AnnouncementsCast of CharactersChargeElectric FieldVoltageVoltage ConventionsVoltage Conventions: NotationSlide 8Voltage Conventions: GroundCurrent: Moving ChargeCurrent Reference DirectionResistancePowerPower: Sign ConventionPower CalculationsCurrent-Voltage RelationshipBasic Circuit ElementsResistorIdeal Voltage SourceWireIdeal Current SourceAirEE 42 Lecture 21/22/2004AnnouncementsProf. Ross’s office hours (in 477 Cory): Tu Th 1:30 PM – 2:30 PMTu Th after class – 6:30 PMadditional appointments welcome!GSI Ashwin Ganesan’s office hours (in 493 Cory):M 4 PM – 5 PM F 10 AM – 11 AMGSI Joe Makin’s office hours (in 493 Cory):To be announcedProblems with Tuesday 11-12 discussion, will be held in 521 Cory next week (1/30/04) only; then likely to be rescheduledEE 42 Lecture 21/22/2004Cast of CharactersFundamental quantitiesChargeCurrent VoltagePowerFundamental concernCurrent-Voltage RelationshipFundamental elementsResistorVoltage SourceCurrent SourceEE 42 Lecture 21/22/2004ChargeYou are already familiar with the idea of charge from chemistry or physics.We say a proton has a positive charge, and an electron has a negative charge.Charge is measured in units called Coulombs, abbreviated C.1 proton = 1.6 x 10-19 C1 electron = -1.6 x 10-19 C1 C is a whole lot of protons!6.25 x 1018 protons in 1 C.EE 42 Lecture 21/22/2004Electric FieldWe know that opposite charges attract each other, and like charges repel.The presence of a charged particle creates an electric field. Other phenomena also create an electric field.The electric field is a lot like gravity. It can point in different directions and have different strength depending on location.+EarthVector fields are like wind maps from your weather forecast.EE 42 Lecture 21/22/2004VoltageIt takes energy to move a proton against the direction of an electric field (just like it takes energy to lift an object off the ground, against gravity).Suppose it takes (positive) energy to move a proton from point a to point b. Then we say point b is at a higher electric potential than point a. The difference in electric potential between two points is called voltage. Voltage, measured in Volts (V) indicates how much energy it takes to move a charge from point to point.ab+EE 42 Lecture 21/22/2004Voltage ConventionsVoltage is always measured between two points (just like distance). We need to specify the “start” and “finish”.We could writesaying that b is 5 Vhigher than a.Or, we could writesaying that a is -5 Vhigher than b.When we put down a + and a – to specify a voltage, it is simply a reference frame. We are not making a statement about which point actually has the higher potential, since the voltage in between can be negative! +ab - 5 V + + - 5 V -EE 42 Lecture 21/22/2004Voltage Conventions: NotationWe can use subscript convention to define a voltage between two labeled points:Remember, this is not saying that the potential at “a” is higher than the potential at “b”. The difference could be negative.We can make up voltages with anynames we wish, as long as we provide a reference frame (+ and -).Here, VRoss is the potential rise from leftto right (or, the potential drop from rightto left, or the right potential minus the left).“Vab” means the potential at “a” minus the potential at “b” (that is, the potential drop from “a” to “b”).VRossabEE 42 Lecture 21/22/2004Examples1.5V1.5V9VABCD What is VAD ?Find V1 and Vx.1.5V1.5V 9VABCDV1VX++--The flat end of the battery is at lower potential than the “bump” end.-1.5 V + -1.5 V + 9 V = 6 VV1 = 1.5 VVX = -6 VEE 42 Lecture 21/22/2004Voltage Conventions: GroundMany times, a common point will be used as the starting (-) point for several voltage measurements. This common point is called common or ground.We may define a voltage at point “a” with respect to ground. This refers to the voltage with + reference at “a” and – reference at ground.Voltages with respect to ground are often denoted using a single subscript:Notice the symbol for ground.Also seen is VaazVzEE 42 Lecture 21/22/2004Current: Moving ChargeAn electric field (or applied energy) can cause charge to move.The amount of charge per time unit moving past a point is called current.Current is measured in Coulombs per second, which are called Amperes (abbreviated A and called Amps for short).Mathematically speaking,where i is current in A, q is charge in C, and t is time in sEven though it is usually electrons that do the moving, current is defined as the flow of positive charge.dtdqi EE 42 Lecture 21/22/2004Current Reference DirectionCurrent also needs a reference frame. To define a current, draw an arrow:This says “the current moving through the device from left to right is 5 A”.We could also say, “the current moving through the device from right to left is -5 A”.Drawing an arrow does not make a statement about the direction the current is actually going. It is just a reference frame. You can draw arrows however you want when you need to solve for currents.5 A-5 AEE 42 Lecture 21/22/2004ResistanceCurrent is due the ability of electrons to break away from atoms and move around.In some materials, like metals, where there are few valence electrons, little energy is needed to break bonds and move an electron.In other materials, a strong electric field (voltage) must be applied to break the bonds. These materials are said to have a higher resistance.Resistance, measured in Ohms (Ω), indicates how much voltage is necessary to create a certain amount of current.EE 42 Lecture 21/22/2004PowerPower is the amount of energy absorbed or generated per unit time. It is the time derivative of energy, and it is measured in Watts (W).The power absorbed (or generated) by a device is equal to the product of the current through the device and the voltage over the device: p = v i where p is power in W, v is voltage in V and i is current in A.Sometimes this equation gives you the power absorbed by the device, and sometimes it provides the power generated by the device.EE 42 Lecture 21/22/2004Power: Sign ConventionWhether “p = v i” provides absorbed power or generated power depends on the relationship between the current and voltage directions.If the
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