EE40 Lecture 2 Josh HugLogistical Changes and NotesLab/HW Deadlines and DatesSummary From Last TimeHeating ElementsIntuitive AnswerThen Why Don’t Toasters and Ovens Have Thicker Elements?Toaster Element Design GoalsContinue the Discussion on BSpaceTopic 2Circuit SchematicsTodayCircuit ElementsElectrical SourcesThe Big ThreeSlide 16Terminology: Nodes and BranchesSlide 18Terminology: LoopsKirchhoff’s LawsUsing Kirchhoff’s Current Law (KCL)KCL ExampleA Major Implication of KCLGeneralization of KCLGeneralized KCL ExamplesSlide 26A Major Implication of KVLKVL ExampleAn Underlying Assumption of KVLMini-SummaryNonsense SchematicsVerifying KCL and KVLSlide 33Slide 34iClicker #1On to Solving CircuitsSolving Circuits (naïve way)Slide 38Example: KCL and KVL applied to circuitsBigger exampleiClicker ProofThere are better ways to solve circuitsVoltage DividerVoltage Divider ExampleCurrent DividerCurrent Divider ExampleCircuit SimplificationCircuit Simplification Example Combining Voltage SourcesExample – Combining ResistancesSource CombinationsResistor CombinationsAlgorithm For Solving By Combining Circuit ElementsUsing Equivalent ResistancesSlide 54Slide 55Slide 56Slide 57Slide 58Working BackwardsWorking Backwards ExampleSlide 61Slide 62Slide 63Slide 64Slide 65Equivalent Resistance Between Two TerminalsSlide 67Can Pick Other Pairs of TerminalsSlide 69The Node Voltage TechniqueDefinition: Node Voltage and Ground NodeNode Voltage ExampleiClicker #4: Node VoltagesRelationship: Node and Branch VoltagesWhy are Node Voltages Easier to Find?(Almost) The Node Voltage MethodWhat about Voltage Sources?Full Node Voltage MethodNext ClassQuick iClicker QuestionExtra SlidesSummary (part one)Summary (part two)Short Circuit and Open CircuitIdeal Voltage SourceIdeal Current Source1EE40 Summer 2010HugEE40Lecture 2Josh Hug6/23/20102EE40 Summer 2010HugLogistical Changes and Notes•Friday Lunch is now Monday lunch (starting next Monday)–Email me by Saturday evening if you’d like to come: JHUG aat eecs.berkeley.edu•My office hours will be Wednesday and Friday, 11:00-12:00, room TBA•Google calendar with important dates now online•Did anybody not get my email sent out Monday (that said no discussion yesterday)?•Will curate the reading a little more carefully next time3EE40 Summer 2010HugLab/HW Deadlines and Dates•Discussions start Friday•Labs start next Tuesday•HW0 Due Today•Homework 1 will be posted by 3PM, due Friday at 5 PM•Tuesday homeworks now due at 2PM, not 5PM in Cory 240 HW box4EE40 Summer 2010HugSummary From Last Time•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•Circuit Schematics–Networks of ideal basic circuit elements–Equivalent to a set of algebraic equations–Solution provides voltage and current through all elements of the circuit5EE40 Summer 2010HugHeating Elements•Last time we posed a question:–Given a fixed voltage, should we pick a thick or thin wire to maximize heat output–Note that resistance decreases with wire radius•Most of you said that we’d want a thin wire to maximize heat output, why is that?–Believed that low resistance wire would give the most heat?–Didn’t believe me that thick wire has low resistance?–General intuition?6EE40 Summer 2010HugIntuitive Answer•I blasted through some equations and said “thicker is better, Q.E.D.”, but I’m not sure you guys were convinced, so here’s another view•You can think of a big thick wire as a bunch of small wires connected to a source–The thicker the wire, the more little wires–Since they are all connected directly to the source, they all have same voltage and current and hence power–Adding more wires gives us more total current flow (same voltage), and hence more power7EE40 Summer 2010HugThen Why Don’t Toasters and Ovens Have Thicker Elements?•Thicker elements mean hotter elements–Will ultimately reach higher max temperature–Will get to maximum faster [see message board after 6 or 7 PM tonight for why]•Last time, you guys asked “Well if thickness gives you more heat, why aren’t toaster elements thicker?”•The answer is most likely:–More burned toast. Nobody likes burned toast.8EE40 Summer 2010HugToaster Element Design Goals•Make heating element that can:–Can reach a high temperature, but not too high–Can reach that temperature quickly–Isn’t quickly oxidized into oblivion by high temperature–Doesn’t cost very much money–Will not melt at desired temperature•Nichrome is a typical metal alloy in elements:–Low oxidation–High resistance (so normal gauge wire will not draw too much power and get too hot)•Size was tweaked to attain desired temperature9EE40 Summer 2010HugContinue the Discussion on BSpace•Let’s get working on some more complicated circuits than this:10EE40 Summer 2010HugTopic 2Setting Up and Solving Resistive Circuit Models11EE40 Summer 2010HugCircuit Schematics•Many circuit elements can be approximated as simple ideal two terminal devices or ideal basic circuit elements•These elements can be combined into circuit schematics•Circuit schematics can be converted into algebraic equations•These algebraic equations can be solved, giving voltage and current through any element of the circuit12EE40 Summer 2010HugToday•We’ll enumerate the types of ideal basic circuit elements•We’ll more carefully define a circuit schematic•We’ll discuss some basic techniques for analyzing circuit schematics–Kirchoff’s voltage and current laws–Current and voltage divider–Node voltage method13EE40 Summer 2010HugCircuit Elements•There are 5 ideal basic circuit elements (in our course):–voltage source–current source–resistor–inductor–capacitor•Many practical systems can be modeled with just sources and resistors•The basic analytical techniques for solving circuits with inductors and capacitors are the same as those for resistive circuitsactive elements, capable ofgenerating electric energypassive elements, incapable ofgenerating electric energy14EE40 Summer 2010HugElectrical Sources•An electrical source is a device that is capable of converting non-electric energy to electric energy and vice versa.Examples:–battery: chemical electric–dynamo (generator/motor):
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