# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

7 Pages

### EE 10 Midterm review (online)

Course: EE10 10, Fall 2011
School: UCLA
Rating:

Word Count: 852

#### Document Preview

E UCLA LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review EE10 Midterm Review Example Problems: Supplement P RO B L E M 1 Write down all the equations that are required to solve this circuit problem. All equations should be in terms of Mesh Current variables. Mesh A) Mesh B) 150 (iA iD)35 vs = 0 vs - (iB iD)10 - (iB iC)40 = 0 With iA iB = 3iy Or a Super Mesh equation: Super Mesh...

Register Now

#### Unformatted Document Excerpt

Coursehero >> California >> UCLA >> EE10 10

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
E UCLA LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review EE10 Midterm Review Example Problems: Supplement P RO B L E M 1 Write down all the equations that are required to solve this circuit problem. All equations should be in terms of Mesh Current variables. Mesh A) Mesh B) 150 (iA iD)35 vs = 0 vs - (iB iD)10 - (iB iC)40 = 0 With iA iB = 3iy Or a Super Mesh equation: Super Mesh A-B) 150 (iA iD)35 - (iB iD)10 - (iB iC)40 = 0 With iA iB = 3iy Mesh C) iC = - 5i Mesh D) -(iD iA)35 +15ix (iD iB)10 = 0 And constraint equations iy = iB iC ix = - iA EE 10 M IDTE RM S UPP LEME N T PAGE 1 OF 7 UCLA E LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review P RO B L E M 2 + 30! v1 - 182! 30! i2 10! 60! 27! 44! 5A vS + Use a Delta-to-T circuit transformation to solve for the indicated circuit variables We will start by replacing the 30, 60, and 10 ohm resistances with a T construct a b R1 R2 a Rc b Rb Ra c = R3 c We identify elements and obtain Ra = 10, Rb = 30, and Rc = 60, Then, the corresponding T structure resistances are computed with this transformation EE 10 M IDTE RM S UPP LEME N T PAGE 2 OF 7 UCLA E LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review Expression for the Y structure resistance value in terms of the Delta structure resistance values Rb Rc Ra + Rb + Rc Ra Rc R2 = Ra + Rb + Rc Ra Rb R3 = Ra + Rb + Rc R1 = And, R1 = 18, R2 = 6, and R3 = 3, Now, we can first find vS We combine the resistors appearing in series and parallel into a single resistance producing a 100 value o (The 18 and 182 series in parallel with the 6 and 44 series pair produces a 40 resistance. This lies in series with the 27, 3, and 30 resistances EE 10 M IDTE RM S UPP LEME N T PAGE 3 OF 7 UCLA E LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review Then vS = -500V (note polarity !) Now, we can use the information regarding the current divider and the 5A current flow to determine the current flowing through the 182 and 44 resistors. The current flow through the 182 resistor will be 5A[50/(200+50)] = 1A while the remaining 4A flows through the 44 resistor. Then, the voltage drop across the 60 resistor that would induce a current of polarity as indicated by i2 must be determined by the difference in voltage drops across the 44 and 182 resistors. And v44 v182 = 44(4A) 182(1A) = -6V and i2 = -6V/60 = -0.1A Finally, to compute v1 we can compute the voltage drops across the 30, 182 and 27 resistors combine and this with the net 500V drop. o v1 = 500V 5A(30) 5A (27) 1A(182) = 33V EE 10 M IDTE RM S UPP LEME N T PAGE 4 OF 7 UCLA E LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review P RO B L E M 3 NOTE: Operational Amplifiers will not be included on the Midterm. However, we will use the following problem to illustrate source equivalent methods (and reinforce operational amplifier principles. The non-ideal amplifier in this circuit has an open loop voltage gain of AV , infinite input resistance, but finite output resistance, RO. Find an expression for the Thevinin resistance between the reference and the output terminal, above. First, we introduce the operational amplifier model. v+ v- RO + - A (v - v ) V + RF1 VO + - Vi RF2 EE 10 M IDTE RM S UPP LEME N T PAGE 5 OF 7 UCLA E LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review Then, we recognize that since a dependent source appears, we must use a Test Voltage method to compute RTH. We proceed to replace independent sources by their zero equivalents. This provides the new circuit, Now, we can write a node voltage equation at the output node: IT VT/(RF1 + RF2) + [AV(v+ - v-) - VT ]/RO = 0 Now, we see that v+ = 0 Also, since a voltage divider exists at the inverting input, v- = VTRF2/(RF1 + RF2) Then, the node voltage equation becomes: IT VT/(RF1 + RF2) + [-AVVTRF2/(RF1 + RF2) - VT ]/RO = 0 Or, EE 10 M IDTE RM S UPP LEME N T PAGE 6 OF 7 UCLA E LECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 Midterm Review IT = (VT/RO ) [1 + RO/(RF1 + RF2) + AVRF2/(RF1 + RF2)] Finally, the Thevenin Resistance expression produces the following interesting result: RTH VT/IT = RO / [1 + ( RO + AV RF2) /(RF1 + RF2)] Now, consider the limit of AV large, then RTH = RO [(RF1 + RF2)/AVRF2] This demonstrates that the output resistance of this amplifier is reduced relative to the open loop output resistance, RO , by a factor depending on both open loop gain and the gain of the non-inverting voltage amplifier. Recall that we had found that the gain for this amplifier (for an ideal operational amplifier device) was (RF1 + RF2)/RF2 Note that in the limit where RF2 is large compared to RF1 then the amplifier gain falls to unity and the output resistance reaches RO/AV Note also that in the limit of AV = 0, then RTH = RO / [1 + ( RO /(RF1 + RF2)] = 1 / [1/RO + 1/(RF1 + RF2)] This is just the resistance of RO in parallel with the resistance (RF1 + RF2) EE 10 M IDTE RM S UPP LEME N T PAGE 7 OF 7
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

UCLA - EE10 - 10
LSE - EC - 201
Checking the convexity and nonsatiation assumptions EC201 LSEMargaret Bray October 25, 200911.11.1.1NonsatiationThe simple storyDefinition and conditions for nonsatiationInformally nonsatiation means that &quot;more is better&quot;. This is not a precise st
LSE - EC - 201
The marginal rate of substitution and ordinal utility EC201 LSEMargaret Bray October 9, 200911.1Marginal rate of substitutionWhat is the marginal rate of substitution?The marginal rate of substitution (MRS) is defined either as the gradient of the i
LSE - EC - 201
Uncompensated demand with dierentiable utility functions EC201 LSEMargaret Bray October 19, 201011.1General results on utility maximizationNonsatiation and the budget lineNonsatiation means that the utility can be increased by increasing one or both
LSE - EC - 201
Compensated demand and the expenditure function with differentiable utility functions EC201 LSEMargaret Bray November 22, 200911.1General results on expenditure minimizationNonsatiation and expenditure minimizationIf the prices of the two goods are
LSE - EC - 201
Uncompensated demandThis is an example to show what goes wrong if you work with preferences that are not convex. The utility function is ux 1 , x 2 x 2 x 2 . 1 2 Uncompensated demand requires maximizes utility ux 1 , x 2 subject to the budget constraint
LSE - EC - 201
Uncompensated demand with perfect complements EC201 LSEMargaret Bray October 26, 2009A perfect complements utility function has the form u (x1 , x2 ) = min (a1 x1 , a2 x2 ) , where min (a1 x1 , a2 x2 ) is the minimum of a1 x1 and a2 x2 . Here the utilit
LSE - EC - 201
Compensated demand and the expenditure function with perfect complements EC201 LSEMargaret Bray October 9, 2009 This example works with the same perfect complements utility function u (x1 , x2 ) = min 1 x1 , x2 2 as consumer theory worked example 6 wher
LSE - EC - 201
Finding Elasticities1 DefinitionsIf the demand for good 1 is x1 (p2 , p2 , m) where p1 and p2 are prices and m is income the own price elasticity of demand is defined as x1 p1 . p1 x1 This is the limit of the proportional change in quantity proportional
LSE - EC - 201
Cost functions and conditional fact demandMargaret Bray LSE November 23, 20091IntroductionThese notes take you through the definitions and properties of conditional factor demand and cost functions. It is conventional to work with two inputs K and L a
LSE - EC - 201
Conditional factor demand and cost functions with a Cobb-Douglas production function EC201 LSEMargaret Bray November 19, 20101IntroductionThis note is about .nding conditional factor demand and .rst the long run and then the short run cost function wi
LSE - EC - 201
Conditional Factor Demand and Costs with a Fixed Proportions Production Function EC201 LSEMargaret Bray November 22, 2009This example works with the perfect complements production function f (K, L) = min(3K, L). Production functions of the form f (K, L)
LSE - EC - 201
Industrial Organization: Perfect CompetitionIndustrial Organization Worked Example 1 Perfect CompetitionAll firms in a perfectly competitive industry are identical with a total cost function c(q) = 5 + 5q2 where q is the firm's output. In the short run
LSE - EC - 201
Industrial Organization Worked Example 2Industrial Organization Worked Example 2MonopolyA monopoly supplies 1000 customers each of whom demands q = 100 4p where p is the price. The monopoly's cost function is 5Q where Q is the monopoly's output. Total
LSE - EC - 201
EC201 Industrial Organization Worked Example 3 Cournot-Nash EquilibriumMargaret Bray London School of Economics March 17, 2011In a Cournot -Nash equilibrium the strategic variable is quantity. In a Cournot-Nash equilibrium each firm produces the quantit
LSE - EC - 201
Industrial Organization Worked Example 4: Bertrand-Nash EquilibriumMargaret Bray London School of Economics April 10, 2012In a Bertrand Nash equilibrium the strategic variable is price; each .rm charges the price which maximises its pro.ts given the pri
LSE - EC - 201
Adverse Selection and CreditAn entrepreneur with no current wealth requires 10,000 to fully fund a project. Partially funded projects are worthless. The entrepreneur can be one of two types, where her type is her private information. A &quot;stolid&quot; entrepren
LSE - EC - 201
Risk AttitudesWhich of these lotteries do you prefer?A: 90% chance of winning 5 million and 10% chance of winning 0, or B: 100% chance of winning 1 million?Which of these lotteries do you prefer?C: 9% chance of winning 5 million and 91% chance of winn
LSE - EC - 201
Insurance Demand Banker has a job paying 300 that she will lose with Banker is expected-utility maximiser with utility-ofwealth function u(w)=!(w/3) p300+(1-p)27 probability 1-p, in which case her income falls to 27. Expected value of banker's income Ex
LSE - EC - 201
Negative Externalities from Alcohol ConsumptionExcess alcohol consumption estimated to cost the NHS 2.7 annually Government proposes a price floor to curb excessive drinking Suppose that demand for alcohol is Q=2-p Total cost c(Q)=(1/2)Q2 Externality on
LSE - EC - 201
Arrow's Impossibility Theorem, the Borda Count and Alternative Voting This note explores the properties of two alternatives to the &quot;first-pastthe-post&quot; voting system used in British parliamentary elections, where each voter casts a vote for one candidate,
LSE - EC - 201
An Illustration of the Second Welfare TheoremAn exchange economy consists of two consumers, A and B, and two goods, x and y. Consumer A has utility function uA xA , y A = xA 1/2 Consumer B has utility function uB xB , y B = xB yB . A owns 6 units of x
LSE - EC - 201
General Competitive Equilbirium in Production Economy There are two consumers, A and B, and two firms, 1 and 2. A owns the share A (1) = 2 of Firm 1 as well as the share A (2) = 3 of Firm 2. B owns 3 4 1 the share B (1) = 3 of Firm 1 as well as the share
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsFM212 - Class Assignments (Michaelmas Term) Each class assignment in Part 1 consists of 3 questions. Students should attempt written answers to the questions before the respective class.Class 11. A parce
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 24. Mike Polanski is 30 years of age and his salary next year will be \$40,000. Mike forecasts that his salary will increase at the steady rate of 5 percent per annum until his retirement at age 60.
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 1 1. NPV = -\$1,300,000 + (\$1,500,000/1.10) = +\$63,636 Since the NPV is positive, you would construct the motel. Alternatively, we can compute r as follows: r = (\$1,500,000/\$1,300,000) 1 = 0.1538 = 15.3
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 2 4. Annuity with growth: a. Let St = salary in year tPV = t =1 30St = (1.08) tt =13040,000 (1.05) t -1 (1.08) t=t =130(40,000/1.05) = (1.08 / 1.05) tt =13038,095.24 (1.0286) t 1 1 = 38,0
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 3 7. NoGrowth Corporation currently pays a dividend of \$0.5 per quarter, and it will continue to pay this dividend forever. What is the ex-dividend price per share if its equity cost of capital is 15
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 4 10. Answer the following questions: a. Briefly explain the difference between beta as a measure of risk and variance as a measure of risk. b. What is the correlation coefficient between two stocks
LSE - FM - 212
FM212 MT 2011 Class 3 Solutions1.Since dividends are paid quarterly, we can value them as a perpetuity using a quarterly1discount rate of (1.15) 4 - 1 = 3.556% then, P=\$0.5/0.03556=\$14.06. 2. a. We know that g, the growth rate of dividends and earning
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 4 10. a. Variance measures the total risk of a security and is a measure of stand-alone risk. Total risk has both unique risk and market risk. In a well-diversified portfolio, unique risks tend to canc
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 5 13. The Treasury bill rate is 4 percent, and the expected return on the market portfolio is 12 percent. Using the capital asset pricing model: a. Draw a security market line. b. What is the risk pr
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 5 13. CAPM20 Expected Return 15 10 5 0 0 0.5 1 Beta 1.5 2a. b. Market risk premium = rm rf = 0.12 0.04 = 0.08 = 8.0%. c. Use the security market line: r = rf + (rm rf) r = 0.04 + [1.5 (0.12 0.04)] =
LSE - FM - 212
Hand in Problem Set 1GE Values as of 28/10/11 1a 1b 2a 2b 3 Current Stock Price Market cap. rate Dividend Return of Equity Payout Ratio Growth next 5 yrs 17.25 0.09 0.6 0.1180 0.48 0.1474 Formulae 1 0.69 2 0.79 3 0.91 4 1.04 5 1.19Dividend Discount Meth
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsHand in Problem Set 1 Please hand a paper copy of your work to your class teacher at the beginning of class 4 (week 5). As a new analyst for a brokerage firm, you are anxious to demonstrate the skills you
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 6 16. Which of the following observations appear to indicate market inefficiency? Explain whether the observation appears to contradict the weak, semi-strong or strong form of the market efficiency h
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 7 19. The following table lists prices of options on IBM stock. Stock IBM Time to Exercise (months) 1 Exercise Price 120 Stock Price 126.36 Put Price 1.27 Call Price 8.1a. Using the information abov
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 6 16. a. No contradiction with market efficiency: taxpaying investors must be indifferent between both kinds of bond, since they're equally risky. b. Strong form. c. In an efficient market, predictable
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 7 19. From the Put-Call Parity we can derive the implied interest rate: a. P+S=C+EX/(1+r) solving for r=0.39% monthly rate b. Using the derived rate we can calculate the future value of call and put pr
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 8 22. CH4 trading stock price is \$100 and in each 3 month period will either increase by 25 percent or fall by 20 percent. A 6-month call on CH4 stock has an exercise price of \$90. The risk-free 3-mo
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 8 22. a. Note: at this point we do not need to specify whether this is an American or European option as they both have the same value (American call without dividends is never exercised early). The po
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsHand in Problem Set 2 Please hand a paper copy of your work to your class teacher at the beginning of class 8 (week 9). You may send your excel spreadsheet to your class teacher (this is optional). Your bo
LSE - FM - 212
Lecture 1: Present ValuePresent Value Introduction to Present Value Foundations of the Net Present Value RuleBased on Chapter 2 in BMAFM212 Principles of Corporate FinanceValues and DiscountingDiscount Rate Interest rate used to compute present valu
LSE - FM - 212
Lecture 2: How To Calculate Present ValuesHow To Calculate Present Values Valuing Long-Lived Assets PV Shortcuts Perpetuities and Annuities Compound Interest &amp; Present Values Nominal and Real Rates of InterestBased on Chapters 2 and 3.5 in BMAFM212 Pr
LSE - FM - 212
Lecture 3: Value of Bonds and Stocks Value of Bonds and Common Stocks Using PV Formulas to Value Bonds How Common Stocks are Traded How Common Stocks are Valued Estimating the Cost of Equity Capital Stock Prices and EPSBased on Chapters 3.1 and 4 in BMA
LSE - FM - 212
Lecture 4: Risk and ReturnRisk and Return Over a Century of Capital Market History Measuring Portfolio Risk Calculating Portfolio Risk Beta and Unique Risk Diversification &amp; Value AdditivityBased on Chapter 7 in BMAFM212 Principles of Corporate Financ
LSE - FM - 212
Lecture 6: Market EfficiencyThe Six Lessons of Market Efficiency What is an Efficient Market? Random Walk Efficient Market Theory The Evidence on Market Efficiency Puzzles and Anomalies Six Lessons of Market EfficiencyBased on Chapter 13 in BMAFM212
LSE - FM - 212
Lecture 5: Portfolio TheoryPortfolio Theory and Asset Pricing Equilibrium Markowitz Portfolio Theory Mean Variance Optimization Role of the CAPM Evidence regarding CAPM Some Alternative Theories to CAPMBased on Chapter 8 in BMAFM212 Principles of Corp
LSE - FM - 212
Lecture 7: Put and Call OptionsPut and Call Options Calls, Puts and Shares Financial Alchemy with Options What Determines Option ValueBased on Chapter 20 in BMAFM212 Principles of Corporate FinanceTerminologyDerivatives: Any financial instrument who
LSE - FM - 212
Lecture 8: Options Pricing TheoryOptions Pricing Theory Two Option Valuation Methods Binomial and Continuous-time Models The Black-Scholes Model Option Pricing with DividendsBased on Chapter 21 in BMAFM212 Principles of Corporate FinanceRisk Adjusted
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 9 25. You have estimated spot rates as follows: Year 1 2 3 4 5 Spot Rate 0.25% 0.50% 0.75% 1.00% 1.25% a. What are the forward rates for each period? b. Calculate the PVs of the following government
LSE - FM - 212
Lecture 9: Valuing Government Bonds Valuing Government Bonds Real and Nominal Rates of Interest The Term Structure and Yield to Maturity (YTM) How Interest Rate Changes Affect Bond Prices Explaining the Term StructureBased on Chapter 3 in BMAFM212 Prin
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 9 25. Price of a bond and yield curve a. Use the following non-arbitrage relation to calculate the implied forward rates:(1 + rn ) n = (1 + r1 )(1 + f 2 ).(1 + f n )Year 1 2 3 4 5 Spot Rate 0.25% 0.5
LSE - FM - 212
Hand in Problem Set 2 Your first data observations should look like this: Annual Tbill Rate Date S&amp;P 500 GE S&amp;P 500 return GE Return % 07/10/2002 885.76 18.73 01/11/2002 936.31 0.0571 1.6 20.11 0.0737 02/12/2002 879.82 -0.0603 1.24 18.19 -0.0955 -0.0274 1
LSE - FM - 212
Lecture 10: Forwards and FuturesForwards and Futures Hedging with Commodity Forwards Cash Settlement vs. Delivery Marking-to-market Forwards and Futures Financial Futures Pricing Commodity Futures Pricing Differences between Forwards and Futures Based o
LSE - FM - 212
FM212/FM492 Principles of Finance MT Problem SetsClass 10 28. Yesterday you sold six-month futures on the German DAX stock market index at a price of 6,260. Today the DAX closed at 6,250 and DAX futures closed at 6,268. You get a call from your broker, w
LSE - FM - 212
FM212 Michaelmas Term 2011 Class work SolutionsClass 10 28. 6-months future on equity index: a. She is asking you to pay 8 Euros (your sale is showing a loss). Position diagram for a short position on a future contractb.With 1% implied annual dividend
LSE - FM - 212
1/4/2012List of Topics in Lent Capital Budgeting and the NPV Rule Real Options Payout Policy Does Debt Policy Matter? How Much Should A Firm Borrow? The Many Different Types of Debt Mergers, Corporate Governance, and Control Initial Public Offerings Ris
LSE - FM - 212
FM212/FM492 Principles of Finance Problem Set SolutionsClass 10 28. Insurance companies have advantages/disadvantages in bearing risk Advantages in bearing risk Skills in estimating probabilities Skills in identifying risk-reduction techniques Diversifie
LSE - FM - 212
Class 10 28. Large businesses spend millions of dollars annually on insurance. Why? Should they insure against all risks or does insurance make more sense for some risks than others? 29. A gold-mining firm is concerned about short-term volatility in its r
LSE - FM - 212
Solutions to Data Case1. Home Depot bond, Coupon 4.40%, Maturity 4/1/2021, Moody's rating A3, Yield 2.552% (as of 3/3/12). 2. Estimating spreads using Reuter's Corporate spreads for 10 year maturity: a. 10-year U.S.Treasury Bond yield =1.97% (coupon 2.0%