Competence in Counseling Essay Example for Free

Competence in Counseling Essay Counseling is the professional guidance in resolving personal conflicts and emotional problems. It is advice, opinion, or instruction given in direction the judgment or conduct of another. Knowing how to posses personal qualities such as maturity, empathy, warmth, understanding, and knowledge. From a legal stand point ethics, morality, and law must be strongly conformed. It is accurate decision-making, knowing appropriate words to use, and knowledge of the governing standards that is required. Also knowing accurate information about culture and ethnicity of the present society. Aspects of Counseling Counseling has been misrepresented over the past years for different types of endorsements of products. In todays time the profession as far as counseling goes is now corresponded within its practice. The focus is on growth and wellness as well as clarification of mental disorders. In order to relate to the counseling field an understanding of guidance and psychotherapy must be understood along with having history of the profession. Guidance is leadership, instruction, or direction by helping others make important choices that affect their future in maintaining a productive and healthy lifestyle. An individual being taught guidance must learn to choose what values them the most in order to produce change within their life. This will give that particular individual a sense of direction by following instructions to becoming a leader. The goal in guidance is to promote resourceful and happy lives of individuals by helping them adjust to social actualities. Psychotherapy is a process focused on helping heal and learn more beneficial ays to deal with problems or issues within an individuals life. It is also a supportive process when going through a difficult time period or either under increased stress. It traditionally focused on serious problems associated with internal issues, personal issues, and conflicts. Normally psychotherapy is recommended when a person is struggling with a life, relationship, work issue, or a specific health concern causing the individual a great deal of pain or upset for longer than a few days. Counselors hold an important position that affect many lives throughout the course of a career. A counselor serves as an advice-giving role in a wide number of areas. There are many types of counselors, including school guidance counselors, psychological counselors, counselors for victims, youth camp counselors and more. Aspects of Counseling The vast majority of counselors are extremely caring people who are dedicated to their work and enjoy helping to make others lives better. There is a wide range of ideal personality traits that are associated with being a top counselor. One of the most important personality traits, if not the most important, is a keen ability to listen. In order to help people and find solutions to problems, the counselor must be a keen listener in order to best help the person seeking counsel. Counselors should also have an understanding of human psychology and possess a strong sense of sensitivity. Another ideal character trait for a counselor is having a strong sense of direction in order to find the best path to success for the people whom they counsel. Having a strong sense of direction usually solves problems more quickly and efficiently. Ideal counselor personality traits are a commitment to the profession, humanity and the client. The ideal counselor serves the assistance of the clients. The counselor will develop meaningful and trusting relationships with their clients and insure that this trust is not shaken or broken. An ideal counselors personality has a consumer first attitude and should represent a supporter and guidance role with nurturing characteristics to assist in the creation of a reliable bond between the client and the counselor. Other quality traits include their knowledge of the profession and its standards of practice, along with some background in psychology. A good organizational personality trait of a counselor is their willingness to promote efficient case management techniques. Aspects of Counseling As an effective counselor one of the main qualities needed is patience. Go to the next step of explanation only when the patient has clearly understood the content of the information you have provided. Therefore the counselor needs to have enough sufficient time for the patient, and should also be a good listener. Let the patient express everything he/she has to say, and give your inputs once when the patient has finished talking. A counselor should be very observant and able to interpret non-verbal communication for example if the patient looks angry, and then find out the cause of his/her anger first. An effective counselor should provide non-possessive warmth in a counseling environment. Smile and show concern and acceptance by showing comfort, empathy, and understanding to the patient. Counselors should have good knowledge on the topic /problem like compliance to medication. Some people do not take medication for the same reasons, while others demand medication. Understanding the factors why people may not do certain activities at specific time will help you to assist them better. Try to understand the feelings the patient is having in the counseling process. In other words put yourself in his/her position. Give the patient the opportunity to make his/her own decision from your message. Lastly be sure to make it aware to the patient that you as their counselor maintain confidentiality on what the patient tells you. This means that counseling must be done individually and privately. Letting the patient know that you maintain a high degree of personal reliability, trustworthiness and mutual trust as an effective counselor. Aspects of Counseling As there are three different levels of counseling relationships to be aware of nonprofessional, paraprofessional, and professional. Nonprofessionals would be considered as family, friends, colleagues, untrained volunteers, or supervisors who try in assisting those who are in need. Secondly, paraprofessionals are individuals who have received some sort of training in human relations. Lastly professionals are those who are educated with the nowledge to provide assistance on a protective and corrective level. While being the ideal, effective, and professional counselor you must also keep in mind that you must follow the ethical and legal aspects of counseling also. Ethics is defined as a philosophical discipline that is concerned with human conduct and moral decision-making. You should also familiarize yourself with morality, which involves judgment or evaluation of action, and another major definition to know is law, which is the precise organization of governing standards that are established to ensure legal and moral justice. The law does not dictate what is considered to be ethical but what is considered to be legal. Ethical codes are there to protect the profession from government. They allow the professions to control itself and functions independently instead of being controlled by legislation. In making ethical decisions counselors familiarize themselves with casebooks, professional colleagues, and principles. It is very crucial that counselors become well knowledgeable with ethics for the sake of their own well-being and of their patients as well. Multicultural psychology focuses on the cultural differences in thought processes and acceptable vs. nacceptable behaviors. It relates to normal lives such as home, education, work and relationships but also to what is considered abnormal or normal. Aspects of Counseling Knowing your patient plays a huge factor in counseling sessions as well. To know the cultural background of your patient can help you better relate to them as an individual. Many cultural ethnic groups live in the United States. A culture is behaviors, thoughts, perceptions, values, goals, and cognitive processes. An issue in multicultural counseling is the dominance of theories based on cultural values. A second issue is sensitivity to cultures in general, believes that are essential to counselors is knowledge of culturally different patients. Knowing that everyone is their own unique person, and have their own views on different things in today’s society. The counselor must also have the skills to work with patients of different cultures. Counselors must work in order to know their patients and their problems. European Americans when taken into consideration is a larger diverse population they are very common to the people of the United States. When counseling African Americans a counselor must understand the history, and coping mechanisms. Hispanics/Latinos a very diverse group as well, and regardless to their background they are very bicultural. Asian and Pacific Islanders are considered as hard working, successful, and not prone to mental or emotional distress. When dealing with many diverse groups like this a common theme is that counselors who work with a variety of culturally different patients must be knowledgeable about them collectively.

Construction of Desire in Sapphic Poetry Essay -- Sappho Poem Poet Ess

Construction of Desire in Sapphic Poetry Many scholars in the past, looking at Sappho through the eyes of male experience, have heaped lukewarm praise on Sappho’s "chaste" poems, have translated them with an unyielding heterosexual bent. However, when read through a woman's experience, when read through people who do not wish to hide Sappho's desire for other women or hetero-sexualize it, Sappho's writing takes on a new light, and we can begin to piece together her desire and its contexts. In the work of Sappho, the goddess Aphrodite is frequently given homage, making her a kind of patron (a matron perhaps?) of lesbian desire. Sappho constructs her desire with three distinct components: a visual component, a physical component, and a repetition and renewal component. She also modified traditional mythological viewpoints to enhance the image of her view of desire. Through this woman-centered interpretation of Sappho, I want to place emphasis on Sappho's lesbian identity and reconstruct the desire that she felt towards other women. Sappho frequently gives poetical space to Aphrodite, the goddess of Love and Desire. In fragment 2, Sappho creates this space by inviting Aphrodite in. "... to this sacred/temple, where you have a pretty grove/of apple trees, and alters smoking with incense/here icy water echoes through the apple/boughs, shadows of roses cover/the ground, from shimmering leaves/a heavy sleep descends." Author Jane Snyder, in her own translation of Sappho's works, remarks that "lesbian desire, as Sappho envisions it, blossoms in a nurturing space under the benevolent patronage of the Cyprian goddess [Aphrodite] herself." Snyder also states that "Sappho fragment 2 creates a private 'female' space in the descripti... ...helming force that resembles a wind with the force of a tornado, which completely overpowers the body. Sappho's view of lesbian is very unique and unmatched, for indeed we have very little else that gives us the language of desire between two women in the ancient world. Under Aphrodite's homage, with components of visual, physical, and repetitious components, and with her unique view on traditional narratives, Sappho gives us her view of desire between two women. I hope that my woman-centered reading of Sappho helped reconstruct her lesbian identity and conceptualize her desire and passion for other women. Works Cited Bing, Peter and Rip Cohen. Games of Venus: An Anthology of Greek and Roman Erotic Verse from Sappho to Ovid. London: Routledge, 1991. Snyder, Jane McIntosh. Lesbian Desire in the Lyrics of Sappho. New York: Columbia University Press, 1997.

J. Galsworthy. the Broken Boot A Sample of Complex Stylistic Analysis Essay

John Ronald Reuel Tolkien (1892-1973) was a major scholar of the English language, specialising in Old and Middle English. Twice Professor of Anglo-Saxon (Old English) at the University of Oxford, he also wrote a number of stories, including most famously The Hobbit (1937) and The Lord of the Rings (1954-1955). The name â€Å"Tolkien† (pron.: Tol-keen; equal stress on both syllables) is believed to be of German origin; Toll-kà ¼hn: foolishly brave, or stupidly clever – hence the pseudonym â€Å"Oxymore† which he occasionally used. His father, Arthur Reuel Tolkien, was a bank clerk. Mabel Tolkien was diagnosed as having diabetes, usually fatal in those pre-insulin days. She died on 14 November By this time Ronald was already showing remarkable linguistic gifts. He had mastered the Latin and Greek which was the staple fare of an arts education at that time, and was becoming more than competent in a number of other languages, both modern and ancient, notably Gothic, and later Finnish. He was already busy making up his own languages, purely for fun. He went up to Exeter College, Oxford in 1911, where he stayed, immersing himself in the Classics, Old English, the Germanic languages (especially Gothic), Welsh and Finnish, until 1913. As a result of this he changed his school from Classics to the more congenial English Language and Literature. Unlike so many of his contemporaries, Tolkien did not rush to join up immediately on the outbreak of war, but returned to Oxford, where he worked hard and finally achieved a first-class degree in June 1915. At this time he was also working on various poetic attempts, and on his invented languages, especially one that he came to call Qenya [sic], which was heavily influenced by Finnish – but he still felt the lack of a connecting thread to bring his vivid but disparate imaginings together. He and Edith married in Warwick on 22 March 1916.Their first son, John Francis Reuel (later Father John Tolkien) had already been born on 16 November 1917. When the Armistice was signed on 11 November 1918, Tolkien had already been  putting out feelers to obtain academic employment, and by the time he was demobilised he had been appointed Assistant Lexicographer on the New English Dictionary (the â€Å"Oxford English Dictionary†), then in preparation. While doing the serious philological work involved in this, he also gave one of his Lost Tales its first public airing – he read The Fall of Gondolin to the Exeter College Essay Club, where it was well received by an audience which included Neville Coghill and Hugo Dyson, two future â€Å"Inklings†. However, Tolkien did not stay in this job for long. In the summer of 1920 he applied for the quite senior post of Reader (approximately, Associate Professor) in English Language at the University of Leeds, and to his surprise was appointed. His family life was equally straightforward. Edith bore their last child and only daughter, Priscilla, in 1929. Tolkien got into the habit of writing the children annual illustrated letters as if from Santa Claus, and a selection of these was published in 1976 as The Father Christmas Letters. He also told them numerous bedtime stories, of which more anon. In adulthood John entered the priesthood, Michael and Christopher both saw war service in the Royal Air Force. Afterwards Michael became a schoolmaster and Christopher a university lecturer, and Priscilla became a social worker. They lived quietly in North Oxford, and later Ronald and Edith lived in the suburb of Headington. Meanwhile Tolkien continued developing his mythology and languages. She asked Tolkien to finish it, and presented the complete story to Stanley Unwin, the then Chairman of the firm. He tried it out on his 10-year old son Rayner, who wrote an approving report, and it was published as The Hobbit in 1937. It immediately scored a success, and has not been out of children’s recommended reading lists ever since. It was so successful that Stanley Unwin asked if he had any more similar material available for publication. By this time Tolkien had begun to make his Legendarium into what he believed to be a more presentable state, and as he later noted, hints of it had already made their way into The Hobbit. He was now calling the full account Quenta Silmarillion, or Silmarillion for short. He presented some of his â€Å"completed† tales to Unwin, who sent them to his reader. The reader’s reaction was mixed: dislike of the poetry and praise for the prose (the material was the story of Beren and Là ºthien) but the overall decision at the time was that these were not commercially publishable. Unwin tactfully relayed this message to Tolkien, but asked him again if he was willing to write a sequel to The Hobbit. Tolkien was disappointed at the apparent failure of The Silmarillion, but agreed to take up the challenge of â€Å"The New Hobbit†. Despite all the fuss over The Lord of the Rings, between 1925 and his death Tolkien did write and publish a number of other articles, including a range of scholarly essays, many reprinted in The Monsters and the Critics and Other Essays (see above); one Middle-earth related work, The Adventures of Tom Bombadil; editions and translations of Middle English works such as the Ancrene Wisse, Sir Gawain, Sir Orfeo and The Pearl, and some stories independent of the Legendarium, such as the Imram, The Homecoming of Beorhtnoth Beorhthelm’s Son, The Lay of Aotrou and Itroun – and, especially, Farmer Giles of Ham, Leaf by Niggle, and Smith of Wootton Major. After his retirement in 1959 Edith and Ronald moved to Bournemouth. On 22 November 1971 Edith died, and Ronald soon returned to Oxford, to rooms provided by Merton College. Ronald died on 2 September 1973. He and Edith are buried together in a single grave in the Catholic section of Wolvercote cemetery in the northern suburbs of Oxford. (The grave is well signposted from the entrance.) The legend on the headstone reads:

Applied Electricity Lecture Notes

Module 4 Single-phase AC Circuits Version 2 EE IIT, Kharagpur Lesson 13 Representation of Sinusoidal Signal by a Phasor and Solution of Current in R-L-C Series Circuits Version 2 EE IIT, Kharagpur In the last lesson, two points were described: 1. How a sinusoidal voltage waveform (ac) is generated? 2. How the average and rms values of the periodic voltage or current waveforms, are computed? Some examples are also described there. In this lesson, the representation of sinusoidal (ac) voltage/current signals by a phasor is first explained. The polar/Cartesian (rectangular) form of phasor, as complex quantity, is described.Lastly, the algebra, involving the phasors (voltage/current), is presented. Different mathematical operations – addition/subtraction and multiplication/division, on two or more phasors, are discussed. Keywords: Phasor, Sinusoidal signals, phasor algebra After going through this lesson, the students will be able to answer the following questions; 1. What is mean t by the term, ‘phasor’ in respect of a sinusoidal signal? 2. How to represent the sinusoidal voltage or current waveform by phasor? 3. How to write a phasor quantity (complex) in polar/Cartesian (rectangular) form? 4.How to perform the operations, like addition/subtraction and multiplication/division on two or more phasors, to obtain a phasor? This lesson forms the background of the following lessons in the complete module of single ac circuits, starting with the next lesson on the solution of the current in the steady state, in R-L-C series circuits. Symbols i or i(t) Instantaneous value of the current (sinusoidal form) I Im ? Current (rms value) Maximum value of the current Phasor representation of the current Phase angle, say of the current phasor, with respect to the reference phasor I Same symbols are used for voltage or any other phasor. Representation of Sinusoidal Signal by a Phasor A sinusoidal quantity, i. e. current, i (t ) = I m sin ? t , is taken up as an example. In Fig. 13. 1a, the length, OP, along the x-axis, represents the maximum value of the current I m , on a certain scale. It is being rotated in the anti-clockwise direction at an angular speed, ? , and takes up a position, OA after a time t (or angle, ? = ? t , with the x-axis). The vertical projection of OA is plotted in the right hand side of the above figure with respect to the angle ? It will generate a sine wave (Fig. 13. 1b), as OA is at an angle, ? with the x-axis, as stated earlier. The vertical projection of OA along y-axis is OC = AB = Version 2 EE IIT, Kharagpur i (? ) = I m sin ? , which is the instantaneous value of the current at any time t or angle ? . The angle ? is in rad. , i. e. ? = ? t . The angular speed, ? is in rad/s, i. e. ? = 2 ? f , where f is the frequency in Hz or cycles/sec. Thus, i = I m sin ? = I m sin ? t = I m sin 2? ft So, OP represents the phasor with respect to the above current, i.The line, OP can be taken as the rms value, I = I m / 2 , instead of maximum value, Im . Then the vertical projection of OA, in magnitude equal to OP, does not represent exactly the instantaneous value of I, but represents it with the scale factor of 1 / 2 = 0. 707 . The reason for this choice of phasor as given above, will be given in another lesson later in this module. Version 2 EE IIT, Kharagpur Generalized case The current can be of the form, i (t ) = I m sin (? t ? ? ) as shown in Fig. 13. 1d. The phasor representation of this current is the line, OQ, at an angle, ? may be taken as negative), with the line, OP along x-axis (Fig. 13. 1c). One has to move in clockwise direction to go to OQ from OP (reference line), though the phasor, OQ is assumed to move in anti-clockwise direction as given earlier. After a time t, OD will be at an angle ? with OQ, which is at an angle ( ? ? ? = ? t ? ? ), with the line, OP along x-axis. The vertical projection of OD along y-axis gives the instantaneous value of the current, i = 2 I sin (? t ? ? ) = I m sin (? t ? ? ) . Phasor representation of Voltage and Current The voltage and current waveforms are given as, v = 2 V sin ? and i = 2 I sin (? + ? ) It can be seen from the waveforms (Fig. 13. 2b) of the two sinusoidal quantities – voltage and current, that the voltage, V lags the current I, which means that the positive maximum value of the voltage is reached earlier by an angle, ? , as compared to the positive maximum value of the current. In phasor notation as described earlier, the voltage and current are represented by OP and OQ (Fig. 13. 2a) respectively, the length of which are proportional to voltage, V and current, I in different scales as applicable to each one.The voltage phasor, OP (V) lags the current phasor, OQ (I) by the angle ? , as two phasors rotate in the anticlockwise direction as stated earlier, whereas the angle ? is also measured in the anticlockwise direction. In other words, the current phasor (I) leads the voltage phasor (V). Version 2 EE IIT, Kha ragpur Mathematically, the two phasors can be represented in polar form, with the voltage phasor ( V ) taken as reference, such as V = V ? 0 0 , and I = I . In Cartesian or rectangular form, these are, V = V ? 0 0 = V + j 0 , and I = I = I cos ? + j I sin ? , where, the symbol, j is given by j = ? . Of the two terms in each phasor, the first one is termed as real or its component in x-axis, while the second one is imaginary or its component in y-axis, as shown in Fig. 13. 3a. The angle, ? is in degree or rad. ? ? ? ? ? Phasor Algebra Before discussing the mathematical operations, like addition/subtraction and multiplication/division, involving phasors and also complex quantities, let us take a look at the two forms – polar and rectangular, by which a phasor or complex quantity is represented. It may be observed here that phasors are also taken as complex, as given above.Representation of a phasor and Transformation A phasor or a complex quantity in rectangular form (Fig. 13 . 3) is, A = ax + j a y Version 2 EE IIT, Kharagpur ? where a x and a y are real and imaginary parts, of the phasor respectively. In polar form, it is expressed as A = A a = A cos ? a + j A sin ? a ? where A and ? a are magnitude and phase angle of the phasor. From the two equations or expressions, the procedure or rule of transformation from polar to rectangular form is a x = A cos ? a and a y = A sin ? a From the above, the rule for transformation from rectangular to polar form is 2 2 A = a x + a y and ? = tan ? 1 (a y / a x ) The examples using numerical values are given at the end of this lesson. Addition/Subtraction of Phasors Before describing the rules of addition/subtraction of phasors or complex quantities, everyone should recall the rule of addition/subtraction of scalar quantities, which may be positive or signed (decimal/fraction or fraction with integer). It may be stated that, for the two operations, the quantities must be either phasors, or complex. The example of ph asor is voltage/current, and that of complex quantity is impedance/admittance, which will be explained in the next lesson.But one phasor and another complex quantity should not be used for addition/subtraction operation. For the operations, the two phasors or complex quantities must be expressed in rectangular form as A = a x + j a y ; B = bx + j b y If they are in polar form as A = A a ; B = B b In this case, two phasors are to be transformed to rectangular form by the procedure or rule given earlier. The rule of addition/subtraction operation is that both the real and imaginary parts have to be separately treated as ? ? ? ? where c x = (a x  ± b x ) ; c y = (a y  ± b y ) Say, for addition, real parts must be added, so also for imaginary parts.Same rule follows for subtraction. After the result is obtained in rectangular form, it can be transformed to polar one. It may be observed that the six values of a' s , b' s and c' s – parts of the two phasors and the resultant one, are all signed scalar quantities, though in the example, a' s and b' s are taken as positive, resulting in positive values of c' s . Also the phase angle ? ‘ s may lie in any of the four quadrants, though here the angles are in the first quadrant only. This rule for addition can be extended to three or more quantities, as will be illustrated through example, which is given at the end of this lesson.C = A  ± B = (a x  ± bx ) + j (a y  ± b y ) = c x + j c y ? ? ? Version 2 EE IIT, Kharagpur The addition/subtraction operations can also be performed using the quantities as ? ? ? phasors in polar form (Fig. 13. 4). The two phasors are A (OA) and B (OB) . The find the sum C (OC ) , a line AC is drawn equal and parallel to OB. The line BC is equal and parallel to OA. Thus, C = OC = OA + AC = OA + OB = A + B . Also, OC = OB + BC = OB + OA ? ? ? ? To obtain the difference D (OD) , a line AD is drawn equal and parallel to OB, but in opposite direction to AC or OB.A line OE is also drawn equal to OB, but in opposite direction to OB. Both AD and OE represent the phasor ( ? B ). The line, ED is equal to OA. Thus, D = OD = OA + AD = OA ? OB = A ? B . Also OD = OE + ED = ? OB + OA . The examples using numerical values are given at the end of this lesson. ? ? ? ? Multiplication/Division of Phasors Firstly, the procedure for multiplication is taken up. In this case no reference is being made to the rule involving scalar quantities, as everyone is familiar with them. Assuming that the two phasors are available in polar from as A = A a and B = B b .Otherwise, they are to be transformed from rectangular to polar form. This is also valid for the procedure of division. Please note that a phasor is to be multiplied by a complex quantity only, to obtain the resultant phasor. A phasor is not normally multiplied by another phasor, except in special case. Same is for division. A phasor is to be divided by a complex quantity only, to obtain the resultant phasor. A phas or is not normally divided by another phasor. ? ? ? To find the magnitude of the product C , the two magnitudes of the phasors are to be multiplied, whereas for phase angle, the phase angles are to added.Thus, Version 2 EE IIT, Kharagpur C = C c = A? B = A A ? B B = ( A ? B ) ? (? a + ? b ) ? ? ? where C = A ? B and ? c = ? a + ? b ? Please note that the same symbol, C is used for the product in this case. ? ? ? To divide A . by B to obtain the result D . , the magnitude is obtained by division of the magnitudes, and the phase is difference of the two phase angles. Thus, D = D d = ? ? A ? = B where D = A / B and ? d = ? a ? ? b ? ? A a ? A ? = ? ? ? (? a ? ? b ) B b ? B ? If the phasors are expressed in rectangular form as A = a x + j a y and B = bx + j by here A = (a 2 x ? 2 + a y ; ? a = tan ? 1 (a y / a x ) ) The values of B are not given as they can be obtained by substituting b' s for a' s . To find the product, C = C c = A ? B = (a x + j a y ) ? (bx + j b y ) = (a x bx ? a y b y ) + j (a x b y + a y bx ) ? ? ? Please note that j 2 = ? 1 . The magnitude and phase angle of the result (phasor) are, C = (a x bx ? a y b y ) + (a x b y + a y bx ) 2 [ 1 2 2 ] = (a 2 x 2 + ay ? ) (b 2 x 2 + b y = A ? B , and ) ? c = tan ? 1 ? ? ? a x b y + a y bx ? ? a x bx ? a y b y ? ? ? The phase angle, ? c = ? a + ? b = tan ? 1 ? ? a x b y + a y bx = tan ? 1 ? ?a b ? a b y y ? x x ? ? ? ? ay ? ax ? ? ? ? ? ? b ? + tan ? 1 ? y ? ?b ? ? x ? (a / a ) + (b y / bx ) ? ? ? = tan ? 1 ? y x ? ? ? 1 ? (a y / a x ) ? (b y / bx )? ? ? ? The above results are obtained by simplification. ? To divide A by B to obtain D as D = dx + j dy = ? ? A ? = ax + j a y bx + j by ? B To simplify D , i. e. to obtain real and imaginary parts, both numerator and denominator, are to be multiplied by the complex conjugate of B , so as to convert the ? denominator into real value only. The complex conjugate of B is Version 2 EE IIT, KharagpurB * = bx + j b y = B ? ? ? b In the complex conjugate, the sign of the imaginary part is negative, and also the phase angle is negative. ? (a x + j a y )? (bx ? j by ) = ? a x bx + a y by ? + j ? a y bx ? a x by ? ? ? ? ? D = dx + j dy = (bx + j by )? (bx ? j by ) ? bx2 + by2 ? ? bx2 + by2 ? ? ? ? ? The magnitude and phase angle of the result (phasor) are, [(a b D= x x + a y b y ) + (a y bx ? a x b y ) 2 1 2 2 (b 2 x +b 2 y ) ] = (a (b 2 x 2 x 2 + ay 2 + by ) A = , and ) B ? a y bx ? a x b y ? ? ? d = tan ? 1 ? ?a b +a b ? y y ? ? x x The phase angle, ? ay ? ax ? ? ? ? tan ? 1 ? y ? b ? ? x ? ? a b ? a xby ? ? = tan ? 1 ? y x ? ?a b +a b y y ? ? x x ? ? ? ? ? d = ? a ? ? b = tan ? 1 ? ? The steps are shown here in brief, as detailed steps have been given earlier. Example ? The phasor, A in the rectangular form (Fig. 13. 5) is, A = A a = A cos ? a + j A sin ? a = a x + j a y = ? 2 + j 4 where the real and imaginary parts are a x = ? 2 ; ? ? ay = 4 To transform the phasor, A into the polar form, the magnitude and phase angle are Version 2 E E IIT, Kharagpur 2 2 A = a x + a y = (? 2) 2 + 4 2 = 4. 472 ? 4 ? ? = tan ? 1 ? ? ? 116. 565 ° = 2. 034 rad ? ? ? 2? ? Please note that ? a is in the second quadrant, as real part is negative and imaginary part is positive. ? a = tan ? 1 ? ? ? ay ? ax ? Transforming the phasor, A into rectangular form, the real and imaginary parts are a x = A cos? a = 4. 472 ? cos116. 565 ° = ? 2. 0 a y = A sin ? a = 4. 472 ? sin 116. 565 ° = 4. 0 Phasor Algebra ? ? ? Another phasor, B in rectangular form is introduced in addition to the earlier one, A B = 6 + j 6 = 8. 485 ? 45 ° Firstly, let us take the addition and subtraction of the above two phasors. The sum and ? difference are given by the phasors, C and D respectively (Fig. 13. 6). C = A+ B = (? 2 + j 4) +(6 + j 6) = (? 2 + 6) + j (4 + 6) = 4 + j 10 = 10. 77 ? 68. 2 ° D = A? B = (? 2 + j 4) ? (6 + j 6) = (? 2 ? 6) + j (4 ? 6) = ? 8 ? j 2 = 8. 246 ? ? 166. 0 ° It may be noted that for the addition and subtraction operations involvi ng phasors, they should be represented in rectangular form as given above. If any one of the phasors Version 2 EE IIT, Kharagpur ? ? ? ? ? ? is in polar form, it should be transformed into rectangular form, for calculating the results as shown.If the two phasors are both in polar form, the phasor diagram (the diagram must be drawn to scale), or the geometrical method can be used as shown in Fig 13. 6. The result obtained using the diagram, as shown are the same as obtained earlier. [ C (OC) = 10. 77, ? COX = 68. 2 ° ; and D ( OD) = 8. 246, ? DOX = 166. 0 ° ] Now, the multiplication and division operations are performed, using the above two phasors represented in polar form. If any one of the phasors is in rectangular form, it may be transformed into polar form. Also note that the same symbols for the phasors are used here, as was used earlier.Later, the method of both multiplication and division using rectangular form of the phasor representation will be explained. ? ? ? The res ultant phasor C , i. e. the product of the two phasors is C = A? B = 4. 472 ? 116. 565 ° ? 8. 485 ? 45 ° = (4. 472 ? 8. 485) ? (116. 565 ° + 45 °) = 37. 945 ? 161. 565 ° = ? 36 + j 12 The product of the two phasors in rectangular form can be found as C = (? 2 + j 4) ? (6 + j 6) = (? 12 ? 24) + j (24 ? 12) = ? 36 + j 12 ? ? ? ? ? ? ? The result ( D ) obtained by the division of A by B is D= ? ? A ? = B = 0. 167 + j 0. The above result can be calculated by the procedure described earlier, using the rectangular form of the two phasors as D= ? ? 4. 472 ? 116. 565 ° ? 4. 472 ? =? ? ? (116. 565 ° ? 45 °) = 0. 527 ? 71. 565 ° 8. 485 ? 45 ° ? 8. 485 ? A ? = B 12 + j 36 = = 0. 167 + j 0. 5 72 ? 2 + j 4 ( ? 2 + j 4) ? (6 ? j 6) (? 12 + 24) + j (24 + 12) = = 6+ j6 ( 6 + j 6) ? ( 6 ? j 6) 62 + 62 The procedure for the elementary operations using two phasors only, in both forms of representation is shown. It can be easily extended, for say, addition/multiplication, using thre e or more phasors.The simplification procedure with the scalar quantities, using the different elementary operations, which is well known, can be extended to the phasor quantities. This will be used in the study of ac circuits to be discussed in the following lessons. The background required, i. e. phasor representation of sinusoidal quantities (voltage/current), and algebra – mathematical operations, such as addition/subtraction and multiplication/division of phasors or complex quantities, including transformation of phasor from rectangular to polar form, and vice versa, has been discussed here.The study of ac circuits, starting from series ones, will be described in the next few lessons. Version 2 EE IIT, Kharagpur Problems 13. 1 Use plasor technique to evaluate the expression and then find the numerical value at t = 10 ms. i ( t ) = 150 cos (100t – 450 ) + 500 sin (100t ) + d ? cos 100t – 30 0 ) ? ? dt ? ( 13. 2 Find the result in both rectangular and polar f orms, for the following, using complex quantities: 5 – j12 15 ? 53. 1 ° b) ( 5 – j12 ) +15 ? – 53. 1 ° a) 2 ? 30 ° – 4 ? 210 ° 5 ? 450 ° 1 ? ? d) ? 5 ? 0 ° + ? . 2 ? 210 ° 3 2 ? – 45 ° ? ? c)Version 2 EE IIT, Kharagpur List of Figures Fig. 13. 1 (a) Phasor representation of a sinusoidal voltage, and (b) Waveform Fig. 13. 2 (a) Phasor representation of voltage and current, and (b) Waveforms Fig. 13. 3 Representation of a phasor, both in rectangular and polar forms Fig. 13. 4 Addition and subtraction of two phasors, both represented in polar form Fig. 13. 5 Representation of phasor as an example, both in rectangular and polar forms Fig. 13. 6 Addition and subtraction of two phasors represented in polar form, as an example Version 2 EE IIT, Kharagpur

And Then There Were None Chapt. 13 On Essays - Free Essays

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Addressing Envelopes

Addressing Envelopes Addressing Envelopes Addressing Envelopes By Maeve Maddox Heres a question from Alfonso Rodriguez from Lima, Peru: Would you be so kind as to tell me what is the correct way to write down an address when the building has no number, I think there is an abbreviation form. If any of you readers outside the U.S. know of an abbreviation that designates a building without a street number, please tell us in the comments. In the United States, new construction requires the existence of a street number before a building is built. As for older buildings, according to the person I talked to at the USPS 800 number, all buildings in towns have street numbers. Rural addresses may make use of the abbreviation RR: D.Q. Jones RR 5 Box 19 Molesville TX 77293 Many buildings have both names and street addresses. If a building is well-known in the town where it is, the name can serve in lieu of a numbered address, as long as the town and state are included. For example, an envelope addressed to someone at the Empire State Building, New York, N.Y. would probably reach its destination without the address 350 5th Ave. USPS address-reading machinery reads addresses from the bottom up: 4†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦D. Q. Jones 3†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..12233 Jefferson Ave Apt 1 2†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. Newport News, VA 23602 1†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦USA According to the official USPS guidelines, designations such as Apt (apartment), Dept (department), and Ste (suite) go on the same line as the street address: 234 Hilltop Dr Apt 504 Greenwich PA 23853 NOT 234 Hilltop Dr Apt 504 Greenwich PA 23853 In the event that the space available for the address is not large enough for Apt to be written out, the symbol # can be used in its place: 234 Hilltop Dr #504 Greenwich PA 23853 It a street address is especially long, some of the vowels may be omitted. For example, 23 Espendhade-Dogwood Terrace could be shortened to: 23 Espnshd-Dgwd Ter. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Business Writing category, check our popular posts, or choose a related post below:20 Great Opening Lines to Inspire the Start of Your Story10 Techniques for More Precise Writing15 English Words of Indian Origin

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