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2 = 8I1 + 4I2 2 = 8(1.5) + 4I2 2 = 12 + 4I2 4I2 = −10 I2 = −2.5 For a 3x3, this process is iterated as follows: Equation 2 would be solved for I3 and this would be substituted back into equation 1 yielding a new equation (let’s call it A) with only I1 and I2 terms. Similarly, Equation 3 would be solved for I3 and this ... | ACElectricalCircuitAnalysis_Page_401_Chunk901 |
Determinants Determinants Determinants revolve around the concept of a matrix which itself is little more than an ordered collection of coefficients and/or constants. It is imperative that the unknowns be in the same order in each equation (i.e., I1 ascending to IX left to right) A simple coefficient matrix for the ori... | ACElectricalCircuitAnalysis_Page_402_Chunk902 |
I1 = 1.5 In like fashion I2 is found: 20 10 8 2 I2 = -------- 20 8 8 4 −40 I2 = ----- 16 I2 = −2.5 Sarrus’ Rule may also be used with a 3x3 matrix. This is achieved by extending the matrix. Fourth and fifth columns are added to the right of the 3x3 matrix by simply making copies of the first two columns. This creates t... | ACElectricalCircuitAnalysis_Page_403_Chunk903 |
Expansion by Minors Expansion by Minors Expansion by Minors is another method that may be used to generate a determinant solution. This involves breaking the matrix into a series of smaller matrices (minors) that are combined using row-column coefficients. The position of these coefficients will also indicate whether t... | ACElectricalCircuitAnalysis_Page_404_Chunk904 |
Appendix C Appendix C Equation Proofs Equation Proofs RMS Equivalents for Non-Sines For any waveform, the root-mean-square equivalence factor is computed by normalizing the peak value to unity, squaring the waveform, finding the mean value of that intermediate result, and then taking the square root of the mean. This v... | ACElectricalCircuitAnalysis_Page_405_Chunk905 |
Maximum Power Transfer: Finding the Maximizing Value of P = R/(R2+2R+1) While the algebraic and graphing technique explored in Chapter 5 leads to a proper answer, it is incomplete. A more rigorous treatment using differential calculus follows. We have already determined that the reactive portion of the load must have t... | ACElectricalCircuitAnalysis_Page_406_Chunk906 |
Finding k0 : Determining f1 and f2 in Resonant Circuits The coefficient k0 was defined such that: f 1 = f 0 k 0 and f 2 = f 0×k 0 We start with the definition of circuit Q based on bandwidth and resonant frequency, and expand, solving in terms of f2. Qcircuit = f 0 BW = f 0 f 2 −f 1 f 2 = f 0 Qcircuit +f 1 (EQ 1) The r... | ACElectricalCircuitAnalysis_Page_407_Chunk907 |
Appendix D Appendix D Answers to Selected Odd-Numbered Problems Answers to Selected Odd-Numbered Problems 1 Fundamentals 1 Fundamentals 1. 10, 7.07, 0, 1 kHz, 1 ms, 0° 3. 20, −3, 50 Hz, 20 ms, 0° 5. 10, 7.07, 0, 100 Hz, 10 ms, 45° 7. 1, 10, 400 Hz, 2.5 ms, −45° 9. 200 μs, 10 μs 11. 36° 13. 14.1445°, 11.2−63.4°, 1021... | ACElectricalCircuitAnalysis_Page_408_Chunk908 |
37. 284 nF, 482 pF, 339 pF, 132.6 nF, 212 nF 39. 892 nH, 525 μH, 748 μH, 1.91 μH, 1.19 μH 41. a 43. b 409 | ACElectricalCircuitAnalysis_Page_409_Chunk909 |
2 Series RLC Circuits 2 Series RLC Circuits 1. 2k − j1.94 k Ω 3. 270 + j125.7 Ω 5. 1 k − j1.278 k Ω 7. 300 − j400 9. 1.447 μF 11. v(t)=0.1sin2π1000t (i and v are in phase) 13. i is 241 mA p-p and lags by 90° 15. v is 16.6 V p-p and leads by 90° 17. 1 k − j318 Ω 19. i = 953E−617.6° amps, vR = 953E−317.6° volts, vC = 3... | ACElectricalCircuitAnalysis_Page_410_Chunk910 |
41. i = 2.24E−363.4° amps, vB = 8.94−26.6° volts, vC = 2.24153.4° volts, vAC = 12−4.8° volts 43. i = 35.36E−3−45° amps, vC = 2.12−135° volts, vR = 1.414−45° volts, vL = 3.5445° volts 45. vR = 100° volts, vC = 5.3−90° volts, vL = 7.0790° volts 47. vR = 2.40° volts, vL = 85.4E−390° volts, vC = 424E−390° vol... | ACElectricalCircuitAnalysis_Page_411_Chunk911 |
3 Parallel RLC Circuits 3 Parallel RLC Circuits 1. 73.2−12.5° (71.4 −j15.8) 3. 99−8.04° (98 −j13.8) 5. 182.952.4° (111.5 + j145) 7. f = 45.2 MHz 9. 11. is = 0.1200010.18°, iR = 0.120°, iC = 377E−690° 13. is = 9.43E−3−58°, iR = 5E−30°, iC = 2E−390°, iL = 10E−3−90° 15. is = 47.4E−316.3°, iR = 45.5E−30°, iC = ... | ACElectricalCircuitAnalysis_Page_412_Chunk912 |
iR = 2.23E−360° iL = 1.044E−3−95° 29. 2.84 μF 31. 7.7 nF 33. 34.5 nF 35. 65.7 nF 37. 390 nF 39. 507 nF 41. 128 mH 4 Series-Parallel RLC Circuits 4 Series-Parallel RLC Circuits 1. Z10k ≈ 1250°, Z1M ≈ 125−0.8°, Z100M ≈ 68.8−24.2° Ω 3. Z300 ≈ 0.7590°, Z30k ≈ 77.589.4°, Z3M ≈ 9075.4° Ω 5. Z = 18051.6° Ω 7. is = 9.... | ACElectricalCircuitAnalysis_Page_413_Chunk913 |
5 Analysis Theorems and Techniques 5 Analysis Theorems and Techniques 1. vb = 2.993.5° 3. i82 = 13.3E−359.8° 5. vb = 1.08165° 7. i2.2k = 1.3E−349.2° 9. vb = 7.8498.9°, vcd = 10.2−44.2° 11. iS1 = 337E−6−73.6°, iS2 = 401E−6152° 13. vab = 14.3−25.4° 15. vab = 972E−3−166° 17. va = 1.31−174°, vb = 2.58−154° 19. ... | ACElectricalCircuitAnalysis_Page_414_Chunk914 |
61. 63. 65. −j43.8 Ω 415 | ACElectricalCircuitAnalysis_Page_415_Chunk915 |
6 Nodal and Mesh Analysis 6 Nodal and Mesh Analysis 1. vc = 34.437.7° 3. i43 = 33.2E−344.4° 5. vc = 180−106° 7. i4Ω = 772E−347.1° 9. vac = 18.35−80.8° 11. i22 = 3.07−153° 13. vc = 6.09−3.68° 15. i3.3k = 9.86E−318.8° 17. vc = 1838.9° 19. vbc = 1.0959.8° 21. vba = 964E−3127.3° 23. vcb = 15.2149° 25. Loop orde... | ACElectricalCircuitAnalysis_Page_416_Chunk916 |
7 AC Power 7 AC Power 1. S = 6.25 mVA, P = 4.88 mW, Q = 3.9 mVAR (ind), PF = 0.781 3. S = 64.4 VA, P = 57.7 W, Q = 28.8 VAR (ind), PF = 0.894 5. S = 315 VA, P = 162 W, Q = 270 VAR (ind), PF = 0.515 7. S = 751 VA, P = 720 W, Q = 216 VAR (cap), PF = 0.958 9. i = 4.286 A, P = 90.9 W 11. P = 6.4 kW, Q = 4.8 kVAR, L = 2.86 ... | ACElectricalCircuitAnalysis_Page_417_Chunk917 |
8 Resonance 8 Resonance 1. BW = 14.67 kHz, f1 = 432.7 kHz, f2 = 447.3 kHz 3. Qcoil = 50, Rcoil = 1.88 Ω 5. 15 kΩ || j600 Ω 7. Rp = 20.36 kΩ, Lp = 75 μH 9. f0 = 247 kHz, Q = 10.2 11. f0 = 5.03 kHz, Qsys = 8.35, BW = 602 Hz 13. f0 = 10.07 kHz, Qsys = 4.22, BW = 2.39 kHz, vC = 4.22 15. f0 = 10.07 kHz, Qsys = 3.51, BW = 2.... | ACElectricalCircuitAnalysis_Page_418_Chunk918 |
10 Decibels and Bode Plots 10 Decibels and Bode Plots 1) A) 10 dB B) 19 dB C) 26.99 dB D) 0 dB E) −6.99 dB F) −15.23 dB 3) 33 dB 5) G = 501, Pout = 12.53 W 7) A) 1.06 B) 1 C) 199.5 D) 3.43 E) 0.398 F) 0.188 9) A = 8.57 A' = 18.66 dB 11) A) 0 dBW B) 13.6 dBW C) 8.13 dBW D) −7 dBW E) −26.4 dBW F)30.8 dBW G) −43.5 dBW H) ... | ACElectricalCircuitAnalysis_Page_419_Chunk919 |
29) 31) At 4 kHz: 78.7 degrees, at 20 Hz: 45 degrees, at 100 Hz: 11.3 degrees 33) 35) Net gain at 20 kHz = 35.87 dB Net phase at 20 kHz = 51.7 degrees At 100 kHz: phase = −5.1 degrees, A'v = 40 dB At 800 kHz: phase = −70.5 degrees, A'v = 30.5 dB 37) 420 f A'v 200 kHz 18 dB f θ 0° -180° -270° 2 MHz 20 kHz f A'v 20 Hz 32... | ACElectricalCircuitAnalysis_Page_420_Chunk920 |
39) 41) Each lag network rolls off at 20 dB/decade for a 60 dB/decade total (i.e., above 1.2 MHz). 43) 0.775 V 45) 360 W 47) 71.5 dBV 49) Greater than 30 Hz. 421 f A'v 750 kHz 36 dB 1.2 MHz 100 kHz | ACElectricalCircuitAnalysis_Page_421_Chunk921 |
Appendix E Appendix E A Closing Observation A Closing Observation This title is the twelfth in a series of free open educational resources, now at five texts and seven laboratory manuals. People occasionally ask why these titles have not gone through the typical route of using a traditional publisher (indeed, the Opera... | ACElectricalCircuitAnalysis_Page_422_Chunk922 |
DC Electrical Circuit Analysis DC Electrical Circuit Analysis A Practical Approach A Practical Approach James M. Fiore James M. Fiore | DCElectricalCircuitAnalysis_Page_1_Chunk923 |
2 | DCElectricalCircuitAnalysis_Page_2_Chunk924 |
DC Electrical Circuit Analysis DC Electrical Circuit Analysis A Practical Approach A Practical Approach by James M. Fiore Version 1.0.11, 11 January 2024 3 | DCElectricalCircuitAnalysis_Page_3_Chunk925 |
This DC Electrical Circuit Analysis, by James M. Fiore is copyrighted under the terms of a Creative Commons license: This work is freely redistributable for non-commercial use, share-alike with attribution Device data sheets and other product information are copyright by their respective owners and have been obtained t... | DCElectricalCircuitAnalysis_Page_4_Chunk926 |
Preface Preface Welcome to DC Electrical Circuit Analysis, an open educational resource (OER). The goal of this text is to introduce the theory and practical application of analysis of DC electrical circuits. It is offered free of charge under a Creative Commons non-commercial, share-alike with attribution license. For... | DCElectricalCircuitAnalysis_Page_5_Chunk927 |
For Those Without and Those Within “All we can do...is to run over several instances, and examine carefully the principle, which binds the different thoughts to each other, never stopping till we render the principle as general as possible.” — David Hume, An Enquiry Concerning Human Understanding (1748) 6 | DCElectricalCircuitAnalysis_Page_6_Chunk928 |
Table of Contents Table of Contents Chapter 1: Fundamentals . . . . . . . 10 1.0 Chapter Objectives . . . . . . . . 10 1.1 Introduction . . . . . . . . . 10 1.2 Significant Digits and Resolution . . . . . . 11 1.3 Scientific and Engineering Notation . . . . . . 14 1.4 The Metric System . . . . . . . . 16 1.5 The Scient... | DCElectricalCircuitAnalysis_Page_7_Chunk929 |
Chapter 4: Parallel Resistive Circuits . . . . . 110 4.0 Chapter Objectives . . . . . . . . 110 4.1 Introduction . . . . . . . . . 110 4.2 The Parallel Connection . . . . . . . 111 4.3 Combining Parallel Components . . . . . . 111 4.4 Kirchhoff's Current Law . . . . . . . 115 4.5 Parallel Analysis . . . . . . . . 117 4... | DCElectricalCircuitAnalysis_Page_8_Chunk930 |
Chapter 8: Capacitors . . . . . . . 260 8.0 Chapter Objectives . . . . . . . . 260 8.1 Introduction . . . . . . . . . 260 8.2 Capacitance and Capacitors . . . . . . . 261 8.3 Initial and Steady-State Analysis of RC Circuits . . . . . 272 8.4 Transient Response of RC Circuits . . . . . . 274 Summary . . . . . . . . . 28... | DCElectricalCircuitAnalysis_Page_9_Chunk931 |
1 1 Fundamentals Fundamentals 1.0 Chapter Learning Objectives 1.0 Chapter Learning Objectives After completing this chapter, you should be able to: • Describe significant digits and resolution. • Express and compute numeric values using scientific and engineering notation. • Describe the metric system and detail its ad... | DCElectricalCircuitAnalysis_Page_10_Chunk932 |
At this point we need to distinguish between electricity and electronics. The term electricity tends to refer to the general relationships between electrical quantities such as voltage and current. In practical use, an electrical system tends to refer to a system where electrical energy is used directly to perform some... | DCElectricalCircuitAnalysis_Page_11_Chunk933 |
lowest level digit displayed. For example, a bathroom scale may show weights in whole pounds. Thus, one pound would be the resolution of the measurement. Even if the scale was otherwise perfectly accurate, we could not be assured of a person's weight to within better than one pound using this scale as there is no way o... | DCElectricalCircuitAnalysis_Page_12_Chunk934 |
total distance is 60 miles plus 51.17 feet? No, it is not. Why? Because we cannot expect the car's odometer to be accurate to within 0.01 feet, like the tape measure. In fact, the odometer is reading out a value with one-tenth mile resolution. One-tenth of a mile is 528 feet, or more than ten times the entire measureme... | DCElectricalCircuitAnalysis_Page_13_Chunk935 |
Example 1.2 Perform the following computations, leaving the answer with the appropriate number of significant digits. A. 55 ∙ 10.1 B. 2312.5 / 16.2 C. 1756.2 + 345.1 D. 750.2 − 0.004 Answers: A. 555.5 which rounds to 560 (55 has only two significant digits). B. 142.7469136... which rounds to 143 (16.2 has three signifi... | DCElectricalCircuitAnalysis_Page_14_Chunk936 |
particularly useful is when multiplying or dividing. For multiplying, multiply the mantissas and add the exponents. For dividing, divide the mantissas and subtract the exponents. For example, multiply 20000 by 360000. This is equivalent to 2E4 times 3.6E5. The result is 7.2E9 (i.e., 7200000000). Similarly, dividing the... | DCElectricalCircuitAnalysis_Page_15_Chunk937 |
Answers: A. 2.1 kilograms (2.1 kg) B. 5 millimeters (5 mm) C. 32 Megabits per second (32 Mbps) D. 74.1 microseconds (74.1 μs) Notice that the final answers are much more compact and less error prone. After some initial effort, certain common shortcuts will become second nature. For example (and keeping it generic), mic... | DCElectricalCircuitAnalysis_Page_16_Chunk938 |
the meter (roughly 39.37 inches). If we want to talk about particularly small or large values we would simply add our engineering notation prefixes to come up with millimeters or kilometers for everyday conversion (although if a value happened to be particularly large or small we would say something like 2.3E9 meters).... | DCElectricalCircuitAnalysis_Page_17_Chunk939 |
to study the planet Mars suffered a spectacular failure. A subcontractor had used USA customary units for its software which then fed values to other systems that were expecting metric/SI units (as specified in the system contract). The result was the destruction of the orbiter as it attempted orbital insertion. The co... | DCElectricalCircuitAnalysis_Page_18_Chunk940 |
biologist J. B. S. Haldane (Haldane was being somewhat snippy, but in general, he meant anything that would be clearly out of the expected time-line, in this case a small mammal predating even the most simple creatures with backbones). A hypothesis is tested by repeated cycles of prediction, observation and measurement... | DCElectricalCircuitAnalysis_Page_19_Chunk941 |
You might now formulate a hypothesis: namely that the mass of a stone doesn’t have an effect on how fast it falls from a given height and that height and fall time are directly related. Your hypothesis is predictive. Although you used only four sizes of stones and a few heights, your broadened hypothesis should apply t... | DCElectricalCircuitAnalysis_Page_20_Chunk942 |
1.6 Critical Thinking: Avoiding Being Fooled 1.6 Critical Thinking: Avoiding Being Fooled As humans, we need to recognize that we are fallible. No matter how good our intentions, we make mistakes and can be fooled. The first step toward reducing and ultimately eliminating these sources of error is to understand them. W... | DCElectricalCircuitAnalysis_Page_21_Chunk943 |
Logical Fallacies Logical Fallacies Logical fallacies represent faulty reasoning. They are “thinking traps” that people sometimes fall into. Familiarity with them will help reduce their occurrence. There are dozens of logical fallacies but we shall only investigate a representative few. To help explain the process, we'... | DCElectricalCircuitAnalysis_Page_22_Chunk944 |
stands, they are unique. That unique character is lost when everyone stands. Turning to a different fallacy, the Latin phrase post hoc ergo propter hoc can be translated as “Before this, therefore because of this”. This fallacy is sometimes referred to as the post hoc fallacy or the causation fallacy. It is an error re... | DCElectricalCircuitAnalysis_Page_23_Chunk945 |
Finally, ad hominem is a Latin term meaning “to the person”. The ad hominem attempts to disprove a point by arguing against the person making a claim, not the claim itself. For example, suppose Doug makes a claim in favor of a new theory of gravity. Fran's counterargument is that Doug is an evil person because he likes... | DCElectricalCircuitAnalysis_Page_24_Chunk946 |
these logos, however, a finished product will bear the standard RoHS compliance label, as shown in Figure 1.8. 1.8 Summary 1.8 Summary An electrical system is one that refers to the direct use of electrical energy in terms of power generation, transmission or application. In contrast, an electronic system is one that t... | DCElectricalCircuitAnalysis_Page_25_Chunk947 |
loop. If the hypothesis is repeatedly verified and not rejected, it may be elevated to a scientific theory. It is important during this process to be aware of logical fallacies and cognitive biases that can lead to false interpretations of the experimental results. Finally, RoHS, or the Restriction of Hazardous Substan... | DCElectricalCircuitAnalysis_Page_26_Chunk948 |
7. Convert the following to scientific notation: a) 41.56 b) 954000 c) 84.035 d) 0.0001632 8. Convert the following to scientific notation: a) 11200 b) 30000000 c) 325.2 d) 0.00002504 9. Convert the following to engineering notation: a) 12000 b) 470 c) 6.5 d) 0.00198 10. Convert the following to engineering notation: a... | DCElectricalCircuitAnalysis_Page_27_Chunk949 |
For problems 23 through 26 determine the result of the computation in SI base units (meters, kilograms, seconds) with appropriate engineering notation units (kilo, milli, etc.). 23. Determine the result of 20 meters times 0.10 kilograms in kg·m. 24. Determine the result of 34 kilometers divided by 10 millimeters. 25. D... | DCElectricalCircuitAnalysis_Page_28_Chunk950 |
Notes Notes ♫♫ ♫♫ 29 | DCElectricalCircuitAnalysis_Page_29_Chunk951 |
2 2 Basic Quantities Basic Quantities 2.0 Chapter Learning Objectives 2.0 Chapter Learning Objectives After completing this chapter, you should be able to: • Describe a basic, functional atomic model. • Describe fundamental quantities and relations including charge, current, energy, voltage, power, resistance and condu... | DCElectricalCircuitAnalysis_Page_30_Chunk952 |
core are negatively charged electrons, each following a nice, regular, planar path much like a planet around the sun. Unfortunately, this model is not accurate to say the least, although its popularity can sometimes lead to wildly erroneous and darkly humorous conclusions. In spite of its inaccuracy, the components (nu... | DCElectricalCircuitAnalysis_Page_31_Chunk953 |
polarity: protons are positively charged while electrons are negatively charged. An important thing to remember is that particles with the same polarity repel each other while opposites attract3. Charge is measured in coulombs, named after Charles-Augustin de Coulomb a French physicist of the eighteenth century. The ch... | DCElectricalCircuitAnalysis_Page_32_Chunk954 |
Shells are denoted by their principal quantum number, n; 1, 2, 3, etc. The higher the number, the more subshells it can contain. Subshells are designated by letters, the first four being s, p, d, and f. Shell 1 contains only subshell s while shell 2 contains subshell types s and p. Shell 3 contains subshell types s, p ... | DCElectricalCircuitAnalysis_Page_33_Chunk955 |
model for copper would simply show four rings, the first three being filled and with a single electron in the fourth ring. This is shown in Figure 2.6. In this version, the individual electrons are drawn in each shell and the atomic number is indicated at the nucleus. Again, please do not imagine this representing indi... | DCElectricalCircuitAnalysis_Page_34_Chunk956 |
through a wire in a period of one second. Consider Figure 2.7. Here we have a wire with electrons flowing through it in the direction of the arrow. We cut this wire with an imaginary plane, leaving us with the highlighted disk. Now imagine that we could count the number of electrons passing through this disk over the c... | DCElectricalCircuitAnalysis_Page_35_Chunk957 |
Total electrons = Q×number of electrons per coulomb Total electrons = 50 mC×6.242E18 Total electrons = 3.121E17electrons In sum, the larger the charge transferred within a given time period, the greater the current. Modern electrical and electronic systems might deal with currents of under a picoamp or, at the other ex... | DCElectricalCircuitAnalysis_Page_36_Chunk958 |
in VA, then the second, or reference, point is assumed to be the system common or ground. In this case, we're referring to the voltage at point A relative to the system common point. Finally, by definition, VAB = VA − VB, as they have the same reference. Example 2.3 100 joules are expended to move a 20 coulomb charge f... | DCElectricalCircuitAnalysis_Page_37_Chunk959 |
Anyone who has opened a box filled with polystyrene packing peanuts can attest to the troublesome nature of the triboelectric effect, as the very light peanuts can easily adhere to other objects due to the electric charge generated through their displacement. No amount of manic brushing or throwing of the pieces will r... | DCElectricalCircuitAnalysis_Page_38_Chunk960 |
considerably higher, its potential energy would be much greater. Therefore, the impact on Mr. Hume's head would be increased dramatically and he would have little difficulty heading the ball down field (i.e., the transformation of potential energy into kinetic energy), although the chances of him gaining a concussion a... | DCElectricalCircuitAnalysis_Page_39_Chunk961 |
is, what do we do with the energy, and more to the point, how fast do we use it? For example, that sandwich might be sufficient to allow someone to run a 5k (3.1 mile) road race in 17 minutes. In contrast, it also might be sufficient to allow that same person to watch television for three hours. It's the same amount of... | DCElectricalCircuitAnalysis_Page_40_Chunk962 |
Example 2.5 If a 9 volt battery delivers a current of 0.1 amps, determine the power delivered in watts. P = I×V P = 0.1amps × 9volts P = 0.9W Efficiency Efficiency Efficiency is the ratio of useful output power to applied power expressed as a percentage. It is denoted by the Greek letter η (eta) and is always less than... | DCElectricalCircuitAnalysis_Page_41_Chunk963 |
Example 2.7 An audio amplifier has a maximum rated output of 100 watts to a loudspeaker. If it exhibits an efficiency of 70%, determine the input power required and the amount of power wasted. η = Pout Pin × 100% Pin = Pout η × 100% Pin = 100W 70 % × 100% Pin = 142.9watts As 142.9 watts are drawn by the amplifier and o... | DCElectricalCircuitAnalysis_Page_42_Chunk964 |
cents per kWh, then the cost to run that toaster oven is 7.5 cents. If it is used for a full hour then it costs 15 cents, and so on. To put usage in perspective, a typical home in the USA or Canada uses about 900 kWh per month while households in many countries in Europe might use one half to one quarter of that amount... | DCElectricalCircuitAnalysis_Page_43_Chunk965 |
First, it should be noted that 15 incandescent bulbs will be needed. At 50 cents each, that's $7.50 for the bulbs. The cost to run them is, Cost = P× t × rate Cost = 75W × 15000 hours × 0.12 $/kWh Cost = $135.00 The total is $ 142.50. Now for the single LED required: Cost = P× t × rate Cost = 14W × 15000 hours × 0.12 $... | DCElectricalCircuitAnalysis_Page_44_Chunk966 |
The maximum current output of a battery is likewise limited. If such were not the case, we might expect even very small batteries to produce phenomenally large currents for very shorts periods of time. This is not the case. A graph of discharge curves at various load currents is shown in Figure 2.12. Notice how the bat... | DCElectricalCircuitAnalysis_Page_45_Chunk967 |
Remember, 20 hours is only an approximation. For a more accurate rendering, consider the following example. Example 2.11 Using the graph of Figure 2.12, determine the expected lifespan with a 100 milliamp draw for a lower voltage limit of 1.2 volts. Also determine the effective amp-hour rating at this point. The 50 mA ... | DCElectricalCircuitAnalysis_Page_46_Chunk968 |
A table of typical amp hour ratings for common battery sizes is shown in Figure 2.14. These values are appropriate for good quality alkaline batteries. Rechargeable NiMH (nickel-metal hydride) would be around the same. Remember, these are just approximations. 2.7 Resistance and Conductance 2.7 Resistance and Conductanc... | DCElectricalCircuitAnalysis_Page_47_Chunk969 |
In this simple scenario, resistance is a function of the material the current is passing through along with its shape. This is illustrated in Figure 2.15 where the arrow shows the direction of current flow. An obvious question is “What is this block made of?” It should come as no surprise that the material chosen has a... | DCElectricalCircuitAnalysis_Page_48_Chunk970 |
area the same, the resulting resistance would be unchanged. In general, the increase in mass by itself does not necessarily alter the resistance but it may have an impact on the power handling capability of the device. In contrast, if we take that that original mass and reshape it, or just apply the current to a differ... | DCElectricalCircuitAnalysis_Page_49_Chunk971 |
Consequently, the effective resistance in this orientation will be considerably less than that seen in the original. Example 2.12 A certain material has a resistivity of 0.2 ohm-centimeters. Determine the resistance of a piece that is 0.3 cm wide, 0.5 cm high and 4 cm long. A =h×w A =0.5cm×0.3cm A =0.15 cm2 R = ρl A R ... | DCElectricalCircuitAnalysis_Page_50_Chunk972 |
The amount of resistance seen in Example 2.13 would be considered excessive if the item to be connected is something as simple as a loudspeaker, which typically would be around 8 Ω. And while no one would likely need 200 meters of cable to connect a loudspeaker in their home, that sort of distance would be unremarkable... | DCElectricalCircuitAnalysis_Page_51_Chunk973 |
A table of gauge sizes and associated parameters is shown in Figure 2.18. This table assumes copper is being used for the wire. Note that as the diameter of the wire decreases, the amount of resistance for a particular length increases, as expected from Equation 2.11. Using this table we can perform a quick crosscheck ... | DCElectricalCircuitAnalysis_Page_52_Chunk974 |
With the increasing desire to shrink components, modern production designs use surface mounting techniques in place of through-hole construction. At the bottom-center is a small dot which is, in fact, a surface mount resistor capable of ½ watt of power dissipation. A close-up is shown in Figure 2.20. Obviously, these d... | DCElectricalCircuitAnalysis_Page_53_Chunk975 |
Resistors are available in standardized ohmic values and at standardized power ratings (see Appendix A). Along with their resistance value, resistors also have a specified tolerance. This specifies an allowable range of variation of the stated value. For example, a 220 ohm resistor may have a tolerance of 10%. This mea... | DCElectricalCircuitAnalysis_Page_54_Chunk976 |
The tolerance band colors are as follows: For basic parts silver is ±10% and gold is ±5%. If the fourth band is omitted, this indicates a tolerance of ±20%, although it is seldom used in modern designs. For precision parts some colors are reused but follow the color code numerals: Brown is ±1% tolerance and red is ±2% ... | DCElectricalCircuitAnalysis_Page_55_Chunk977 |
An example of a resistor data sheet is shown in Figure 2.25. This data sheet is for a series of surface mount chip resistors. The available tolerance grades range from 0.5% to 20%. Also, for each variant there are two temperature coefficients available with the most stable being 100 ppm/°C (ppm is short for “parts per ... | DCElectricalCircuitAnalysis_Page_56_Chunk978 |
Note how the power dissipation is constant at temperatures at and below 70 °C. This temperature is considered the maximum normal operating temperature for this device and the power dissipation at this temperature is the one quoted in the data sheet. If the device is operated in a warmer environment, the power dissipati... | DCElectricalCircuitAnalysis_Page_57_Chunk979 |
Other Resistive Devices Other Resistive Devices Along with standard fixed resistors, there are several other kinds of resistive devices that have been designed to be sensitive to changes in their environment. Thus, they can serve as sensors because as their resistance changes, it impacts the flow of current and the res... | DCElectricalCircuitAnalysis_Page_58_Chunk980 |
Photoresistor As their name implies, photoresistors are sensitive to changes in light level. They are also called LDRs, short for Light Dependent Resistor. Different materials may be used in their construction, but the most common is cadmium sulfide, CdS. As a consequence, photoresistors are sometimes generically refer... | DCElectricalCircuitAnalysis_Page_59_Chunk981 |
To put the brightness of the light into common terms, 0.01 foot-candles (roughly 0.1 lux) is equivalent to a clear moon-lit evening. At this level, the photoresistor is showing over 1 megohm of resistance. In contrast, 100 foot-candles (roughly 1000 lux) is equivalent to an overcast day (for reference, direct sunlight ... | DCElectricalCircuitAnalysis_Page_60_Chunk982 |
narrow ranges of temperature. For wider ranges, there will be noticeable deviation from a straight line as the curve is logarithmic in nature. A basic NTC thermistor is shown in Figure 2.33. Generic thermistor performance graphs are shown in Figure 2.34 with the idealized straight line response at top and the more real... | DCElectricalCircuitAnalysis_Page_61_Chunk983 |
hundred volts to this. The resulting voltage could be so high that it would damage electronic equipment attached to the outlet. To alleviate this problem, a varistor can be placed across the incoming voltage lines. The vertical break point voltages would be set for a value just over 170 volts, the normal maximum. Under... | DCElectricalCircuitAnalysis_Page_62_Chunk984 |
2.8 Instrumentation and Laboratory 2.8 Instrumentation and Laboratory At this point we need to shift gears and focus on a few practical aspects, the sort of things we might deal with in an electrical laboratory. It is one thing to discuss abstract concepts such as voltage and current, and quite another to deal with the... | DCElectricalCircuitAnalysis_Page_63_Chunk985 |
Schematic Symbols Schematic Symbols Clearly, it would not be practical to create circuit drawings (schematics) using pictures of the actual devices. Instead, we use simple schematic symbols to represent them. There are two widely used schemes: ANSI (American National Standards Institue) and IEC (International Electrote... | DCElectricalCircuitAnalysis_Page_64_Chunk986 |
Measurement – The Digital Multimeter Measurement – The Digital Multimeter Perhaps the most handy measurement device in the electrical laboratory is the digital multimeter, or DMM for short. These handheld devices are used to measure voltage, current and resistance; and depending on model may have other measurement capa... | DCElectricalCircuitAnalysis_Page_65_Chunk987 |
to resolve the measurement to the nearest volt. Indeed, this is so important that some meters have auto-ranging, meaning that they will automatically choose the scale setting to give the best result. The accuracy specification for a DMM is in two parts. The first part is the percent deviation around the measured value.... | DCElectricalCircuitAnalysis_Page_66_Chunk988 |
2.9 Summary 2.9 Summary In this chapter we have examined the basic quantities that make up an electrical circuit. Charge, measured in coulombs, is a characteristic of subatomic particles; protons being positively charged and electrons being negatively charged. Like charges repel and opposite charges attract. The Bohr m... | DCElectricalCircuitAnalysis_Page_67_Chunk989 |
Review Questions Review Questions 1. Describe the Bohr atomic model. 2. How does charge relate to current and voltage? 3. What is the relationship between energy and power? 4. What is the relationship between resistance and conductance? 5. Define efficiency. How does it relate to operating cost? 6. Define count in term... | DCElectricalCircuitAnalysis_Page_68_Chunk990 |
13. How much charge must be transferred in 0.1 seconds in order to achieve a current of 5 amps? 14. How much charge must be transferred in 20 seconds in order to achieve a current of 10 microamps? 15. Determine the resulting voltage if it takes 2 joules to move 10 coulombs of charge. 16. Determine the voltage if 15 jou... | DCElectricalCircuitAnalysis_Page_69_Chunk991 |
32. Assume that a certain piece of material has a resistance of 2 k ohms. Determine the new resistance if the width and height of the piece are doubled and no other parameters are changed. 33. Assume that a certain piece of material has a resistance of 4 ohms. Determine the new resistance if the resistivity is doubled ... | DCElectricalCircuitAnalysis_Page_70_Chunk992 |
46. Determine the value of the resistors pictured in Figure 2.45 (left-to-right: silver-orange-violet-yellow, green-blue-yellow-gold, gold-black-orange- yellow). 47. Determine the maximum and minimum allowed values of the resistors pictured in Figure 2-42. 48. Determine the maximum and minimum allowed values of the res... | DCElectricalCircuitAnalysis_Page_71_Chunk993 |
56. Assume that you can buy standard 60 watt incandescent light bulbs for 50 cents each and that each has an expected life span of 1000 hours. In comparison, you can buy an LED light bulb that produces the same amount of light but only consumes 7 watts. The LED bulbs cost $5.50 each and have an expected life of 20,000 ... | DCElectricalCircuitAnalysis_Page_72_Chunk994 |
Notes Notes ♫♫ ♫♫ 73 | DCElectricalCircuitAnalysis_Page_73_Chunk995 |
3 3 Series Resistive Circuits Series Resistive Circuits 3.0 Chapter Learning Objectives 3.0 Chapter Learning Objectives After completing this chapter, you should be able to: • Describe the differences between conventional current flow and electron flow. • Identify series resistive circuits that include one or more volt... | DCElectricalCircuitAnalysis_Page_74_Chunk996 |
modern concept of an atomic model with electrons and protons did not exist and electricity was conceived of as a sort of fluid. Franklin surmised that the “electrical flow” moved from positive to negative. This idea was accepted and became the conventional view. Today we call this idea conventional current flow. In thi... | DCElectricalCircuitAnalysis_Page_75_Chunk997 |
circuit. In a short circuit, an unintended alternate path for current flow exists and this also can create a malfunction. In the case of our battery and lamp, a short circuit can occur if a piece of wire or metal accidentally fell across the terminals of the lamp. The current would then have a high conductance (i.e., l... | DCElectricalCircuitAnalysis_Page_76_Chunk998 |
even if items D and E in Figure 3.5 have the same numeric value for current, we would not say that they are in series, anymore than we would say that any two people with the same last name would have to be siblings. 3.4 Combining Series Components 3.4 Combining Series Components Typically, a series connection will incl... | DCElectricalCircuitAnalysis_Page_77_Chunk999 |
Example 3.2 Determine the equivalent series value of the voltage sources presented in Figure 3.8. If we use point b as our reference, by inspection the top of the 12 volt source is 12 volts above point b (reminder, the long bar denotes the positive terminal). Also, by inspection, the right side of the 3 volt source (po... | DCElectricalCircuitAnalysis_Page_78_Chunk1000 |
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