Homework Solutions Physics 8B Spring 2012 Chpt. 32 5,18,25,27,36,42,51,57,61,76


 Lorin Russell
 2 years ago
 Views:
Transcription
1 Homework Solutons Physcs 8B Sprng 202 Chpt. 32 5,8,25,27,3,42,5,57,, Model: Assume deal connectng wres and an deal battery for whch V bat =. Please refer to Fgure EX32.5. We wll choose a clockwse drecton for. Note that the choce of the current s drecton s arbtrary because, wth two batteres, we may not be sure of the actual current drecton. The 3 V battery wll be labeled and the V battery wll be labeled 2. Solve: (a) Krchhoff s loop law, gong clockwse from the negatve termnal of the 3V battery s V = ( V) = V + V + V = closed loop bat R bat V +3 V (8 Ω) + V = 0 = = 0.5 A 8 Ω Thus, the current through the 8 Ω resstor s 0.5 A. Because s postve, the current s left to rght (.e., clockwse). (b) Assess: The graph shows a 3 V gan n battery, a 9 V loss n the resstor, and a gan of V n battery 2. The fnal potental s the same as the ntal potental, as rured Model: Assume deal connectng wres but not an deal battery. The crcut for an deal battery s the same as the crcut n Fgure EX32.8, except that the Ω resstor s not present. Solve: n the case of an deal battery, we have a battery wth = 5 V connected to two seres resstors of 0 Ω and 20 Ω resstance. Because the uvalent resstance s R = 0 Ω + 20 Ω = 30 Ω and the potental dfference across R s 5 V, the current n the crcut s The potental dfference across the 20 Ω resstor s V 20 V 5 V = = = = 0.50 A R R 30 Ω = R = (0.50 A)(20 Ω) = 0.0 V n the case of a real battery, we have a battery wth = 5 V connected to three seres resstors: 0 Ω, 20 Ω, and an nternal resstance of.0 Ω. Now the uvalent resstance s The potental dfference across R R = 0 Ω + 20 Ω +.0 Ω = 3 Ω s the same as before ( = 5 V). Thus, V 5 V = = = = A R R 3 Ω Therefore, the potental dfference across the 20 Ω resstor s
2 ( )( ) V 20 = R = A 20 Ω = 9.8 V That s, the potental dfference across the 20 Ω resstor s reduced from 0.0 V to 9.8 V due to the nternal resstance of Ω of the battery. The percentage change n the potental dfference s 0.0 V 9.8 V 00 = 3.2% 0.0 V Solve: Model: The connectng wres are deal wth zero resstance. n the frst step, the resstors 00 Ω, 00 Ω, and 00 Ω n the top branch are n seres. Ther combned resstance s 300 Ω. n the mddle branch, the two resstors, each 00 Ω, are n seres. So, ther uvalent resstance s 200 Ω. n the second step, the three resstors are n parallel. Ther uvalent resstance s The uvalent resstance of the crcut s 54.5 Ω. R = 300 Ω Ω + 00 Ω R = 54.5 Ω Model: Groundng does not affect a crcut s behavor. Please refer to Fgure EX Solve: Because the earth has V earth = 0 V, pont d has a potental of zero. n gong from pont d to pont a, the potental ncreases by 9 V. Thus, pont a s at a potental of 9 V. Let us calculate the current n the crcut before calculatng the potentals at ponts b and c. Applyng Krchhoff s loop rule, startng clockwse from pont d, ( V) = V9 V bat + V2 + V V bat + V Ω Ω = 0 +9 V (2 Ω) V ( Ω) = 0 = 3 V = A 3 Ω There s a drop n potental from pont a to pont b by an amount R = ( A)(2 Ω) = 2 V. Thus, the potental at pont b s 9 V 2 V = 7 V. The potental decreases from 7 V at pont b to 7 V V = V at pont c. There s a further decrease n potental across the Ω resstor of R = ( A)( Ω) = V. That s, the potental of V at c becomes 0 V at pont d, as t must. n summary, the potentals at a, b, c, and d are 9 V, 7 V, V, and 0 V Please refer to Fgure P32.3. Solve: Bulbs D and E are n seres, so the same current wll go through both and make them ually brght (D = E). Bulbs B and C are n parallel, so they have the same potental dfference across them. Because they are dentcal bulbs wth ual resstances, they wll have ual currents and be ually brght (B = C). Now the uvalent resstance of B + C n parallel s less than the resstance of E, so the total resstance along the path through A s less than the total resstance along path through D. The two paths have the same total potental dfference the emf of the battery so more current wll flow through the A path than through the D path. Consuently, A wll have more current than D and E and wll be brghter than D and E (A > D = E). Bulbs B and C each have half the current of A, because the current splts at the juncton, so A s also brghter than B and C (A > B = C). The remanng ssue s how B and C compare to D and E. Suppose B and C were replaced by wres wth zero resstance, leavng just bulb A n the mddle path. Then the resstance of the path through A would be half of the 2
3 resstance of the path through D. Ths would mean that the current through A would be twce the current through D, so A = 2 D. When B and C are present, ther resstance adds to the resstance of A to lower the current through the mddle path. So n realty, A < 2 D. We already know that B = C = 2 A, so we can conclude that B = C < D. Snce the current through B and C s less than the current through D and E, D and E are brghter than B and C. The fnal result of our analyss s A > D = E > B = C Model: Use the laws of seres and parallel resstances. Solve: Despte the dagonal orentaton of the 2 Ω resstor, the Ω, 2 Ω, and 4 Ω resstors are n parallel because they have a common connecton at both the top end and at the bottom end. Ther uvalent resstance s R = + + = 2 Ω Ω 2 Ω 4 Ω The trckest ssue s the 0 Ω resstor. t s n parallel wth a wre, whch s the same thng as a resstor wth R = 0 Ω. The uvalent resstance of 0 Ω n parallel wth 0 Ω s R = + = ( ) = = 0 Ω 0 Ω 0 Ω n other words, the wre s a short crcut around the 0 Ω, so all the current goes through the wre rather than the resstor. The 0 Ω resstor contrbutes nothng to the crcut. So the total crcut s uvalent to a 2 Ω resstor n seres wth the 2 Ω uvalent resstance n seres wth the fnal 3 Ω resstor. The uvalent resstance of these three seres resstors s R ab = 2 Ω + 2 Ω + 3 Ω = 7 Ω Model: Assume an deal battery and deal connectng wres. 3
4 Solve: (a) Groundng one pont doesn t affect the basc analyss of the crcut. n Fgure P32.5, there s a sngle loop wth a sngle current flowng n the clockwse drecton. Applyng Krchhoff s loop law clockwse from the lower rght corner gves 2 V V = V 4 2 = 0 V = = 0.50 A 24 Ω Knowng the current, we can use V = R to fnd the potental dfference across each resstor: V 8 = 4 V V 4 = 2 V V 2 = V The purpose of groundng one pont n the crcut s to establsh that pont as the specfc potental V = 0 V. Groundng pont d makes that potental there Vd = 0 V. Then we can use the known potental dfferences to fnd the potental at other ponts n the crcut. Pont a s 4 V less than pont d (because potental decreases n the drecton of current flow), so V a = V d 4 V = 4 V. Pont b s 2 V more than pont a because of the battery. So V b = V a + 2 V = 8 V. Pont c s 2 V less than pont b, so V c = V b 2 V = V. Pont d s V less than pont c, so V d = V c V = 0 V. Ths s a consstency check makng one complete loop brngs us back to the potental at whch we started, namely 0 V. (b) The nformaton about the potentals s shown n the graph above. (c) Movng the ground to pont a doesn t change the basc analyss of part (a) or the potental dfferences found there. All that changes s that now V a = 0 V. Pont b s 2 V more than pont a because of the battery. So, V b = V a + 2 V = 2 V. Pont c s 2 V less than pont b, so V c = V b 2 V = 0 V. Pont d s V less than pont c, so V d = V c V = 4 V. Pont a s 4 V less than pont d, so V a = V d 4 V = 0 V. Ths brngs us back to where we started. The nformaton about the potentals s shown n the graph above Model: The voltage source/battery and the connectng wres are deal. Please refer to Fgure P Solve: Let us frst apply Krchhoff s loop law startng clockwse from the lower left corner: Vn +V n R (00 Ω) = 0 V = R + 00 Ω The output voltage s Vn Vout 00 Ω Vout = ( 00 Ω ) = ( 00 Ω) = R + 00 Ω V R+ 00 Ω For V 0 out = V n, the above uaton can be smplfed to obtan R: Vn 0 00 Ω = R + 00 Ω = 000 Ω R = 900 Ω V R+ 00 Ω n n 32.. Model: The battery and the connectng wres are deal. The fgure shows how to smplfy the crcut n Fgure P32. usng the laws of seres and parallel resstances. Havng reduced the crcut to a sngle uvalent resstance, we wll reverse the procedure and buld up the crcut usng the loop law and the juncton law to fnd the current and potental dfference of each resstor. Solve: From the last crcut n the dagram, = 2 V 2 A Ω = Ω = Thus, the current through the battery s 2 A. As we rebuld the crcut, we note that seres resstors must have the same current and that parallel resstors must have the same potental dfference V. 4
5 n Step, the Ω resstor s returned to a 3 Ω and 3 Ω resstor n seres. Both resstors must have the same 2 A current as the Ω resstance. We then use Ohm s law to fnd V 3 = (2 A)(3 Ω) = V As a check, V + V = 2 V, whch was V of the Ω resstor. n Step 2, one of the two 3 Ω resstances s returned to the 4 Ω, 48 Ω, and Ω resstors n parallel. The three resstors must have the same V = V. From Ohm s law, V 4 = =.5 A 4 Ω V 48 = = A 48 Ω 8 V 3 = = A Ω 8 Resstor Potental dfference (V) Current (A) 3 Ω 4 Ω 48 Ω Ω Model: The connectng wres are deal. The capactors dscharge through the resstors. The fgure shows how to smplfy the crcut n Fgure P32.7 usng the laws of seres and parallel resstors and the laws of seres and parallel capactors. Solve: The 30 Ω and 20 Ω resstors are n parallel and are uvalent to a 2 Ω resstor. Ths 2 Ω resstor s n seres wth the 8 Ω resstor so the uvalent resstance of the crcut R = 20 Ω. The two 0 µf capactors are n seres producng an uvalent capactance of 30 µf. Ths 30 µf capactor s n parallel wth the 20 µf capactor so the uvalent capactance C of the crcut s 50 µf. The tme constant of ths crcut s τ = R C = (20 Ω)(50 µf) =.0 ms The current due to the three capactors through the 20 Ω uvalent resstor s the same as through the 8 Ω resstor. So, the voltage across the 8 Ω resstor follows the decay uaton V = V0e t/τ. For V = V 0 /2, we get t t/.0 ms V0/2 = V 0 e ln = 2.0 ms t = 0.9 ms 5
Chapter 31B  Transient Currents and Inductance
Chapter 31B  Transent Currents and Inductance A PowerPont Presentaton by Paul E. Tppens, Professor of Physcs Southern Polytechnc State Unversty 007 Objectves: After completng ths module, you should be
More informationThe circuit shown on Figure 1 is called the common emitter amplifier circuit. The important subsystems of this circuit are:
polar Juncton Transstor rcuts Voltage and Power Amplfer rcuts ommon mtter Amplfer The crcut shown on Fgure 1 s called the common emtter amplfer crcut. The mportant subsystems of ths crcut are: 1. The basng
More information(6)(2) (6)(4) (4)(6) + (2)(3) + (4)(3) + (2)(3) = 1224 + 24 + 6 + 12 6 = 0
Chapter 3 Homework Soluton P3., 4, 6, 0, 3, 7, P3.3, 4, 6, P3.4, 3, 6, 9, P3.5 P3.6, 4, 9, 4,, 3, 40  P 3. Determne the alues of, 4,, 3, and 6
More informationLOOP ANALYSIS. The second systematic technique to determine all currents and voltages in a circuit
LOOP ANALYSS The second systematic technique to determine all currents and voltages in a circuit T S DUAL TO NODE ANALYSS  T FRST DETERMNES ALL CURRENTS N A CRCUT AND THEN T USES OHM S LAW TO COMPUTE
More information1E6 Electrical Engineering AC Circuit Analysis and Power Lecture 12: Parallel Resonant Circuits
E6 Electrcal Engneerng A rcut Analyss and Power ecture : Parallel esonant rcuts. Introducton There are equvalent crcuts to the seres combnatons examned whch exst n parallel confguratons. The ssues surroundng
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationThe Magnetic Field. Concepts and Principles. Moving Charges. Permanent Magnets
. The Magnetc Feld Concepts and Prncples Movng Charges All charged partcles create electrc felds, and these felds can be detected by other charged partcles resultng n electrc force. However, a completely
More informationFaraday's Law of Induction
Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy
More informationChapter 12 Inductors and AC Circuits
hapter Inductors and A rcuts awrence B. ees 6. You may make a sngle copy of ths document for personal use wthout wrtten permsson. Hstory oncepts from prevous physcs and math courses that you wll need for
More informationChapter 6 Inductance, Capacitance, and Mutual Inductance
Chapter 6 Inductance Capactance and Mutual Inductance 6. The nductor 6. The capactor 6.3 Seresparallel combnatons of nductance and capactance 6.4 Mutual nductance 6.5 Closer look at mutual nductance Oerew
More informationSystematic Circuit Analysis (T&R Chap 3)
Systematc Crcut Analyss TR Chap ) Nodeoltage analyss Usng the oltages of the each node relate to a ground node, wrte down a set of consstent lnear equatons for these oltages Sole ths set of equatons usng,
More informationPassive Filters. References: Barbow (pp 265275), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationCIRCUIT ELEMENTS AND CIRCUIT ANALYSIS
EECS 4 SPING 00 Lecture 9 Copyrght egents of Unversty of Calforna CICUIT ELEMENTS AND CICUIT ANALYSIS Lecture 5 revew: Termnology: Nodes and branches Introduce the mplct reference (common) node defnes
More informationSection C2: BJT Structure and Operational Modes
Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v
More informationz(t) = z 1 (t) + t(z 2 z 1 ) z(t) = 1 + i + t( 2 3i (1 + i)) z(t) = 1 + i + t( 3 4i); 0 t 1
(4.): ontours. Fnd an admssble parametrzaton. (a). the lne segment from z + to z 3. z(t) z (t) + t(z z ) z(t) + + t( 3 ( + )) z(t) + + t( 3 4); t (b). the crcle jz j 4 traversed once clockwse startng at
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationImplementation of Deutsch's Algorithm Using Mathcad
Implementaton of Deutsch's Algorthm Usng Mathcad Frank Roux The followng s a Mathcad mplementaton of Davd Deutsch's quantum computer prototype as presented on pages  n "Machnes, Logc and Quantum Physcs"
More informationHALL EFFECT SENSORS AND COMMUTATION
OEM770 5 Hall Effect ensors H P T E R 5 Hall Effect ensors The OEM770 works wth threephase brushless motors equpped wth Hall effect sensors or equvalent feedback sgnals. In ths chapter we wll explan how
More informationHÜCKEL MOLECULAR ORBITAL THEORY
1 HÜCKEL MOLECULAR ORBITAL THEORY In general, the vast maorty polyatomc molecules can be thought of as consstng of a collecton of two electron bonds between pars of atoms. So the qualtatve pcture of σ
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Symoblc approach
More informationProfessor Iordanis Karagiannidis. 2010 Iordanis Karagiannidis
Fnancal Modelng Notes Basc Excel Fnancal Functons Professor Iordans Karagannds Excel Functons Excel Functons are preformatted formulas that allow you to perform arthmetc and other operatons very quckly
More informationInterleaved Power Factor Correction (IPFC)
Interleaved Power Factor Correcton (IPFC) 2009 Mcrochp Technology Incorporated. All Rghts Reserved. Interleaved Power Factor Correcton Slde 1 Welcome to the Interleaved Power Factor Correcton Reference
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationMultiple stage amplifiers
Multple stage amplfers Ams: Examne a few common 2transstor amplfers:  Dfferental amplfers  Cascode amplfers  Darlngton pars  current mrrors Introduce formal methods for exactly analysng multple
More informationEXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR
EXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More information21 Vectors: The Cross Product & Torque
21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rghthand rule for the cross product of two vectors dscussed n ths chapter or the rghthand rule for somethng curl
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A
Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationFormula of Total Probability, Bayes Rule, and Applications
1 Formula of Total Probablty, Bayes Rule, and Applcatons Recall that for any event A, the par of events A and A has an ntersecton that s empty, whereas the unon A A represents the total populaton of nterest.
More informationThe FullWave Rectifier
9/3/2005 The Full Wae ectfer.doc /0 The FullWae ectfer Consder the followng juncton dode crcut: s (t) Power Lne s (t) 2 Note that we are usng a transformer n ths crcut. The job of ths transformer s to
More informationToday in Physics 217: the divergence and curl theorems
Today n Physcs 217: the dvergence and curl theorems Flux and dvergence: proof of the dvergence theorem, à lá Purcell. rculaton and curl: proof of tokes theorem, also followng Purcell. ee Purcell, chapter
More informationLaws of Electromagnetism
There are four laws of electromagnetsm: Laws of Electromagnetsm The law of BotSavart Ampere's law Force law Faraday's law magnetc feld generated by currents n wres the effect of a current on a loop of
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationThe difference between voltage and potential difference
Slavko Vjevć 1, Tonć Modrć 1 and Dno Lovrć 1 1 Unversty of Splt, Faclty of electrcal engneerng, mechancal engneerng and naval archtectre Splt, Croata The dfference between voltage and potental dfference
More informationTexas Instruments 30Xa Calculator
Teas Instruments 30Xa Calculator Keystrokes for the TI30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More information1 Battery Technology and Markets, Spring 2010 26 January 2010 Lecture 1: Introduction to Electrochemistry
1 Battery Technology and Markets, Sprng 2010 Lecture 1: Introducton to Electrochemstry 1. Defnton of battery 2. Energy storage devce: voltage and capacty 3. Descrpton of electrochemcal cell and standard
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationPhysics 9 Fall 2009 Homework 6  Solutions
. Chapter 32  Exercise 8. Physics 9 Fall 29 Homework 6  s How much power is dissipated by each resistor in the figure? First, let s figure out the current in the circuit. Since the two resistors are
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationCHAPTER 9 SECONDLAW ANALYSIS FOR A CONTROL VOLUME. blank
CHAPTER 9 SECONDLAW ANALYSIS FOR A CONTROL VOLUME blank SONNTAG/BORGNAKKE STUDY PROBLEM 91 9.1 An deal steam turbne A steam turbne receves 4 kg/s steam at 1 MPa 300 o C and there are two ext flows, 0.5
More informationCHAPTER 8 Potential Energy and Conservation of Energy
CHAPTER 8 Potental Energy and Conservaton o Energy One orm o energy can be converted nto another orm o energy. Conservatve and nonconservatve orces Physcs 1 Knetc energy: Potental energy: Energy assocated
More informationA Master Time Value of Money Formula. Floyd Vest
A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.
More informationGibbs Free Energy and Chemical Equilibrium (or how to predict chemical reactions without doing experiments)
Gbbs Free Energy and Chemcal Equlbrum (or how to predct chemcal reactons wthout dong experments) OCN 623 Chemcal Oceanography Readng: Frst half of Chapter 3, Snoeynk and Jenkns (1980) Introducton We want
More informationPeak Inverse Voltage
9/13/2005 Peak Inerse Voltage.doc 1/6 Peak Inerse Voltage Q: I m so confused! The brdge rectfer and the fullwae rectfer both prode fullwae rectfcaton. Yet, the brdge rectfer use 4 juncton dodes, whereas
More informationsdomain Circuit Analysis
SDoman naly Doman rcut naly Tme doman t doman near rcut aplace Tranform omplex frequency doman doman Tranformed rcut Dfferental equaton lacal technque epone waveform aplace Tranform nvere Tranform 
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationGoals Rotational quantities as vectors. Math: Cross Product. Angular momentum
Physcs 106 Week 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap 11.2 to 3 Rotatonal quanttes as vectors Cross product Torque expressed as a vector Angular momentum defned Angular momentum as a
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More informationChapter 11 Torque and Angular Momentum
Chapter 11 Torque and Angular Momentum I. Torque II. Angular momentum  Defnton III. Newton s second law n angular form IV. Angular momentum  System of partcles  Rgd body  Conservaton I. Torque  Vector
More informationESCI 341 Atmospheric Thermodynamics Lesson 9 Entropy
ESCI 341 Atmosherc hermodynamcs Lesson 9 Entroy References: An Introducton to Atmosherc hermodynamcs, sons Physcal Chemstry (4 th edton), Levne hermodynamcs and an Introducton to hermostatstcs, Callen
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More informationA) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.
ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose
More informationLaddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems
Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) Laddered Multlevel DC/AC Inverters used n Solar Panel Energy Systems Fang Ln Luo, Senor Member IEEE
More informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More informationTraffic State Estimation in the Traffic Management Center of Berlin
Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG,
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationModule 2. AC to DC Converters. Version 2 EE IIT, Kharagpur 1
Module 2 AC to DC Converters erson 2 EE IIT, Kharagpur 1 Lesson 1 Sngle Phase Fully Controlled Rectfer erson 2 EE IIT, Kharagpur 2 Operaton and Analyss of sngle phase fully controlled converter. Instructonal
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationWeek 6 Market Failure due to Externalities
Week 6 Market Falure due to Externaltes 1. Externaltes n externalty exsts when the acton of one agent unavodably affects the welfare of another agent. The affected agent may be a consumer, gvng rse to
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationFORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER
FORCED CONVECION HEA RANSFER IN A DOUBLE PIPE HEA EXCHANGER Dr. J. Mchael Doster Department of Nuclear Engneerng Box 7909 North Carolna State Unversty Ralegh, NC 276957909 Introducton he convectve heat
More informationLecture 2: Single Layer Perceptrons Kevin Swingler
Lecture 2: Sngle Layer Perceptrons Kevn Sngler kms@cs.str.ac.uk Recap: McCullochPtts Neuron Ths vastly smplfed model of real neurons s also knon as a Threshold Logc Unt: W 2 A Y 3 n W n. A set of synapses
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationExhaustive Regression. An Exploration of RegressionBased Data Mining Techniques Using Super Computation
Exhaustve Regresson An Exploraton of RegressonBased Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The
More informationTime Domain simulation of PD Propagation in XLPE Cables Considering Frequency Dependent Parameters
Internatonal Journal of Smart Grd and Clean Energy Tme Doman smulaton of PD Propagaton n XLPE Cables Consderng Frequency Dependent Parameters We Zhang a, Jan He b, Ln Tan b, Xuejun Lv b, HongJe L a *
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationPhysics 41 HW Set 11 Chapters 20 and 21
Physcs 41 HW Set 11 Chapters 0 and 1 Chapter 0 1 An deal gas ntally at P,, and T s taken through a cycle as shown Fnd the net work done on the gas per cycle What s the net energy added by heat to the system
More informationFINANCIAL MATHEMATICS
3 LESSON FINANCIAL MATHEMATICS Annutes What s an annuty? The term annuty s used n fnancal mathematcs to refer to any termnatng sequence of regular fxed payments over a specfed perod of tme. Loans are usually
More information= (0.400 A) (4.80 V) = 1.92 W = (0.400 A) (7.20 V) = 2.88 W
Physics 2220 Module 06 Homework 0. What are the magnitude and direction of the current in the 8 Ω resister in the figure? Assume the current is moving clockwise. Then use Kirchhoff's second rule: 3.00
More informationForecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network
700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School
More informationRiskbased Fatigue Estimate of Deep Water Risers  Course Project for EM388F: Fracture Mechanics, Spring 2008
Rskbased Fatgue Estmate of Deep Water Rsers  Course Project for EM388F: Fracture Mechancs, Sprng 2008 Chen Sh Department of Cvl, Archtectural, and Envronmental Engneerng The Unversty of Texas at Austn
More informationSolutions to Bulb questions
Solutions to Bulb questions Note: We did some basic circuits with bulbs in fact three main ones I can think of I have summarized our results below. For the final exam, you must have an understanding of
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationTime Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University
Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton
More informationSafety instructions VEGAVIB VB6*.GI*******
Safety nstructons VEGAVIB VB6*.GI******* Kosha 14AV4BO0107 Ex td A20, A20/21, A21 IP66 T** 0044 Document ID: 48578 Contents 1 Area of applcablty... 3 2 General nformaton... 3 3 Techncal data... 3 4 Applcaton
More informationInterest Rate Forwards and Swaps
Interest Rate Forwards and Swaps Forward rate agreement (FRA) mxn FRA = agreement that fxes desgnated nterest rate coverng a perod of (nm) months, startng n m months: Example: Depostor wants to fx rate
More informationHosted Voice Self Service Installation Guide
Hosted Voce Self Servce Installaton Gude Contact us at 18773551501 learnmore@elnk.com www.earthlnk.com 2015 EarthLnk. Trademarks are property of ther respectve owners. All rghts reserved. 107107629
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationThe Mathematical Derivation of Least Squares
Pscholog 885 Prof. Federco The Mathematcal Dervaton of Least Squares Back when the powers that e forced ou to learn matr algera and calculus, I et ou all asked ourself the ageold queston: When the hell
More informationDamage detection in composite laminates using cointap method
Damage detecton n composte lamnates usng contap method S.J. Km Korea Aerospace Research Insttute, 45 EoeunDong, YouseongGu, 35333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The contap test has the
More information