Resistors in Series and Parallel

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[...]... electronics in today’s modern world It is currently being offered in a large number of electrical engineering curricula in schools in the United States and throughout the world The number of schools offering an EMC course will no doubt continue to rapidly increase The reasons for EMC having grown in importance at such a rapid pace are due to (1) the increasing speeds and use of digital electronics in today’s... more critical in order to avoid unnecessary costs of EMC suppression measures that are added to bring the products into compliance Frequencies of use even in analog systems are escalating well into the GHz range, and it is difficult to find a product (including washing machines, automobiles, etc.) that doesn’t use digital electronics as a primary factor in that product’s performance These mandatory governmental... feels that this topic is one of the—if not the—most important topic in EMC, and this repositioning is intended to get the reader to begin thinking in terms of signal spectra early on Use of SPICE (simulation program with integrated circuit emphasis) [PSPICE (personal computer SPICE)] in computing signal spectra has now been included in that chapter Chapter 4, Transmission Lines and Signal Integrity, has... getting lost in detail Section 11.5, Diagnostic Tools, is new to the text and reflects the author’s view that it is virtually impossible to design a digital device to pass the regulatory requirements on the first testing It is crucially important in this age of low product cost and reduced development schedules to be able to determine the exact cause of the noncompliance and to determine how to bring... such courses in EMC that was introduced into an EE undergraduate curriculum was organized in the early 1980s at the University of Kentucky by the author It was taught as a senior technical elective and continues to be taught as an elective course there and at the author’s present institution, Mercer University The subject is rapidly increasing in importance, due in part to the increasing use and speeds... contains links to the latest revisions of the regulations But more importantly it contains numerous highly detailed and informative tutorial articles and other references on EMC The author also owes a significant debt of gratitude for this association with and insights gained from working with colleagues in the EMC group at IBM Information Products Division in Lexington, Kentucky (now Lexmark International)... The transition time of the pulse from off to on and vice versa is perhaps the most important factor in determining the spectral content of the pulse Fast (short) transition times generate a wider range of Introduction to Electromagnetic Compatibility, Second Edition, by Clayton R Paul Copyright # 2006 John Wiley & Sons, Inc 1 2 INTRODUCTION TO ELECTROMAGNETIC COMPATIBILITY (EMC) frequencies than do slower... implementing reduced susceptibility of a receptor to noise would be the use of error-correcting codes in a digital receptor Although undesired electromagnetic energy is incident on the receptor, the error-correcting codes may allow the receptor Resistors in Series and Parallel Resistors in Series and Parallel Bởi: OpenStaxCollege Most circuits have more than one component, called a resistor that limits the flow of charge in the circuit A measure of this limit on charge flow is called resistance The simplest combinations of resistors are the series and parallel connections illustrated in [link] The total resistance of a combination of resistors depends on both their individual values and how they are connected (a) A series connection of resistors (b) A parallel connection of resistors Resistors in Series When are resistors in series? Resistors are in series whenever the flow of charge, called the current, must flow through devices sequentially For example, if current flows through a person holding a screwdriver and into the Earth, then R1 in [link](a) could be the resistance of the screwdriver’s shaft, R2 the resistance of its handle, R3 the person’s body resistance, and R4 the resistance of her shoes [link] shows resistors in series connected to a voltage source It seems reasonable that the total resistance is the sum of the individual resistances, considering that the current has to pass through each resistor in sequence (This fact would be an advantage to a person wishing to avoid an electrical shock, who could reduce the current by wearing high-resistance rubber-soled shoes It could be a disadvantage if one of the resistances 1/19 Resistors in Series and Parallel were a faulty high-resistance cord to an appliance that would reduce the operating current.) Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right) To verify that resistances in series indeed add, let us consider the loss of electrical power, called a voltage drop, in each resistor in [link] According to Ohm’s law, the voltage drop, V, across a resistor when a current flows through it is calculated using the equation V = IR, where I equals the current in amps (A) and R is the resistance in ohms ( Ω ) Another way to think of this is that V is the voltage necessary to make a current I flow through a resistance R So the voltage drop across R1 is V1 = IR1, that across R2 is V2 = IR2, and that across R3 is V3 = IR3 The sum of these voltages equals the voltage output of the source; that is, V = V1 + V2 + V3 This equation is based on the conservation of energy and conservation of charge Electrical potential energy can be described by the equation PE=qV , where q is the electric charge and V is the voltage Thus the energy supplied by the source is qV, while that dissipated by the resistors is qV1 + qV2 + qV3 Connections: Conservation Laws The derivations of the expressions for series and parallel resistance are based on the laws of conservation of energy and conservation of charge, which state that total charge and total energy are constant in any process These two laws are directly involved in all electrical phenomena and will be invoked repeatedly to explain both specific effects and the general behavior of electricity These energies must be equal, because there is no other source and no other destination for energy in the circuit Thus, qV = qV1 + qV2 + qV3 The charge q cancels, yielding V = V1 + V2 + V3, as stated (Note that the same amount of charge passes through the 2/19 Resistors in Series and Parallel battery and each resistor in a given amount of time, since there is no capacitance to store charge, there is no place for charge to leak, and charge is conserved.) Now substituting the values for the individual voltages gives V = IR1 + IR2 + IR3 = I(R1 + R2 + R3) Note that for the equivalent single series resistance Rs, we have V = IRs This implies that the total or equivalent series resistance Rs of three resistors is Rs = R1 + R2 + R3 This logic is valid in general for any number of resistors in series; thus, the total resistance Rs of a series connection is Rs = R1 + R2 + R3 + , as proposed Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up Calculating Resistance, Current, Voltage Drop, and Power Dissipation: Analysis of a Series Circuit Suppose the voltage output of the battery in [link] is 12.0 V, and the resistances are R1 = 1.00 Ω , R2 = 6.00 Ω , and R3 = 13.0 Ω (a) What is the total resistance? (b) Find the current (c) Calculate the voltage drop in each resistor, and show these add to equal the voltage output of the source (d) Calculate the power dissipated by each resistor (e) Find the power output of the source, and show that it equals the total power dissipated by the resistors Strategy and Solution for (a) The total resistance is simply the sum of the individual resistances, as given by this equation: Rs = R1 + R2 + R3 = 1.00 Ω + 6.00 Ω + 13.0 Ω = 20.0 Ω Strategy and Solution for (b) 3/19 Resistors in Series and Parallel The current is found using Ohm’s law, V = IR Entering the value of the applied voltage and the total resistance ...TeAm YYePG Digitally signed by TeAm YYePG DN: cn=TeAm YYePG, c=US, o=TeAm YYePG, ou=TeAm YYePG, email=yyepg@msn.com Reason: I attest to the accuracy and integrity of this document Date: 2005.03.13 22:26:27 +08'00' QOS IN PACKET NETWORKS THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE QOS IN PACKET NETWORKS by Kun I. Park, Ph.D. The MITRE Corporation USA Springer eBook ISBN: 0-387-23390-3 Print ISBN: 0-387-23389-X Print ©2005 Springer Science + Business Media, Inc. All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Boston ©2005 Springer Science + Business Media, Inc. Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Dedication For Meyeon and Kyunja. This page intentionally left blank Contents DEDICATION v PREFACE xiii CHAPTER 1 INTRODUCTION 1. 2. 3. NEED FOR QOS D EFINITION OF QOS ORGANIZATION OF THE BOOK 1 1 4 6 CHAPTER 2 BASIC MATHEMATICS FOR QOS 1. PROBABILITY THEORY 9 9 9 1.1 1.2 1.3 RANDOM EXPERIMENTS, OUTCOMES AND EVENTS DEFINITION OF PROBABILITY AXIOMATIC APPROACH TO PROBABILITY 2. RANDOM VARIABLES 10 12 17 17 19 22 24 25 25 25 26 27 30 2.1 2.2 2.3 2.4 2.5 DEFINITION CDF AND PDF MEAN AND VARIANCE THE NORMAL DISTRIBUTION THE POISSON DISTRIBUTION 3. S TOCHASTIC PROCESSES 3.1 3.2 3.3 3.4 DEFINITION OF A STOCHASTIC PROCESS CDF AND PDF OF STOCHASTIC PROCESS AUTOCORRELATION AND CROSS-CORRELATION THE NORMAL PROCESS viii QOS IN PACKET NETWORKS STATISTICAL CHARACTERIZATION OF A STOCHASTIC PROCESS STATIONARITY 3.5 3.6 30 33 33 36 37 37 40 40 41 41 42 43 44 44 48 49 51 52 52 53 57 57 58 3.6.1 3.6.2 STRICT SENSE STATIONARITY (SSS) W IDE SENSE STATIONARITY (WSS) 4. QUEUING THEORY BASICS 4.1 4.2 4.3 4.4 REAL-LIFE EXAMPLES OF QUEUING DEFINITION OF QUEUING SYSTEM BIRTH-DEATH PROCESS MODEL ARRIVAL RATE 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 DEFINITION EMPIRICAL DETERMINATION OF ARRIVAL RATE STATIONARITY ERGODICITY THE POISSON ARRIVAL MARKOV MODULATED POISSON PROCESS (MMPP) 4.5 4.6 4.7 SERVICE RATE UTILIZATION FACTOR QUEUING SYSTEM PERFORMANCE METRICS 4.7.1 LITTLE’S THEOREM 4.8 M/M/1 QUEUE 5. EXERCISES 5.1 5.2 PROBLEMS SOLUTIONS CHAPTER 3 QOS METRICS 1. NETWORK TYPES 1.1 1.2 CONNECTION-ORIENTED PACKET NETWORK SERVICES CONNECTIONLESS PACKET NETWORK SERVICES 61 61 61 63 63 63 64 67 69 69 70 71 72 74 75 76 77 77 79 2. DIGITAL COMMUNICATIONS SYSTEM 2.1 SOURCE CODING 2.1.1 2.1.2 WAVEFORM CODING LINEAR PREDICTIVE CODING (LPC) 2.2 PACKETIZATION 2.2.1 2.2.2 VOICE OVER ATM PACKETIZATION VOICE OVER IP PACKETIZATION 2.3 CHANNEL CODING 2.3.1 2.3.2 2.3.3 INTERLEAVING ERROR CORRECTION MODULATION 3. QOS OF REAL TIME SERVICES 3.1 QUANTIZATION NOISE 3.1.1 3.1.2 SOURCE OF QUANTIZATION NOISE EFFECT OF QUANTIZATION NOISE QOS IN PACKET NETWORKS ix 3.2 DELAY 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 3.2.9 FRAME DELAY PACKETIZATION DELAY INTERLEAVING DELAY ERROR CORRECTION CODING DELAY JITTER BUFFER DELAY PACKET QUEUING DELAY PROPAGATION DELAY EFFECT OF DELAY END-TO-END DELAY OBJECTIVES 3.3 DELAY VARIATION OR “JITTER” 3.4 3.5 SOURCE OF DELAY VARIATION 3.3.1 PACKET LOSS PROBABILITY SUBJECTIVE TESTING 80 80 82 83 84 84 84 86 87 87 BioMed Central Page 1 of 6 (page number not for citation purposes) Journal of NeuroEngineering and Rehabilitation Open Access Research A new electromechanical trainer for sensorimotor rehabilitation of paralysed fingers: A case series in chronic and acute stroke patients Stefan Hesse 1 , H Kuhlmann 1 , J Wilk 1 , C Tomelleri 1 and Stephen GB Kirker* 2 Address: 1 Klinik Berlin, Department Neurological Rehabilitation, Charité – University Medicine Berlin, Germany and 2 Addenbrooke's Rehabilitation Clinic, Cambridge University Hospitals NHS Foundation Trust, Cambridge, CB2 2QQ, UK Email: Stefan Hesse - s.hesse@medicalpark.de; H Kuhlmann - labor@reha-hesse.de; J Wilk - labor@reha-hesse.de; C Tomelleri - labor@reha- hesse.de; Stephen GB Kirker* - stephen.kirker@addenbrookes.nhs.uk * Corresponding author Abstract Background: The functional outcome after stroke is improved by more intensive or sustained therapy. When the affected hand has no functional movement, therapy is mainly passive movements. A novel device for repeating controlled passive movements of paralysed fingers has been developed, which will allow therapists to concentrate on more complicated tasks. A powered cam shaft moves the four fingers in a physiological range of movement. Methods: After refining the training protocol in 2 chronic patients, 8 sub-acute stroke patients were randomised to receive additional therapy with the Finger Trainer for 20 min every work day for four weeks, or the same duration of bimanual group therapy, in addition to their usual rehabilitation. Results: In the chronic patients, there was a sustained reduction in finger and wrist spasticity, but there was no improvement in active movements. In the subacute patients, mean distal Fugl-Meyer score (0–30) increased in the control group from 1.25 to 2.75 (ns) and 0.75 to 6.75 in the treatment group (p < .05). Median Modified Ashworth score increased 0/5 to 2/5 in the control group, but not in the treatment group, 0 to 0. Only one patient, in the treatment group, regained function of the affected hand. No side effects occurred. Conclusion: Treatment with the Finger Trainer was well tolerated in sub-acute & chronic stroke patients, whose abnormal muscle tone improved. In sub-acute stroke patients, the Finger Trainer group showed small improvements in active movement and avoided the increase in tone seen in the control group. This series was too small to demonstrate any effect on functional outcome however. Introduction The annual stroke incidence is approximately 180 patients per 100,000 inhabitants in the industrialized world. About 30% of the surviving patients suffer from a severe upper limb paresis with a non functional hand. The prog- nosis for regaining meaningful hand activity six months after stroke onset is poor [1]: this may partly be because current rehabilitation practice puts more emphasis on the compensatory use of the non-affected upper extremity [2]. Powered machines which can allow prolonged repetition of a controlled movement are a promising way of increas- Published: 4 September 2008 Journal of NeuroEngineering and Rehabilitation 2008, 5:21 doi:10.1186/1743-0003-5-21 Received: 8 February 2008 Accepted: 4 September 2008 This article is available from: http://www.jneuroengrehab.com/content/5/1/21 © 2008 Hesse et al; licensee BioMed Central Ltd. This is an Open Access article BioMed Central Page 1 of 12 (page number not for citation purposes) Journal of Orthopaedic Surgery and Research Open Access Research article Fourier-transform infrared anisotropy in cross and parallel sections of tendon and articular cartilage Nagarajan Ramakrishnan, Yang Xia* and Aruna Bidthanapally Address: Department of Physics and Center for Biomedical Research, Oakland University, Rochester, MI 48309, USA Email: Nagarajan Ramakrishnan - ramakris@oakland.edu; Yang Xia* - xia@oakland.edu; Aruna Bidthanapally - bidthana@oakland.edu * Corresponding author Abstract Background: Fourier Transform Infrared Imaging (FTIRI) is used to investigate the amide anisotropies at different surfaces of a three-dimensional cartilage or tendon block. With the change in the polarization state of the incident infrared light, the resulting anisotropic behavior of the tissue structure is described here. Methods: Thin sections (6 μm thick) were obtained from three different surfaces of the canine tissue blocks and imaged at 6.25 μm pixel resolution. For each section, infrared imaging experiments were repeated thirteen times with the identical parameters except a 15° increment of the analyzer's angle in the 0° – 180° angular space. The anisotropies of amide I and amide II components were studied in order to probe the orientation of the collagen fibrils at different tissue surfaces. Results: For tendon, the anisotropy of amide I and amide II components in parallel sections is comparable to that of regular sections; and tendon's cross sections show distinct, but weak anisotropic behavior for both the amide components. For articular cartilage, parallel sections in the superficial zone have the expected infrared anisotropy that is consistent with that of regular sections. The parallel sections in the radial zone, however, have a nearly isotropic amide II absorption and a distinct amide I anisotropy. Conclusion: From the inconsistency in amide anisotropy between superficial to radial zone in parallel section results, a schematic model is used to explain the origins of these amide anisotropies in cartilage and tendon. Background Tendon is a soft connective tissue that lies in between bones and muscles in animal and human body to transfer the force experienced by muscle to the bone. Tendon therefore has the nature to resist mechanical tension. Depending upon the joint where it is placed, tendon can have different anatomic shapes [1]. Investigation on ten- don has been carried out in various aspects [2-6] such as understanding the shape, structure, mechanical proper- ties, tissue repair and structure-function relationship. Like tendon, articular cartilage is also a soft connective tissue, which covers the end surfaces of bones in synovial joints to distribute compressive loading. While type I collagen fibrils are commonly found in tendon as the highly organ- Published: 6 October 2008 Journal of Orthopaedic Surgery and Research 2008, 3:48 doi:10.1186/1749-799X-3-48 Received: 6 May 2008 Accepted: 6 October 2008 This article is available from: http://www.josr-online.com/content/3/1/48 © 2008 Ramakrishnan et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the SERIES AND PARALLEL CIRCUITS What are "series" and "parallel" circuits? Circuits consisting of just one battery and one load resistance are very simple to analyze, but they are not often found in practical applications. Usually, we find circuits where more than two components are connected together. There are two basic ways in which to connect more than two circuit components: series and parallel. First, an example of a series circuit: Here, we have three resistors (labeled R 1 , R 2 , and R 3 ), connected in a long chain from one terminal of the battery to the other. (It should be noted that the subscript labeling those little numbers to the lower-right of the letter "R" are unrelated to the resistor values in ohms. They serve only to identify one resistor from another.) The defining characteristic of a series circuit is that there is only one path for electrons to flow. In this circuit the electrons flow in a counter- clockwise direction, from point 4 to point 3 to point 2 to point 1 and back around to 4. Now, let's look at the other type of circuit, a parallel configuration: Again, we have three resistors, but this time they form more than one continuous path for electrons to flow. There's one path from 8 to 7 to 2 to 1 and back to 8 again. There's another from 8 to 7 to 6 to 3 to 2 to 1 and back to 8 again. And then there's a third path from 8 to 7 to 6 to 5 to 4 to 3 to 2 to 1 and back to 8 again. Each individual path (through R 1 , R 2 , and R 3 ) is called a branch. The defining characteristic of a parallel circuit is that all components are connected between the same set of electrically common points. Looking at the schematic diagram, we see that points 1, 2, 3, and 4 are all electrically common. So are points 8, 7, 6, and 5. Note that all resistors as well as the battery are connected between these two sets of points. And, of course, the complexity doesn't stop at simple series and parallel either! We can have circuits that are a combination of series and parallel, too: In this circuit, we have two loops for electrons to flow through: one from 6 to 5 to 2 to 1 and back to 6 again, and another from 6 to 5 to 4 to 3 to 2 to 1 and back to 6 again. Notice how both current paths go through R 1 (from point 2 to point 1). In this configuration, we'd say that R 2 and R 3 are in parallel with each other, while R 1 is in series with the parallel combination of R 2 and R 3 . This is just a preview of things to come. Don't worry! We'll explore all these circuit configurations in detail, one at a time! The basic idea of a "series" connection is that components are connected end-to-end in a line to form a single path for electrons to flow: The basic idea of a "parallel" connection, on the other hand, is that all components are connected across each other's leads. In a purely parallel circuit, there are never more than two sets of electrically common points, no matter how many components are connected. There are many paths for electrons to flow, but only one voltage across all components: Series and parallel resistor configurations have very different electrical properties. We'll explore the properties of each configuration in the sections to come. • REVIEW: • In a series circuit, all components are connected end-to-end, forming a single path for electrons to flow. • In a parallel circuit, all components are connected across each other, forming exactly two sets of electrically common points. • A "branch" in a parallel circuit is a path for electric current formed by one of the load components (such as a resistor). Simple series circuits Let's start with a series circuit consisting of three resistors and a single battery: The first principle to understand about series circuits is that the amount of current is the same through any component in the circuit. This is because there ... in series Individual resistors in series not get the total source voltage, but divide it Resistors in Parallel [link] shows resistors in parallel, wired to a voltage source Resistors are in parallel. .. both the currents and powers in parallel connections are greater than for the same devices in series 9/19 Resistors in Series and Parallel Major Features of Resistors in Parallel Parallel resistance... drop in the wires and reduces the voltage across the light Check Your Understanding 13/19 Resistors in Series and Parallel Can any arbitrary combination of resistors be broken down into series and