Case On Social Cost Essays - Public Economics, Market Failure, Costs

Case On Social Cost Assuming no pollution, explain why a road is only an example of market failure when it is congested. When a road is not congested and the traffic can move freely along it, the private cost is equal to the social cost. The road is non-rivalrous because everybody who wants to use it can. For every user that uses the road above the amount that makes the road rivalrous, they have to pay the externality of the congestion. As more people join, the externality increases. The externality is also known as the external cost. Because the road becomes congested, the journey time of the users is lengthened. The additional road users should pay the cost of the other users time. On a congested road, a car for example uses more fuel than it would on a non-congested road, this cost should also be considered. Measuring the social cost is very difficult. Listed above are just two factors that determine the extent of the social cost. The social cost can be different at different times of the day, e.g. at 8:30am in the morning, the roads are very busy because of people travelling to work. The same goes for 5pm when people finish work. In the early hours of the morning it is unlikely that you will any cars at all. There is market failure when the Marginal Social Cost (MSC) is greater than the Marginal Private Cost (MPB). This only happens when the road is congested (we can see this from the diagram). This is why a road is an example of market failure only when it is congested. The additional motorists that wish to use a congested road should pay the external cost, we can see this also on the graph.

ACT Prep

Is There Asian-American Discrimination in College Admissions and SAT / ACT Prep SAT / ACT Prep Online Guides and Tips Recently, there has been substantial coverage about whether colleges discriminate against Asian-Americans in admissions and even test prep. What does that mean for these students? How should such students navigate SAT / ACT prep and college admissions? This article surveys the current state of admissions and gives some tips. Disclaimer: The views expressed in this article do not necessarily represent those of PrepScholar or any affiliate. While even broaching this topic can be seen as controversial, I also believe, as an educator, that I’m responsible for giving advice that helps the greatest number of students understand the landscape. This article specifically addresses Asian-Americans applying from the US and not applicants directly applying from Asia. Introduction The intersection of race and college admissions has always been a sensitive issue, but recently it has boiled over to the front pages of newspapers. Sociology professor Thomas Espenshade writes that â€Å"To receive equal consideration by elite colleges, Asian-Americans must outperform Whites by 140 points [on the 1600-scale SAT].† Data from the National Center for Education Statistics show that, while Asians of college age doubled in the last 25 years, their enrollment rates at Ivy-League schools have stayed the same. S.B. Woo, founder of the National Asian-American Educational Foundation,concludes that the â€Å"discrimination is obvious†. Others defend using race as a factor in admissions. Director of Education Equity Khin Aung argues that considering race allows benefits of diversity such as â€Å"creating the most effective learning environment.† Jeff Neal, a spokesperson at Harvard, states that Harvard â€Å"continues to support the use of holistic admissions process," which implicitly includes race. To catch up with the current state of conversation on the topic, all you have to do is Google â€Å"Asian college admissions†. Are Asian-Americans Discriminated Against in College Admissions? The value of affirmative action is controversial, but the existence of affirmative action is undisputed. The vast majority of experts in college admissions and SAT / ACT prep agree that affirmative action exists - college admissions is not totally blind to race. Given an ACT / SAT score range, it is an empirical fact that Asian-Americans have a lower acceptance rate than the average white American in many data setssuch as the Espenshade and Radford 1997 elite college admissions data. Likewise, a survey of the admitted class of 2017 at Harvard revealed that SAT scores for Asians (including Indians) were higher than those of whites. However, as anyone who has studied statistics can tell you (and I do have a Master’s degree in the field), those facts above are correlations and not causations. They suggest, but do not prove, that an Asian-American with otherwise the same application to the same school as a white American will have a lower chance of admission. I call this the Hypothesis that being Asian Lowers Admissions Chances (HALAC). HALAC, of course, implies that being Asian means that getting into a given college will be harderfor you than for a white American. What This Article Does and Does Not Do This article will give you advice as to what an Asian-American may want to consider doing to maximize chances of college admissions. On both the front of the university and the government, policy moves too slowly for it to help most Asian-Americans with this issue. Therefore, this article doesn't take any stance on the correct institutional policies or political views as a response to HALAC. Additionally, given that causality is difficult to prove, this article doesn't take a stance on whether causally the HALAC effect exists. Instead, this article focuses on things you, as an Asian-American, can do right now to maximize your chances of being accepted into top colleges. If you read through the evidence and believe that the HALAC effect exists, then the suggestions below can be useful to you. If you Google the evidence and don't think it supports HALAC, that's fine too - the advice below will be less applicable to you in that case. What Doesn't Work Before I give you the tips for what works for Asian applicants under the HALAC effect, I will first go over what absolutely doesn’t work. First, lying doesn’t work nearly as well as you might think.What if you just don’t check the Asian box? What if you check â€Å"don’t want to disclose†? The problem is that colleges can often tell your race through other means. You do have to give colleges your legal name - if your last name is Nguyen, Lee, Kim, or Patel, for example, the admissions staff will almost certainly figure it out. What about just changing your name or making up your name? This will really get you into hot water as colleges are pretty good about calling your past teachers and running background checks on you. A good rule of thumb is this: if a casual friend who knows you would unambiguously say you’re of Asian ethnicity, it’s hard to get around it. Just put down that you’re Asian and be done with it. By telling the truth on your name and ethnicity box, you at least signal honesty. On the other hand, if you have a legitimate reason for not identifying as Asian, then you can, in fact, consider this path. Suppose you’re genetically 25% Asian and 75% Hispanic, and your parents were both born in the United States. Some college applications ask you to identify with one or as many ethnicities as you want. Under the HALAC effect you probably do want to omit Asian, if allowed. Also, mass action will rarely work to your advantage for admissions. By mass action, I mean protesting the HALAC effect, suing colleges, complaining to the government, and so forth. Colleges may be reluctant to admit a student likely to cause the administration a headache.Remember, university administration is a highly political entity. The government political process also works way too slowly. It will cost millions to fight it out in court and years to reach a judgment. If your goal is to raise your chances of admissions under the HALAC effect, I would think twice about filing an official grievance. Of course, there are other fine reasons that you may want to take mass action in the future, perhaps due to your political or ethical beliefs. However, I’m just telling you that, almost always, taking official or mass action won’t increase your personal short-term chances of getting into a certain school. Who Does This Article Apply To? This article applies much more to Americans of Asian heritage, i.e. students who have studied in the US at least a few years before they apply to college. It applies much less to students who are applying directly from another country. These latter students are better classified as international students. For them, there is a whole set of other factors that are more important - for example appetite of a college for internationalstudents, authenticity of documents, etc. Throughout this article, the term â€Å"Asian† includes Indian and other ethnically related neighbors - since the data across these groups are all similar. How You Can Combat the HALAC Effect Now that you understand what the HALAC effect is, how can you use that information to increase your chances of getting into top schools? Below are three strategies for combating the HALAC effect; read through them to learn how to maximize your chances of admission. Step 1: Account for the HALAC Effect Before you can combat the HALAC effect, first you have to find where it exists. The HALAC effect is not something that can be magically erased by easy action on your part. Therefore, in response to the HALAC effect, the first and most important thing that a student of Asian heritage should do is to account for it correctly. By this, I mean realizing that your chances of getting in are lower and planning accordingly which colleges you’ll apply to and how you’ll apply to them. Accounting for the HALAC effectmeans that you should adjust where your reach, target, and safety schools are. Instead of putting them as high as you might otherwise, target them a little lower. If you target too high, you run the risk of overshooting - not getting into the target schools of your choice and instead getting into a safety school that you didn’t spend much time researching. You should also account for the HALAC effect more at classically â€Å"elite† colleges. Colleges that are US News ranked 1-10 probably suffer most from HALAC, with the effect decreasing through colleges 10-50 in rank. The effect becomes much lower in colleges ranked above 50. In fact, most HALAC studies focus on the top colleges for exactly this reason: the effects are more concentrated and more statistically significant there. There are many potential reasons for the concentration of the HALAC effect on highly ranked colleges. Proportionally, more Asians apply to these colleges, leading to the HALAC effect when colleges diversify away from Asians. Also, these schools tend to care the most about diversity factors because they are already oversubscribed by great academic performers. These diversity factors tend to be big drivers of the HALAC effect. Conversely, a more moderately rated college will show a lesser HALAC effect because, to them, someone academically strong is itself a great asset. How do you account for the HALAC effect? One method is to apply to more colleges when doing applications. Apply to three times the number of reach schools you would otherwise and twice the number of target schools. Applying to more schools ensures that you compensate for lower chances due to HALAC. The more accurate method to account for HALAC is to just do an SAT / ACT score adjustment. That is, lower your SAT by 100 points (on the 1600 scale) or yourACT score by 2 points, and then go through the colleges you’re applying to â€Å"as if† you got your adjusted score. For example, if you really got a 1500 on your SAT, think of your chances of getting into college as if you got a 1400 instead. When you look up your chances using our â€Å"what are my chances table†, use 1400 instead of 1500. By doing this adjustment, you’ll correctly identifythe right reach, target, and safety schools. Why 100 points on the SAT and 2 points on the ACT? These are rough numbers that are closest to a large set of consensus estimates for the HALAC effect. They’re a little lower than the Espenshade study but higher than some other casual surveys. I should disclaim that these numbers are rules of thumb and not hard scientific numbers. Also, for rank 1-10 schools, you should adjust for the full 100 points, but if you’re applying to schools ranked 10-50, a rule of thumb is you can account for just a 50-point adjustment. The adjustment beyond rank 50 will be smaller still. Step 2: Combat the HALAC Effect Through Test Scores Given that Asians need a 100-point increase on the 1600-SAT to reach the same admissions chances, another way to combat the effect is just by having a higher SAT / ACT score.This does require more time and dedication, but it’s definitely possible. It’s not easy to improve by 100 points on the SAT or 2 points on the ACT. However, such improvements are definitely doable. In fact, we at PrepScholar have a 160-point guarantee for the SATand a 4-point guarantee for the ACT.You’ll need to work harder, but you can overcome the HALAC effect this way. Some stereotype Asians as studying more than usual forthe SAT / ACT. However, with their need to score higher just to have the same chances under HALAC, this behavioris much less of a surprise. Step 3: Combat the HALAC Effect Through Diversity in Other Areas To combat HALAC closer to its roots, it’s useful to examine how the HALAC effect arises. Supporters of affirmative action, including the universities themselves, always emphasize diversity as the primary goal. While one can argue about whether that is the sole goal of affirmative action, it is clear that diversity provides a strong channel to drive the HALAC effect. Looking at the diversity driver of the HALAC effect will be another key for Asians to overcome it. Under this diversity driver model, the reason HALAC occurs is because, in the eyes of admissions officers, too many Asian applicants all look the same on paper. They are too similar along too many dimensions. These applicants all do well in school, have high ACT / SAT scores, play violin or piano, and play a racketsport like tennis. Oh and, of course, they are all Asian. The problem from the point of diversity isn’t that an applicant is merely Asian, but rather that an entire host of applicants all look the same along other dimensions. A colorful but useful analogy for the diversity needs of colleges is putting horses into barn stalls. The horses represent applicants, and the barn stalls are the â€Å"spaces† and archetypes that the school has for these applicants. One stall might be labeledâ€Å"Asian, high grades, piano player† - and this stall is overfilled. But if you were white, the â€Å"white, high grades, piano player† stall is only half full! You can’t change your ethnicity, but you can definitely change your other labels, your other dimensions. It turns out that â€Å"Asian, high grades, lacrosse star† is wide open too! Why not fill that stall instead? Put in more theoretical terms, to the extent the HALAC effect is about diversity, you can generate diversity along other dimensions. Instead of being an Asian who’s a top ranked violin player (stereotypical Asian), why not try being a top guitar player? You can go further than that. While a guitar is not stereotypically Asian, it is still a very common instrument. Perhaps you are better off trying to be a top French horn player? Instead of playing badminton, why not try soccer or squash? Generally, think about what the stereotypical Asian applicant looks like. If you can be equally good along a dimension but break the stereotype, it is definitely to your advantage. Being in your state’s top 20 tennis players is probably less advantageous than being one of your state’s top 20 lacrosse players. Being a top 50 debater in your state is probably better than being a top 50 math competitor. It is important that you break the Asian stereotype in ways that are low cost to you. If you can jump from being a top 20 tennis player to a top 20 lacrosse player for free, you definitely should. But life is rarely that simple - and that’s just one of many reasons I don’t like the plain advice â€Å"appear less Asian†. What if you’re a nationally ranked tennis player and don’t know a thing about lacrosse? What if math is your passion and debating is more boring to you than breaking rocks? You have to account for the fact that breaking stereotypes can be costly. I would say that, for an Asian applicant, a rank 50 state debater is stronger than a rank 50 math competitor. But a rank 50 debater is definitely weaker than a rank 5 state math competitor and is probably equal to a rank 20 state math competitor. When it comes to top colleges, they care about what you’re best at and your natural spike. I would be extremely cautious about sacrificing your best dimension in the name of diversity. In fact, I would almost never sacrifice your spike for diversity. The take-away message is this: if you can diversify in extracurriculars at low cost, then do it. However, if you have a special talent, and it happens to be in an area that â€Å"looks Asian†, then don’t give it up. The right calibration is probably a loss of 2x in rank. If you can switch from an Asian-heavy activity to an Asian-light one and lose just 1.5x in rank (e.g. rank 20 to rank 30), then make the switch. But if you have to give up 4x in rank (rank 20 to rank 80), don’t make the switch. Summary Hopefully, the above article gives you a good sense of the unique landscape that Asian-American applicants face in United States college admissions. We started out with some background on the debate - although if you want the full story it’s best to Google the controversy yourself. Then we talked about what the data shows and whether you believe in the Hypothesis of Asians having Lower Admissions Chances. In such a case, we examined how big the HALAC effect can be (about 100 points on the SAT scale). The good news is that there are steps Asian-Americans can take to increase their chances. First, look for diversity in dimensions beyond race; look for diversity in extracurriculars. Second, it’s important to ensure that you’re strong on the SAT / ACT front to make up those 100 points. Do both of these things and you'll give yourself a much better shot at getting into your dream schools. What's Next? Want to improve your SAT score so that you have a better chance of getting into topschools? Learn how studying can get you a perfect SAT score! Wondering which extracurriculars you should join to help yourself stand out? We have guides that include hundreds of extracurriculars ideas andexamples of amazing extracurriculars that are sure to impress colleges. Want more information on what it takes to get into top schools? Learn how to get accepted to Harvard and the Ivy League, written by a Harvard alum. Have friends who also need help with test prep? Share this article! Tweet Dr. Fred Zhang About the Author Fred is co-founder of PrepScholar. He scored a perfect score on the SAT and is passionate about sharing information with aspiring students. 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Nuclear Power Essay Example | Topics and Well Written Essays - 250 words

Nuclear Power - Essay Example This article will focus on nuclear power focusing on potential advantages and disadvantages. Research shows that nuclear energy is sustainable, however; this form of energy has also been associated with the numerous threats it poses to the environment. Some of the most common nuclear disasters known include the Three Mile Island Accident (1979), Chernobyl disaster (1986) and the Fukushima Daiichi nuclear disaster (2011) (Cravens, 2007). However, experts are still carrying out research regarding safety improvements in nuclear energy. This is with the sole aim of finding out if nuclear power’s hazardous side can be eliminated. This will then ensure that opponents of nuclear power embrace its creation, testing and ultimate use. The countries that have significantly invested in nuclear energy include the China, United States and Japan. In this case, the United States was recognized as the largest producer of nuclear energy. In most cases, nuclear energy is employed in propulsion of ships (nuclear marine propulsion), production of electricity and space vehicles among other uses. In the past, most of the countries used nuclear power in construction of weapons of mass destruction. This was most prevalent in the World War II era (Cravens, 2007). In conclusion, nuclear power has been identified as a conventional fuel resource. This involves the use of the uranium element which is a constituent of dirt and rocks found in large water bodies. Furthermore, the World Association of Nuclear Operators (WANO) is an international organization which was set up to promote the safety awareness of nuclear facilities (Cravens,

Essential Questions Essay Example | Topics and Well Written Essays - 500 words

Essential Questions - Essay Example This is done by imparting and acquiring knowledge necessary to eliminate illiteracy and generally changing the mindset. Although in the modern day education is mainly advanced in formal settings such as schools, it can also be done in informal settings. In fact, the first education steps take place in informal settings and in a sub conscious situation from birth. According to Dewey, the sub conscious education from birth is responsible for shaping traits and arousing feelings and emotions in individuals (Dewey, p.1). This implies that education plays an important role in shaping people’s habits and general behavior. This corresponds with the main purpose of education of nurturing growth and general development essential in improving life status in entirety. Fulfilling education purposes requires an outline of appropriate strategies that integrate together to create the desired objective. These strategies stipulate the constituents of education and they tend to lie more on formal education. This is because informal education is seemingly uncontrollable since it entails everyday experiences some that may be adopted sub consciously. As such, determination of what education should entail lies more on improving efficiency and outcome of formal education. This implies that the main focus is on teachers critically examining their techniques and expertise in the teaching practice. This is because teaching techniques specific to the students in play are an appropriate way of advancing education (Ball and Forzani, 2009, p.6). However, other seemingly external factors such as government policies also have influence on education. Nonetheless, the best outcome from formal education has been coupled with student interests (Counts, p.2). This simply means making the learning process student friendly and parallel to some of the acceptable interests. Basically, education should

Comparing the original Sherlock Holmes to the BBCs adaptation Essay

Comparing the original Sherlock Holmes to the BBCs adaptation - Essay Example Literary works produced in earlier years often tend to be adapted and reproduced to fit current lifestyles, especially if such works stirred great interest in their original formats. As such, books, novels, short stories among others can be reproduced in a different genre, for example in a film. The process of adapting and reproducing a literary work is often challenging and can lead to some degree of distortion of the original work. The distortion occurs when the producers, for example, try to fit a character to modern times and the probable scenarios that the character would play. Sherlock, the BBC’s adaptation of â€Å"The Complete Sherlock Holmes† continues to portray Dr. Watson and Sherlock as two males having a close non-sexual relationship just like the original piece. However, the BBC’s version is more daring towards creating doubt on the gender markers of Dr. Watson, by making it appear as if the latter is attracted to Sherlock. The frequent allusions by people that the two could be gay serve to create anxiety in the viewer concerning whether subsequent scenes will reveal that in deed Dr. Watson and Sherlock are romantically involved. However, this scenario does not happen and viewers are kept in anxiety over whether the series will end that way. Keeping the viewers in suspense over the sexual orientation of particularly Dr. Watson is good for interest retention, but the producers concentrate too much on making gay jokes that it almost becomes offensive for gay people and other GSM. A good percentage of the society has come to accep t the GSM and as such, it is not appropriate to keep on joking about such a sensitive matter.

A Two Port Network Biology Essay

A Two Port Network Biology Essay A  two-port network  a kind of  four-terminal network  or quadripole is an  electrical network  circuit or device with two pairs  of terminals to connect to external circuits. Two terminals constitute a  port  if the currents applied to them satisfy the essential requirement known as the  port condition: the  electric current entering one terminal must equal the current emerging from the other. The ports constitute interfaces where the network connects to other networks, the points where signals are applied or outputs are taken. In a two-port network, often port 1 is considered the input port and port 2 is considered the output port. The two-port network model is used in mathematical  circuit analysis techniques to isolate portions of larger circuits. A two-port network is regarded as a black box with its properties specified by a  matrix  of numbers. This allows the response of the network to signals applied to the ports to be calculated easily, without solving for all the internal voltages and currents in the network. It also allows similar circuits or devices to be compared easily. For example, transistors are often regarded as two-ports, characterized by their h-parameters (see below) which are listed by the manufacturer. Any  linear circuit  with four terminals can be regarded as a two-port network provided that it does not contain an independent source and satisfies the port conditions. Examples of circuits analysed as two-ports are  filters,  matching networks,  transmission lines, transformers, and  small-signal models  for transistors (such as the  hybrid-pi model). The analysis of passive two-port networks is an outgrowth of  reciprocity theorems  first derived by Lorentz. In two-port mathematical models, the network is described by a 2 by 2 square matrix of  complex numbers. The common models that are used are referred to as  z-parameters,  y-parameters,  h-parameters,  g-parameters, and  ABCD-parameters, each described individually below. These are all limited to linear networks since an underlying assumption of their derivation is that any given circuit condition is a linear superposition of various short-circuit and open circuit conditions. They are usually expressed in matrix notation, and they establish relations between the variables (Two-Port Networks. (n.d.). In  Wikipedia. Retrieved October 25, 20012, from http://en.wikipe dia.org/wiki/Two-port_network) The experiment is divided into two parts: Part 1 is focused on determining two-port network parameters (admittance and transmission parameters only). The process of measurement and calculations will be briefly illustrated in Theoretical Supplement part. We are aiming to investigate the relationships between the individual parameters and the parameters of two-port networks in cascade and parallel. Part 2 is focused on finding out the transient responses in two-port networks containing capacitive and inductive reactances. Theoretical Supplements: Measurement of Admittance (Y-) Parameters: The equations to determine the parameters are: I1 = y11V1 + y12V2 I2 = y21V1 + y22V2 i.e. [I] = [Y].[V] [Y] = y11 y12 y21 y22 where are the Y parameters of the two-port network. Experimentally these parameters can be determined by short circuiting the ports, one at a time. Hence these parameters are also termed as short-circuit admittance parameters. The following diagrams show the method to calculate the parameters: When output port is shorted (as shown in Figure 2 below): V2 = 0.1 Figure 2 y11 = I1 / V1 y21 = I2 / V1 When input port is shorted (as shown in Figure 3 below): V1 = 0 2 Figure3 y12 = I1 / V2 y22 = I2 / V2 Measurement of Transmission Parameters: The equations to determine the parameters are: V1 = AV2 BI2 I1 = CV2 DI2 Or3 Where [t] is the transmission parameters of the two-port network. Experimentally, the t-parameters can be obtained by short circuiting and open circuiting the output one at a time. The following procedure shows how to calculate the parameters: Output port is open-circuited: i.e. I2 = 0 4 Figure4 A = V1 / V2 C = I1 / V2 Output port is short-circuited: i.e. V2 = 0 1 Figure5 B = V1 / I2 D = I1 / I2 Cascade Interconnection of two 2-port Networks: Considering the 2 networks A and B which are connected in cascade, as shown in Figure 6 below. From this the transmission parameters of the combined cascaded network (N) is obtained. The method is demonstrated below. 5 Figure 6 [t]N = [t]A.[t]B 7 Hence, the following result is obtained. 8 Parallel Interconnection of two 2-Port Networks: Considering the two networks A and B which connected in parallel, as shown in Figure 7 below. The overall y-parameters of the combined network N can be obtained as follows: 6 Figure 7 I1 = I1A + I1B I2 = I2A + I2B V1 = V1A = V1B V2 = V2A = V2B; And H:DropboxCamera Uploads2012-10-25 05.41.34.jpg It can be seen that the overall Y-parameters can be obtained by summing the corresponding Y-parameters of individual networks A and B, when the A and B networks are not altered by the parallel connection. Transient Responses of Two-Port Networks: Damping Ratio  Ã‚ º is defined as the ratio of the actual resistance in damped harmonic motion to that necessary to produce critical damping. It is also known as relative damping ratio. We divide the transient responses into three types on the basis of damping ratio  Ã‚ º, Over damped response ( Ã‚ º > 1), Under damped response ( Ã‚ º Critically damped response ( Ã‚ º = 1). The various conditions stated above are described in detail below. Over damped Response: In this case the roots of the characteristic equation are real and distinct. The solution to the input signal is a decaying exponential function with no oscillations and the transient response will be over damped. The response to the input signal is slow and has no overshoots or undershoots. Under damped: The roots are complex in this case. The transient response will be under damped when  Ã‚ º Critically damped: When  Ã‚ º = 1, the roots are real and equal, and the transient response to the input signal will be critically damped. There will be no oscillations whatsoever. This case is a desirable outcome in many industries. In this experiment, we are mainly using the second type, which is the under damped response. And the characteristic equation is given by: S2 + 2 Ã‚ ºÃƒ Ã¢â‚¬ °nS + à Ã¢â‚¬ °n2 where à Ã¢â‚¬ °n = undamped natural frequency = 1/à ¢Ã‹â€ Ã… ¡( LC ) à Ã¢â‚¬ °n à ¢Ã‹â€ Ã… ¡ (1  Ã‚ º2 ) = damped natural frequency {A484D667-ABED-4193-B38C-40120C378004}  Ã‚ º = damping ratio = Further critical details have been illustrated in the Appendix B of Laboratory manual of Experiment L212. Objectives: To measure the admittance-parameters and transmission parameters of two-port network To investigate the relationships between individual network parameters and two-port networks in cascade and parallel connections To study the transient response of a two-port network containing capacitive and inductive reactances. Equipment: Digital Storage Oscilloscope Function Generator (50ÃŽÂ ©) Digital Multimeter Inductor with 2 inductance steps Capacitors: 22ÃŽÂ ¼F, 100ÃŽÂ ¼F Resistors: 33ÃŽÂ ©, 100ÃŽÂ © (2 numbers), 220ÃŽÂ ©, 330ÃŽÂ ©, 560ÃŽÂ ©, 680ÃŽÂ ©, 3.9kÃŽÂ ©, 4.7kÃŽÂ © (2 numbers), 5.6kÃŽÂ ©, 6.8kÃŽÂ © Bread-board Procedure: Measurement of Admittance-Parameters and Transmission Parameters and to investigate the relationships between individual network parameters and two port networks in cascade and parallel connections Setup A Connect the resistive network A as shown in Figure 8 below. With the network connected in the circuit, apply a sinusoidal voltage of 1 kHz, and amplitude 10 volts from peak to peak at: Port 1 with port 2 open-circuited Port 1 with port 2 short-circuited Port 2 with port 1 short-circuited In each case measure the voltage and current at the input and output terminals The input voltage is measured by observing the peak to peak value on the scope of the oscilloscope while the output voltage is measured with the digital meter. Tabulate the results in Table 1. (all the values measured should be in rms) Figure 8: The resistive network A{DA60CACE-9B44-4522-A111-F57AC9F95897} Setup B: Connect the resistive network as shown in the Figure 9 below. With the network connected in the circuit, apply an identical sinusoidal voltage as in Setup A at: Port 1 with port 2 open-circuited Port 1 with port 2 short-circuited Port 2 with port 1 short-circuited Measure the identical reading as in Setup A in the same way. Tabulate the results in the same Table 1.{0536D217-3D48-4F28-B37B-77F1CB823EEA} Figure 9: The Resistive Network B Cascaded Setup: Connect the networks A and B in cascade as shown in the Figure 10 below. Measure the identical parameters with the identical voltage and applying the voltage at the same positions as was done in the previous two setups A B. Tabulate the readings in Table 1 again.{32E83E0D-6633-4D97-A59B-4374AF22F541} Figure 10: The Cascaded Network of Networks A B Parallel Setup: Reconnect the individual networks A B in parallel as shown in Figure 12 below. Repeat the same procedures above with the same voltage as above to this network. Tabulate the readings in Table 1.{591F8FFC-7083-4E49-88AD-96E019FAD63C} Figure 12: The Parallel Network of Networks A B Table 1: (All values in rms) Results I2 = 0 V2 = 0 V1 = 0 I1 (mA) V1 (V) V2 (V) I1 (mA) I2 (mA) V1 (V) I1 (mA) I2 (mA) V2 (V) Network A (measured) 2.38 3.45 2.52 5.09 3.82 3.45 4.00 5.65 3.46 Network B (measured) 0.72 3.49 3.22 3.27 2.82 3.45 2.89 3.18 3.45 Cascaded (measured) 2.66 3.47 2.07 3.42 1.31 3.44 Parallel (measured) 13.28 11.59 3.46 10.34 12.55 3.46 Questions: The voltages V1 and V2 should not be connected to channel 1 and 2 of the scope simultaneously. Why? It can be observed from the circuit that both the ports V1 and V2 have different grounds. If V1 and V2 are connected simultaneously to channel 1 and 2 of oscilloscope respectively, then the ground terminals of V1 and V2 will be short-circuited as they are connected through the oscilloscope. This would change the circuits configuration and would give us the readings for a completely different circuit which would differ a great deal from the accurate values. What should you do to the readings of peak to peak voltage in order to make them compatible with the currents measured by the digital meter? The relationship between peak to peak values and its respective rms values is: peak to peak voltage = 2 x à ¢Ã‹â€ Ã… ¡2 x rms voltage The current measured by the digital meter is in root-mean-square value (rms). So it is mandatory to convert the peak to peak voltages to its rms value in order to be compatible with the currents measured by the digital meter. Hence the peak to peak value is divided by 2 x à ¢Ã‹â€ Ã… ¡2 to so that it is compatible with the currents measured by the digital meter. Compare the theoretical results with the measurement readings recorded in Table 1 for the interconnected two-port networks. Explain any of the differences in the two sets of results. Two kinds of parameters values are calculated and shown in Table 2 and Table 3. With this parameter values we can compare the difference in values of the measurement and theoretical readings. The parameter values in Table 2 shown below are defined as When the output-port is open, I2 = 0 Then: A = V1 /V2 C = I1/V2 When the output port is shorted, V2 = 0 Hence: B = V1/I2 D = I1/I2 And Cascade (theoretical) is obtained by [t]N = [t]A . [t]B Transmission parameters A B C D Network A (measured) 1.36 677.80 0.00094 1.33 Network B (measured) 1.08 1223.40 0.00022 1.16 Cascade (theoretical) (Network A * Network B) 1.62 2450.07 0.0013 2.69 Cascade (measured) 1.68 2625.95 0.00129 2.61 Percentage difference between cascade (measured) and (theoretical) 3.70% 6.69% 0.78% 3.07% Table 2 As it can be seen from the Table 2 above that there are slight differences between the theoretical and experimental results of the transmission parameters of the individual network and the interconnected two-port networks. The difference is observed due to the experimental human errors, tolerance levels of resistors in networks and slight deviation due to the slight inaccuracy of equipment. The parameter values in Table 3 shown below are defined as When the output port is shorted, V2 = 0. Then: y11 = I1 /V1 y21 = I2/V1 When the input port is shorted, V1= 0. Then: y12 = I1/V2 y22 = I2/V2 And Parallel (theoretical) is obtained by Network A values + Network B values Table 3: Admittance Parameters Admittance parameters y11 y12 y21 y22 Network A (measured) 0.00148 0.00156 0.00107 0.00163 Network B (measured) 0.00095 0.00084 0.00082 0.00092 Parallel (theoretical) (Network A + Network B) 0.00243 0.00240 0.00189 0.00255 Parallel (measured) 0.00384 0.00299 0.00335 0.00363 Percentage difference between Parallel (measured) and Parallel (theoretical) 36.72% 19.73% 43.58% 29.75% From Table 3, it can be observed that the difference between experimental and theoretical admittance parameters are quite large. The large difference is due to the same experimental errors and small tolerance of resistors or the existing voltage drop of the multimeter. Measurement of Transient Response of Two-Port Networks: {ECB52EDE-2A5E-423C-AE62-ECF870EBA09C} Figure 13 Connect the circuit as shown in the Figure 13 above with C = 22  Ã‚ ­F Using a storage scope and with the inductor setting at position 1, inject 10V peak to peak square wave at V1. Choose frequency f of the input voltage such that the square waves leading edge simulate a step input with the transient response completed before the next voltage change. The frequency f is chosen to be about 4 Hz. Record the output waveform V2 with the storage oscilloscope. Sketch the waveforms and when the waveforms have been captured, use the oscilloscope cursor to measure the oscillation period T and the voltages Va and Vb as shown in the Figure 14 below. The waveform is shown in Figure i) below. {71B3E9F8-C513-4F5A-9441-0C73C0A0C9B8} V1 Input Voltage V2 Output Voltage Tin Input signal period T Transient Oscillation Va / Vb Transient Oscillation Voltage Ratio Period Figure 14 Repeat the above procedure for the inductor setting at position 2. The waveform is shown as in Figure ii) below. Repeat the procedure for the two inductor settings with the capacitor changed to 100ÃŽÂ ¼F. The waveforms are show as Figure iii) and iv) below respectively. Add a resistor R2 of 33 ÃŽÂ © in series with inductor L as shown in Figure 15 below and select the inductor setting at position 1 with the capacitor = 100 ÃŽÂ ¼F. The waveform is shown as in Figure v) below. Repeat all the procedures with R2 values of 100 ÃŽÂ © and 220 ÃŽÂ ©. The waveform with R2 as 100 ÃŽÂ © is shown in Figure vi) below. All measurements are recorded in Table 4 below.H:DropboxCamera Uploads2012-10-25 06.12.32.jpg Figure 15 Figure a Figure b Figure c Figure d Figure e Figure f Figure g Condition C=22ÃŽÂ ¼F L = 1H C=22ÃŽÂ ¼F L = 200mH C=100ÃŽÂ ¼F L = 1H C=100ÃŽÂ ¼F L = 200mH C=100ÃŽÂ ¼F L = 1H and add R2=33ÃŽÂ © C=100ÃŽÂ ¼F L = 1H and add R2=100ÃŽÂ © C=100ÃŽÂ ¼F L = 1H and add R2=220ÃŽÂ © T(ms) 48.0 19.0 38.5 94.5 80.20 Period = 253.0 Άt1 =130.0 Άt2 =46.00 V2 =2.531 Va(v) 3.00 1.46 0.791 1.80 1.687 1.250 Vb(v) 0.633 0.700 0.408 0.516 0.3750 0.5000 Table 4 Waveform Figures: L:AAADS0001.BMP Figure i) L:AAADS0003.BMP Figure ii) L:AAADS0006.BMP Figure iii) Figure iv)L:AAADS0007.BMP L:AAADS0008.BMP Figure v) Figure vi) L:AAADS0009.BMP Questions: Why are square waves at a higher frequency not used as input? Square waves at higher frequencies are not used as input because frequency is related to time period by the relationship f = 1/T. So as the frequency is increased, the time period will become shorter and shorter. So it will take shorter time for the output power levels to stabilize after the input circuit stops drawing power. Hence the waveform obtained from the oscilloscope will not be clear enough for proper distinction. What causes the step input voltage to become an oscillating output voltage? The oscillating output voltage is caused due to the presence of the two reactive elements in the circuit, the inductor and the capacitor. The effect of charging and discharging of the capacitor and inductor causes the output to become an oscillating voltage. What are the effects of increasing the values of L and C? The undamped natural frequency à Ã¢â‚¬ °n equals to 1/à ¢Ã‹â€ Ã… ¡( LC ). If the values of L and C are increased, the undamped natural frequency will reduce simultaneously. Hence the oscillations will become more damped. Thus the number of output oscillations will reduce. Calculate the theoretical frequencies of oscillation and compare with the experimental results. The theoretical frequency is given by the relation ft = 1/ (2  Ã‚ ° à ¢Ã‹â€ Ã… ¡(LC)) Hz and the oscillation frequency is given by the relation f = 1/T. Using this relation we can tabulate the values. Figure a Figure b Figure c Figure d T(ms) 48.0 19.0 38.5 94.5 1/T(Hz) 20.83 52.63 25.97 10.58 ft (Hz) 33.93 75.87 35.59 15.92 Percentage difference 38.60% 30.63% 27.03% 33.54% The difference in the values is caused by the tolerance levels of the reactive elements used in the circuit i.e. the inductor and the capacitor. Consider the circuit shown in Figure 13. Obtain the expression for the damping ratio of the circuit.{A484D667-ABED-4193-B38C-40120C378004} Damping Ratio is given by the formula,  Ã‚ º = The natural undamped frequency is given by the relation à Ã¢â‚¬ °n = 1/à ¢Ã‹â€ Ã… ¡ (LC). Since R2 = 0, R1 = 330 à ¢Ã¢â‚¬Å¾Ã‚ ¦ and R3 = 100 à ¢Ã¢â‚¬Å¾Ã‚ ¦, deriving the damping ratio of the circuit as shown in Figure 13, the result is:  Ã‚ º = à ¢Ã‹â€ Ã… ¡(L/C)/860. Obtain the condition for the underdamped response in Figure 13. From the derived result obtained above,  Ã‚ º = à ¢Ã‹â€ Ã… ¡(L/C)/860. For an underdamped response, the damping ratio, ÃŽÂ ¾, should be less than 1, thus à ¢Ã‹â€ Ã… ¡(L/C)/860 What is the effect of adding resistance R2 in the LC circuit? {A484D667-ABED-4193-B38C-40120C378004} According to the formula of damping ratio  Ã‚ º = When R2 is added, the total value of  Ã‚ º increases. Depending on the value of R2,  Ã‚ º 1, even if the number of undershoots and overshoots is reduced, the response will be slower. Conclusion: The parameters of the two-port network, especially the Y-parameters and Transmission parameters (A, B, C, D) were determined experimentally. They can also be calculated theoretically. This experiment is aimed at comparing the differences between the experimental and theoretical values. The relationship between individual network parameters and two-port networks in cascade and parallel connections were also investigated. The results obtained for these were shown in the calculations in the Questions answered previously. Hence if every individual parameter of the networks can be determined, the parameter of the combined system can be determined. Part 2 was focused on studying the transient responses of the experiment. The responses to the change of values in the RLC circuit in the two-port networks were recorded. By varying the values of the capacitor, resistor and inductor, it was observed that increase in the capacitor and inductor values decrease the oscillating frequency and also reduce the number of undershoots and overshoots in the response signal. By adding a resistor in series with the inductor, it was observed that the resistor increases the damping ratio of the circuit but the effect is still dependent on the final damping ratio of the circuit,  Ã‚ º. To summarize the conclusion, all the objectives as stated earlier were met in course of the experiment and a lot of important observations came to light in the area of two-port networks.

The Common Man’s Impact on The Revolution :: American America History

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