q coulombs. This induces and equal but opposite charge of -Q coulombs on plate b. The conductor between plates b and c is electrically isolated from the rest of the circuit so that an equal but opposite charge of +Q coulombs must appear on plate c, which, in turn, induces an equal and opposite charge of -Q coulombs on plate d, and so on. Hence when capacitors are connected in series the charge on each is the same. QT = Q1 = Q2 = Q3 In a series circuit: V = V1 + V2 + V3 (Similar to resistors in series) Since, then (where C is the total equivalent circuit capacitance) Dividing throughout by the common Q giving, (Where C is the total equivalent circuit capacitance) For series connected capacitors, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitance. For special case of two capacitors in series, Hence, i.e. Problem 1: Calculate the equivalent capacitance of two capacitors of 6ÃŽÂ ¼F and 4ÃŽÂ ¼F connected in (a) Parallel (b) Series. Solution 1: Problem 2: What capacitance must be connected in series with a 30ÃŽÂ ¼F capacitor for the equivalent capacitance to be 12ÃŽÂ ¼F? Solution 2: Problem 3: Capacitances of 1ÃŽÂ ¼F, 3ÃŽÂ ¼F, 5ÃŽÂ ¼F and 6ÃŽÂ ¼F are connected in parallel to a direct voltage supply of 100V. Determine (a) the equivalent circuit capacitance, (b) the total charge and (c) the charge on each capacitor. Solution 3: Problem 4: Capacitances of 3ÃŽÂ ¼F, 6ÃŽÂ ¼F and 12ÃŽÂ ¼F are connected in series across a 350V supply. Calculate (a) the equivalent circuit capacitance, (b) the charge on each capacitor, and (c) the p.d. across each capacitor. Solution 4: Problem 5: For the arrangement shown, find (a) the equivalent capacitance of the circuit, (b) the voltage across QR and (c) The charge on each capacitor. Solution 5: SELF ASSESSMENT (5) Capacitors of 2 µF and 6 µF are connected (a) in parallel and (b) in series. Determine the equivalent capacitance in each case. [Answers: (a) 8ÃŽÂ ¼F (b) 1.5ÃŽÂ ¼F] Find the capacitance to be connected in series with a 10 µF capacitor for the equivalent capacitance to be 6 µF. [Answer: 15ÃŽÂ ¼F] What value of capacitance would be obtained if capacitors of 0.15 µF and 0.10 µF are connected in (a) series and (b) parallel? [Answers: (a) 0.06ÃŽÂ ¼F (b) 0.25ÃŽÂ ¼F] Two 6 µF capacitors are connected in series with one having a capacitance of 12 µF. Find the total equivalent circuit capacitance. What capacitance must be added in series to obtain a capacitance of 1.2 µF? [Answers: (a) 2.4ÃŽÂ ¼F (b) 2.4ÃŽÂ ¼F] For the arrangement shown below, find (a) the equivalent circuit capacitance and (b) the voltage across a 4.5ÃŽÂ ¼F capacitor. [Answers: (a) 1.2ÃŽÂ ¼F (b) 100V] Three 12 µF capacitors are connected in series across a 750V supply. Calculate (a) the equivalent capacitance, (b) the charge on each capacitor and (c) the p.d. across each capacitor. [Answers: (a) 4 µF (b) 3mC (c) 250V] If two capacitors having capacitances of 3 µF and 5 µF respectively are connected in series across a 240V supply, determine (a) the p.d. across each capacitor and (b) the charge on each capacitor. [Answers: (a) 150V, 90V (b) 0.45 mC on each] Capacitances of 4 µF, 8 µF and 16 µF are connected in parallel across a 200V supply. Determine (a) the equivalent capacitance, (b) the total charge and (c) the charge on each capacitor. [Answers: (a) 28  µF (b) 5.6mC (c) 0.8mC, 1.6mC, 3.2mC] DIELECTRIC STRENGTH The maximum safe working voltage is the maximum voltage that can be applied to the terminals of a capacitor without causing damage to the capacitor. The manufacturer specifies this voltage. The limit is necessary so that the field strength in the dielectric does not exceed a value that would cause the dielectric to breakdown and loose its insulating properties. The figure quoted by the manufacturer for a capacitor is also known as the dielectric strength and will be in volts per metre. E is the dielectric strength (V/m), V is the applied potential difference across the parallel plates (V) and d is the distance (m). **Note: Equation identical to Electric Field Strength (Potential/Voltage Gradient). Problem1: A capacitor is to be constructed so that its capacitance is 0.2 µF and to take a p.d. of 1.25kV across its terminals. The dielectric is to be mica and has a dielectric strength of 50MV/m. Find (a) the thickness of the mica needed, and (b) the area of a plate assuming a two-plate construction. (Assume ÃŽÂ µr for mica to be 6). Solution 1: ENERGY STORED IN CAPACITORS The energy, W, stored by a capacitor is given by, Where, W is the energy (in Joules), C is the capacitance (in Farads), and V is the potential difference (in Volts). Problem 1: (a) Determine the energy stored in a 3 µF capacitor when charged to 400V. (b) Find also the average power developed if this energy is dissipated in a time of 10 µs. Solution 1: Problem 2: A 12 µF capacitor is required to store 4J of energy. Find the p.d. to which the capacitor must be charged. Solution 2: Problem 3: A capacitor is charged with 10mC. If the energy stored is 1.2J, determine (a) the voltage and (b) the capacitance. Solution 3: SELF ASSESSMENT (6) ** Where appropriate take ÃŽÂ µ0 as 8.85 x 10-12 F/m. When a capacitor is connected across a 200V supply the charge is 4 µC. Find (a) the capacitance and (b) the energy stored. [Answer: (a) 0.02 µF (b) 0.4mJ] Find the energy stored in a 10 µF capacitor when charged to 2kV. [Answer: 20 J] A 3300pF capacitor is required to store 0.5mJ of energy. Find the p.d. to which the capacitor must be charged. [Answer: 550 V] A capacitor is charged with 8mC. If the energy stored is 0.4J, determine (a) the voltage and (b) the capacitance. [Answer: (a) 100V (b) 80  µF] A capacitor, consisting of two metal plates each of area 50 cm2 and spaced 0.2mm apart in air, is connected across a 120V supply. Calculate (a) the energy stored (b) the electric  ¬Ã¢â‚¬Å¡ux density and (c) the potential gradient (i.e. electric field strength). [Answer: (a) 1.593 µJ (b) 5.31 µC/m2 (c) 600kV/m] D.C TRANSIENTS Networks of capacitors and resistors (known as C-R circuits) form the basis of many timing and pulse shaping circuits and are thus often found in practical electronic circuits. When a d.c. voltage is applied to a capacitor C and resistor R connected in series, there is a short period of time immediately after when the voltage is connected that the current flowing in the circuit and voltages across C and R are changing. These changing values are called transients. CHARGING A CAPACITOR The figure above shows a series connected C-R circuit. When the switch S is closed, then by Kirchhoffs valotage law: V = Vc + VR The battery voltage V is constant. The capacitor voltage Vc is given by, The voltage drop across R (i.e. VR) is given by, Hence at all times: At the instant of closing S (i.e. initial circuit condition), assuming there is no initial charge on the capacitor, Q is zero (i.e. Q0), hence Vc is zero (i.e. VC0). (Note: From equation Vc = Q / C). Thus from equation V = Vc + VR, V = 0 + VR (i.e. V = VR = IR) A short time later at time T1 seconds after closing S, the capacitor is partly charged to, say, Q1 coulombs because current has been flowing. The voltage VC1 is now, If the current flowing is I1 amperes, then the voltage drop across R has fallen to VR1 = I1R volts. Thus from equation V = Vc + VR A short time later still, say at time T2 seconds after closing S, the charge has increased to Q2 coulombs and VC has increased to, Since V = VC + VR and V is a constant, then VR decreases to I2R. Thus VC is increasing and I and VR are decreasing as time increases. Ultimately, a few seconds after closing S (i.e. at the final or steady state condition), the capacitor is fully charged to, say Q coulombs, current no longer flows, i.e. I = 0, and hence VR = IR = 0. It follows from equation V = Vc + VR that V = VC. Curves showing the changes in VC, VR and I with time are shown below. The curve showing the variation of VC with time is called an exponential growth curve and the graph is called the capacitor voltage / time characteristic. The curves showing variations of VR and I with time are called exponential decay curves, and the graphs are called resistor voltage / time and current / time characteristics respectively. The name exponential shows that the shape can be expressed mathematically by an exponential mathematical equation, as shown below. Growth of capacitor voltage, Decay of resistor voltage, Decay of resistor current, TIME CONSTANT (à Ã¢â‚¬Å¾ TAU) FOR A C-R CIRCUIT As shown earlier, if a constant d.c. voltage is applied to a series connected C-R circuit, a exponential transient growth curve of capacitor voltage VC results as shown below. With reference to the figure below, the constant voltage supply is replaced by a variable voltage supply at time t1 seconds. The voltage is varied so that the current flowing in the circuit is constant. Since the current flowing is a constant, the curve will follow a tangent, AB, drawn to the curve at point A. Let the capacitor voltage VC reach its final value of V at time t2 seconds. The time corresponding to (t2-t1) seconds is called the time constant of the circuit, denoted by the Greek letter tau, à Ã¢â‚¬Å¾. The value of the time constant is CR seconds, i.e. for a series connected C-R circuit, (seconds) Where C is capacitance (F), R is the resistance (à ¢Ã¢â‚¬Å¾Ã‚ ¦) and à Ã¢â‚¬Å¾ is the time constant (s) DISCHARGING A CAPACITOR When a capacitor is charged (i.e. with the switch in position A), and the switch is then moved to position B, the electrons stored in the capacitor keep the current flowing for a short time. Initially, at the instant of moving from A to B, the current flow is such that the capacitor voltage VC is balanced by equal and opposite voltage (Kirchhoffs 2nd law), i.e. VC = VR = IR. Finally the transients decay exponentially as current is reduced to zero, i.e. VC = VR = 0. The transient curve representing the voltages and current are shown below. The equations representing the transient curves during discharge period of a series connected C-R circuit are: Decay of voltage, Decay of current, When a capacitor has been disconnected from the supply it may still be charged and it may retain this charge for some considerable time. Thus precautions must be taken to ensure that the capacitor is automatically discharged after the supply is switched off. This is done by connecting a high value resistor across the capacitor terminals. Problem 1: A capacitor is charg

Attila The Hun Essay -- essays research papers

Attila the Hun is known as one of the most ferocious leaders of ancient times. He was given the nickname â€Å"Scourge God† because of his ferocity. During the twentieth century, â€Å"Hun† was one of the worst name you could call a person, due to Attila. The Huns were a barbaric and savage group of people, and Attila, their leader, was no exception. He was the stereotypical sacker of cities and killer of babies. The Huns lasted long after their disappearance in mythology and folklore, as the bad guy. Generally, they were not fun people to be around. Priscus saw Attila the Hun at a banquet in 448. Priscus described him as being a short, squat man with a large head and deep-set eyes. He also had a flat nose and a thin beard. Historians say that his general personality was irritable, blustering, and truculent. He was said to be a persistent negotiator, and not at al pitiless. While Priscus was at the banquet in 448, he observed a few other details about Attila. All of Attila’s chief lieutenants were served dainties on silver platters, but he was served only meat on wooden plates. No other real qualities of Attila as a general really survived through time, but he is thought to have been an outstanding commander from his accomplishments as a barbarian. Huns themselves were mysterious and feared people. They first appeared in the Fourth Century around the Roman Empire. They rode their warhorses around and cause the Germanic barbarians and Romans alike to fear them. Yet, it was said that they were very uncivilized. It was said that they made no use of fire, and just ate the roots of plants they found in fields. They were also said to have eaten the almost raw meat of animals. The only reason the meat was â€Å"almost raw† was because they were said to have â€Å"cooked† it by placing it between their thighs and the backs of their horses to give it warmth. The Huns sometimes engaged in regular battle. They would attack in an order of columns, and scream very disorderly and savage cries. Most of the time, though, the Huns just fought in a very random way. They would scream and run about and then all come together in a large group. They would then, as a group, approach the camp or town of the people they were attacking, and destroy it. Most of the time, the people the Huns attacked never even saw them coming. There were many ways in which the Huns chose to fight. They often s... ...y. They sacked many cities, including Aquilieia, Patavium, Verona, Brixia, Bergomum, and Mediolamun. There wasn’t much Aetius could do about this. Luckily, famine and pestilence caused the Huns to leave before crossing the Apennines. In 453, Attila planned to attack the Eastern Empire because the Emperor wasn’t paying the money set in previous treaties (author’s note: Don’t these emperors ever learn anything?). Nothing ever actually came of these plans because, quite suspiciously, Attila died in his bed the night after his marriage. When Attila was buried, the Huns went through a lot of trouble. They had to kill anyone who was involved with the burial, so that no one would know of the exact place that Attila was buried. Attila was succeeded by his sons, between which the empire was divided. Attila didn’t have a huge impact on history, because the Romans very well could have done without him. He mainly caused trouble for the Romans, and killed a lot of innocent people just to get his way. Attila the Hun was one of the most important kings of the Huns, though, and he definitely has his place in history, as a barbaric, baby-killing, rude leader of a very ruthless group of warriors. Attila The Hun Essay -- essays research papers Attila the Hun is known as one of the most ferocious leaders of ancient times. He was given the nickname â€Å"Scourge God† because of his ferocity. During the twentieth century, â€Å"Hun† was one of the worst name you could call a person, due to Attila. The Huns were a barbaric and savage group of people, and Attila, their leader, was no exception. He was the stereotypical sacker of cities and killer of babies. The Huns lasted long after their disappearance in mythology and folklore, as the bad guy. Generally, they were not fun people to be around. Priscus saw Attila the Hun at a banquet in 448. Priscus described him as being a short, squat man with a large head and deep-set eyes. He also had a flat nose and a thin beard. Historians say that his general personality was irritable, blustering, and truculent. He was said to be a persistent negotiator, and not at al pitiless. While Priscus was at the banquet in 448, he observed a few other details about Attila. All of Attila’s chief lieutenants were served dainties on silver platters, but he was served only meat on wooden plates. No other real qualities of Attila as a general really survived through time, but he is thought to have been an outstanding commander from his accomplishments as a barbarian. Huns themselves were mysterious and feared people. They first appeared in the Fourth Century around the Roman Empire. They rode their warhorses around and cause the Germanic barbarians and Romans alike to fear them. Yet, it was said that they were very uncivilized. It was said that they made no use of fire, and just ate the roots of plants they found in fields. They were also said to have eaten the almost raw meat of animals. The only reason the meat was â€Å"almost raw† was because they were said to have â€Å"cooked† it by placing it between their thighs and the backs of their horses to give it warmth. The Huns sometimes engaged in regular battle. They would attack in an order of columns, and scream very disorderly and savage cries. Most of the time, though, the Huns just fought in a very random way. They would scream and run about and then all come together in a large group. They would then, as a group, approach the camp or town of the people they were attacking, and destroy it. Most of the time, the people the Huns attacked never even saw them coming. There were many ways in which the Huns chose to fight. They often s... ...y. They sacked many cities, including Aquilieia, Patavium, Verona, Brixia, Bergomum, and Mediolamun. There wasn’t much Aetius could do about this. Luckily, famine and pestilence caused the Huns to leave before crossing the Apennines. In 453, Attila planned to attack the Eastern Empire because the Emperor wasn’t paying the money set in previous treaties (author’s note: Don’t these emperors ever learn anything?). Nothing ever actually came of these plans because, quite suspiciously, Attila died in his bed the night after his marriage. When Attila was buried, the Huns went through a lot of trouble. They had to kill anyone who was involved with the burial, so that no one would know of the exact place that Attila was buried. Attila was succeeded by his sons, between which the empire was divided. Attila didn’t have a huge impact on history, because the Romans very well could have done without him. He mainly caused trouble for the Romans, and killed a lot of innocent people just to get his way. Attila the Hun was one of the most important kings of the Huns, though, and he definitely has his place in history, as a barbaric, baby-killing, rude leader of a very ruthless group of warriors.

Life lessons

3 Life Lessons Although there are many reasons that our souls come to earth, one of the main reasons I believe we come here is to learn a valuable lesson. If we did not learn this lesson through out a life time, our souls would come back to repeat the process. I believe I have learned a few lessons from my time here on earth. One lesson I have learned is to never take things or people for granted. At some point in our lives, we realize that we take things for granted, we take each other for granted.Meaning we get so comfortable in having certain things in our lives and ertain people around us. It is when we no longer have those things or people that we come to the realization that we have taken things for granted. It's natural to get comfortable. It's human nature. We can't help ourselves. It is wise to stop and think about the things we do have, instead of complaining about what we don't because one day, what you once had, how you once lived, who you once had in your life; will no l onger be there.People habituate affection and cripple the finest part of life. So appreciate everything while it is here. Be grateful, give thanks to God and above all, let those in your life today know that you care about them and that you are grateful they are in your life. Another life lesson I have learned is to not be afraid to make mistakes. Whenever we try anything new, we might make some mistakes. We can't possibly know everything that's going to happen when we try something new. Sometimes we Just have to try something before we can learn about it.Mistakes are a part of life. As Einstein said, the only people who don't make mistakes are those who don't try nything new. If there's something you have a burning desire to do, don't let the fear of making mistakes hold you back. We are not perfect. We are a mere blip on the timeline of existence. Life existed long before we came here and it will continue long after we're gone. You were only given one life to live and only you can make the most of it. No one else can make you take advantage of opportunity; it's up to you to muster the courage to embrace it.As my dad once taught me â€Å"If you want something ouVe never had, you must do something youVe never done. † The final lesson I've learned is to live life with no regrets. I learned this lesson through a song called â€Å"My Way† by Frank Sinatra. As we get older we learn and grow. But that doesn't mean we have to regret what we did before we learned how to do things differently. If we didn't go through those experiences we might not have grown into the strong and knowledgeable people we are today. Many people have heard of the saying â€Å"live today as it were your last.This saying holds true for everyone. When we get older we tend to reflect on what we have done through life and Judge ourselfs. No one wants to lie on their death bed and think about their past mistakes and wish their life had taken a different turn. Wouldn't we want to h ave a positive outlook on life? Those who lived life with no regrets live happier lives and obtain a higher level of wisdom. something it. The few lessons I have learned will never be forgotten. There are still many valuable lessons for me to learn and ill strive to find them.

Reificaition Case Essay

Wikipedia defines reification as â€Å"(Lat. res thing + facere to make) n. the turning of something into a thing or object; the error which consists in treating as a â€Å"thing† something which is not one. Hypostatization, treating an abstract entity as if it were concrete, is a case in point†. In Marxist terms, it is the consideration of a human being as a physical object, deprived of subjectivity. According to Marxists, this is one of the pitfalls of the capitalist system because in such a system the laborers and their work are not valued to their proper extent. Their work is treated as a commodity and is valued according to the unpredictable needs of the market. This concept is closely tied to the Marxist idea of commodity fetishism which Wikipedia describes as â€Å"an inauthentic state of social relations, said to arise in complex capitalist market systems, where social relationships are confused with their medium, the commodity.† Marxist writer, Georg Lukà ¡cs, writes thus: The transformation of the commodity relation into a thing of ‘ghostly objectivity’ cannot there ore content itself with the reduction of all objects for the gratification of human needs to commodities. It stamps its imprint upon the whole consciousness of man; his qualities an abilities are no longer an organic par of his personality, they are things which he can ‘own’ or ‘dispose of’ like the various objects of the external world. Simply put, Marxists criticize capitalist systems for stripping the human person of his social nature. He is transformed into a commodity or a product. One’s labor is transformed into money which is in turn used to purchase the products of other people’s labor. Although this may facilitate the exchange of goods, the problem of the system lies in the fact that because of this abstraction, the use-value (the actual usefulness of the object) is oftentimes totally different from its exchange-value (the value of the object in the marketplace). For example, a person who creates a hammer (which has a variety of uses) will be paid less than a person who makes jewelry (an object which has less use than a hammer). The value given to the work of the laborer is incommensurate to the work and effort that he made in order to produce the good. How can reification be avoided? Marxist measures against reification have proven themselves to be ineffective (including complete control over the market and standardization of wages). This is because these measures tend to remove the element of competition from the formula, thus, causing production to suffer instead. An alternative mode by which reification is avoided is through the respect of human rights. According to John Locke, each person has the natural right to life, liberty and estate which must be protected by the government. These rights must ensure that each person shall be given his due. By treating persons as individuals with human rights and dignity, people will be treated as an end and never as a means. The theory of human rights has been upheld and accepted by most of the world and are embodied in international instruments and conventions, most notable is the Universal Declaration of Human Rights. In the field of labor and employment, modern societies have integrated this idea of human dignity by setting minimum standards and conditions to be strictly followed by employers under the pain of appropriate sanctions should they be defied. For example, there could be a law saying that any employee who works beyond eight hours in a single day shall be given additional overtime pay. Another instance would be a law that would lay down a minimum wage based on the living standards and conditions of the locality where the worker belongs. By recognizing the human dignity of every person, reification is completely obliteration because persons are then given the respect they deserve. They are no longer treated as cogs in the machinery of production but are considered partners in the enterprise. By holding that each person deserves to be treated with dignity, they are esteemed as subjects never objects, and will be given their due.       Bibliography Lukà ¡cs, Georg. 1967. History & Class Consciousness. Translated by Andy Blunden. Merlin Press. Smith, John, Bob Snider, and Diane Hill. 2005. A study of physics. New York: McGraw Hill. Wikipedia. 2006. Commodity fetishism. Wikipedia. http://en.wikipedia.org/wiki/Commodity_fetishism. Ashcraft, Richard. 1986. Revolutionary Politics and Locke’s â€Å"Two Treatises of Government†. Princeton: Princeton University Press. Wikipedia. 2006. Georg Lukà ¡cs. Wikipedia. http://en.wikipedia.org/wiki/Georg_Luk%C3%A1cs. Wikipedia. 2006. Human Rights. Wikipedia. http://en.wikipedia.org/wiki/Human_rights. Wikipedia. 2006. John Locke. Wikipedia. http://en.wikipedia.org/wiki/John_locke. Wikipedia. 2006. Reification. Wikipedia. http://en.wikipedia.org/wiki/Reification.