Physics 212Physics 212yyLecture 10Lecture 10Td ' C tTd ' C tToday's Concept:Today's Concept:Kirchhoff’s RulesKirchhoff’s RulesKirchhoff s RulesKirchhoff s RulesCircuits with resistors & batteriesCircuits with resistors & batteriesPhysics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 11MusicMusicWho is the Artist?Who is the Artist?Who is the Artist?Who is the Artist?A)A) Norah JonesNorah JonesB)B)Diana KrallDiana KrallB)B)Diana KrallDiana KrallC)C) Jane MonheitJane MonheitD)D) Nina SimoneNina SimoneE)E) Marcia BallMarcia Ball•• A little gender equalityA little gender equalitygqygqy•• Anyone know the connection between Oscar Peterson and Diana Anyone know the connection between Oscar Peterson and Diana KrallKrall??•• Both great Canadian jazz pianists Both great Canadian jazz pianists –– Peterson was one of Peterson was one of Krall’sKrall’sPhysics 212 Lecture 10Physics 212 Lecture 10mentorsmentorsYour Comments:Your Comments:“I usually can't RESIST putting some lecture thoughts down but“I usually can't RESIST putting some lecture thoughts down butI usually can t RESIST putting some lecture thoughts down, but I usually can t RESIST putting some lecture thoughts down, but CURRENTLY I need to DROP in my bed to GAIN some sleep. ;)”CURRENTLY I need to DROP in my bed to GAIN some sleep. ;)”“Resistance Is Futile! All voltages will be assimilated your individualResistance Is Futile! All voltages will be assimilated. your individual currents will be added to our own.”“I thought I had this, now you lost me. I don't I thought I had this, now you lost me. I don't understand how to figure out where the currents understand how to figure out where the currents are going.are going.”“h t fl d di ti h“h t fl d di ti hWe’ll start simply, with We’ll start simply, with the checkpoints, then to the checkpoints, then to a calculationa calculation“how current flows and direction, how many “how current flows and direction, how many currents can there be”currents can there be”““Thi i t lThi i t l“The example with the wire connecting A and B “The example with the wire connecting A and B between the resistors was confusing. I worked it between the resistors was confusing. I worked it out on paper and it seems like there should be a out on paper and it seems like there should be a flow”flow”This is a great example This is a great example –– we’ll do it at the end we’ll do it at the end to make sure of the to make sure of the conceptsconceptsPhysics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 33“Saw an Explosions in the Sky concert after the exam last night. It was “Saw an Explosions in the Sky concert after the exam last night. It was electrifying.”electrifying.”flow.flow.Today’s Plan:Today’s Plan:•• Summary of Summary of Kirchoff’sKirchoff’s rules rules –– these are the key these are the key conceptsconcepts••Example problemExample problem••Example problemExample problem••Review CheckpointsReview Checkpointseew hecpontseew hecpontsPhysics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 44Last TimeRit i iCurrent through is same. Resistors in series:...321RRRReffectiveVoltage drop across is IRiResistors in parallel:...1111321RRRReffectiveVoltage drop across is same.Current through is V/RiResistors in parallel:321effectiveCurrent through is V/RiSolved CircuitsR1R2VR1R2R3VR1234I1234==Physics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 555R4R3New CircuitR1V11R2V2RR33How Can We Solve This One?R1RRHow Can We Solve This One?VR12I1234==V1R2V2RR33THE ANSWER: Kirchhoff’s RulesPhysics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 665THE ANSWER: Kirchhoff s RulesKirchoff’s Voltage Rule0VKirchoff's Voltage Rule states that the sum of the voltage 0iVKirchoff s Voltage Rule states that the sum of the voltage changes caused by any elements (like wires, batteries, and resistors) around a circuit must be zero. WHY?WHY?The potential difference between a point and itself is zero !The potential difference between a point and itself is zero !Physics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 77Kirchoff’s Current RuleIIKirchoff's Current Rule states that the sum of all Kirchoff's Current Rule states that the sum of all in outIIKirchoff s Current Rule states that the sum of all Kirchoff s Current Rule states that the sum of all currents entering any given point in a circuit must equal currents entering any given point in a circuit must equal the sum of all currents leaving the same point. the sum of all currents leaving the same point. WHY? WHY? Electric Charge is ConservedElectric Charge is ConservedElectric Charge is ConservedElectric Charge is ConservedPhysics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 88Checkpoint 1Checkpoint 1How many potentially different currents are there in the circuit shown?How many potentially different currents are there in the circuit shown?A. 3 B. 4 C. 5 D. 6 E. 7“There is only one node, splitting the initial current “There is only one node, splitting the initial current into two separate currents, meaning that there are 3 into two separate currents, meaning that there are 3 separate currents in the circuit.”separate currents in the circuit.”ABCD“The original+ 2 split+1 when they join back “The original+ 2 split+1 when they join back together=4”together=4”“Electric potential decreases in every resistor.”“Electric potential decreases in every resistor.”Physics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 99Checkpoint 1Checkpoint 1How many potentially different currents are there in the circuit shown?How many potentially different currents are there in the circuit shown?I1I3II1I3I2A. 3 B. 4 C. 5 D. 6 E. 7Look at the nodes!Look at the nodes!Top node: Top node: II11flows in, flows in, II22and Iand I33flow out flow out II22and Iand I33flow in,flow in,ABCDBottom node: Bottom node: II11flows out flows out That’s all of them!That’s all of them!Physics 212 Lecture 10, Slide Physics 212 Lecture 10, Slide 1010That s all of them!That s all of them!Checkpoint 2Checkpoint 2In the following circuit, consider the loop abc. The direction of the current through each resistor is indicated by black arrows.DROPgyDROPGAINIf we are to write Kirchoff's voltage equation for this loop in the clockwise direction