Announcements Lectures will be in 4 LeConte beginning Friday 8 29 Additional discussion TA Dennis Chang Sections 101 105 Office hours Mo 2 3 PM Th 5 6 PM Lab sections begin Tuesday 9 2 Read Experiment 1 online Download Pre Lab 1 and complete it before going to the lab 140 Cory Discussion sections begin Tuesday 9 2 EECS40 Fall 2003 Lecture 2 Slide 1 Prof King Lecture 2 OUTLINE Introduction to circuit analysis Electrical quantities Charge Current Voltage Power The ideal basic circuit element Sign conventions Reading Chapter 1 EECS40 Fall 2003 Lecture 2 Slide 2 Prof King 1 Electrical System Design Process 1 Identify system performance requirements design specifications 2 Conceive of approach design concept 3 Develop an electric circuit model mathematical model that approximates the behavior of an actual electrical system using ideal circuit components mathematical models of actual electrical components 4 Build and test a physical prototype EECS40 Fall 2003 Lecture 2 Slide 3 Prof King Circuit Analysis Circuit analysis is used to predict the behavior of the electric circuit and plays a key role in the design process Comparison between desired behavior design specifications and predicted behavior from circuit analysis leads to refinements in design In order to analyze an electric circuit we need to know the behavior of each ideal circuit element in terms of its voltage and current and the constraints imposed by interconnecting the various elements EECS40 Fall 2003 Lecture 2 Slide 4 Prof King 2 Electric Charge Macroscopically most matter is electrically neutral most of the time Exceptions clouds in a thunderstorm people on carpets in dry weather plates of a charged capacitor etc Microscopically matter is full of electric charges Electric charge exists in discrete quantities integral multiples of the electronic charge 1 6 x 10 19 coulombs Electrical effects are due to separation of charge electric force voltage charges in motion electric flow current EECS40 Fall 2003 Lecture 2 Slide 5 Prof King Classification of Materials Solids in which all electrons are tightly bound to atoms are insulators Solids in which the outermost atomic electrons are free to move around are metals Metals typically have 1 free electron per atom 5 1022 free electrons per cubic cm Electrons in semiconductors are not tightly bound and can be easily promoted to a free state insulators semiconductors metals Quartz SiO2 Si GaAs Al Cu excellent conductors dielectric materials EECS40 Fall 2003 Lecture 2 Slide 6 Prof King 3 Electric Current Definition rate of positive charge flow Symbol i Units Coulombs per second Amperes A i dq dt where q charge in Coulombs t time in seconds Note Current has polarity EECS40 Fall 2003 Lecture 2 Slide 7 Prof King Electric Current Examples 1 105 positively charged particles each with charge 1 6 10 19 C flow to the right x direction every nanosecond 2 105 electrons flow to the right x direction every microsecond EECS40 Fall 2003 Lecture 2 Slide 8 Prof King 4 Current Density Definition rate of positive charge flow per unit area Symbol J Units A cm2 Example 1 Semiconductor with 1018 free electrons per cm3 Wire attached to end m 2c C1 1 cm C2 10 cm X Suppose we force a current of 1 A to flow from C1 to C2 Electron flow is in x direction electrons 1C sec 6 25 1018 1 6 10 19 C electron sec EECS40 Fall 2003 Lecture 2 Slide 9 Prof King Current Density Example cont d The current density in the semiconductor is Example 2 Typical dimensions of integrated circuit components are in the range of 1 m What is the current density in a wire with 1 m area carrying 5 mA EECS40 Fall 2003 Lecture 2 Slide 10 Prof King 5 Electric Potential Voltage Definition energy per unit charge Symbol v Units Volts V v dw dq where w energy in Joules q charge in Coulombs Note Potential is always referenced to some point a b EECS40 Fall 2003 Subscript convention vab means the potential at a minus the potential at b vab va vb Lecture 2 Slide 11 Prof King Electric Power Definition transfer of energy per unit time Symbol p Units Joules per second Watts W p dw dt dw dq dq dt vi Concept As a positive charge q moves through a drop in voltage v it loses energy energy change qv rate is proportional to charges sec EECS40 Fall 2003 Lecture 2 Slide 12 Prof King 6 The Ideal Basic Circuit Element i v Polarity reference for voltage can be indicated by plus and minus signs Reference direction for the current is indicated by an arrow Attributes Two terminals points of connection Mathematically described in terms of current and or voltage Cannot be subdivided into other elements EECS40 Fall 2003 Lecture 2 Slide 13 Prof King A Note about Reference Directions A problem like Find the current or Find the voltage is always accompanied by a definition of the direction i v In this case if the current turns out to be 1 mA flowing to the left we would say i 1 mA In order to perform circuit analysis to determine the voltages and currents in an electric circuit you need to specify reference directions There is no need to guess the reference direction so that the answers come out positive however EECS40 Fall 2003 Lecture 2 Slide 14 Prof King 7 Sign Convention Example Suppose you have an unlabelled battery and you measure its voltage with a digital voltmeter DVM It will tell you the magnitude and sign of the voltage a With this circuit you are measuring vab 1 401 The DVM indicates 1 401 so va is lower than vb by 1 401 V DVM b Which is the positive battery terminal Note that we have used the ground symbol for the reference node on the DVM Often it is labeled C for common EECS40 Fall 2003 Lecture 2 Slide 15 Prof King Another Example Find vab vca vcb a 2V c 1 V vcd b vbd d Note that the labeling convention has nothing to do with whether or not v is positive or negative EECS40 Fall 2003 Lecture 2 Slide 16 Prof King 8 Sign Convention for Power Passive sign convention p vi p vi i i i v v v i v If p 0 power is being delivered to the box If p 0 power is being extracted from the box EECS40 Fall 2003 Lecture 2 Slide 17 Prof King Summary Current rate of charge flow Voltage energy per unit charge created by charge separation Power energy per unit time Ideal Basic Circuit Element 2 terminal component that cannot be sub divided described mathematically in terms of its terminal voltage and current Passive sign convention Reference direction for current through the element is in the direction of the reference voltage drop across the element EECS40 Fall 2003 Lecture 2 Slide
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