EE40 Lecture 2 Josh Hug 6 23 2010 EE40 Summer 2010 Hug 1 Logistical 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 time EE40 Summer 2010 Hug 2 Lab 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 box EE40 Summer 2010 Hug 3 Summary 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 circuit EE40 Summer 2010 Hug 4 Heating 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 EE40 Summer 2010 Hug 5 Intuitive 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 power EE40 Summer 2010 Hug 6 Then 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 EE40 Summer 2010 Hug 7 Toaster 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 temperature EE40 Summer 2010 Hug 8 Continue the Discussion on BSpace Let s get working on some more complicated circuits than this EE40 Summer 2010 Hug 9 Topic 2 Setting Up and Solving Resistive Circuit Models EE40 Summer 2010 Hug 10 Circuit 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 circuit EE40 Summer 2010 Hug 11 Today 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 method EE40 Summer 2010 Hug 12 Circuit Elements There are 5 ideal basic circuit elements in our course voltage source current source resistor inductor capacitor active elements capable of generating electric energy passive elements incapable of generating electric energy 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 circuits EE40 Summer 2010 Hug 13 Electrical 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 mechanical electric Electrical sources can either deliver or absorb power EE40 Summer 2010 Hug 14 The Big Three i v i vs EE40 Summer 2010 v v is Constant current unknown voltage i R Hug 15 Circuit Schematics A circuit schematic is a diagram showing a set of interconnected circuit elements e g Voltage sources Current sources Resistors Each element in the circuit being modeled is represented by a symbol Lines connect the symbols which you can think of as representing zero resistance wires EE40 Summer 2010 Hug 16 Terminology Nodes and Branches Node A point where two or more circuit elements are connected entire wire Can also think of as the vertices of our schematic EE40 Summer 2010 Hug 17 Terminology Nodes and Branches Branch A path that connects exactly two nodes Branch Not a branch EE40 Summer 2010 Hug 18 Terminology Loops A loop is formed by tracing a closed path in a circuit through selected basic circuit elements without passing through any intermediate node more than once Example nodes branches loops 6 nodes 7 branches 3 loops EE40 Summer 2010 Hug 19 Kirchhoff s Laws Kirchhoff s Current Law KCL The algebraic sum of all the currents at any node in a circuit equals zero What goes in must come out Basically law of charge conservation 10 mA 40 mA 50 mA 20 mA EE40 Summer 2010 Hug 20 Using Kirchhoff s Current Law KCL Often we re considering unknown currents and only have reference directions i2 i3 i1 i4 i1 i2 i3 i4 or i1 i2 i3 i4 0 or i1 i2 i3 i4 0 Use reference directions to determine whether reference currents are said to be entering or leaving the node with no concern about actual current directions EE40 Summer 2010 Hug 21 KCL Example 10 mA 5 10 15 i 5 mA 15 mA EE40 Summer 2010 i i 20mA Hug 22 A Major Implication of KCL KCL tells us that all of the elements along a single uninterrupted path carry the same current We say these elements are connected in series Current entering node Current leaving node i1 i2 To be precise by uninterrupted path I mean all branches along
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