EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossLecture 2Cast of Characters• Basic quantities–Charge– Current – Voltage–Power• Basic elements–Resistor– Voltage Source– Current Source– Capacitor– InductorEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossCHARGEMost matter is macroscopically electrically neutral most of the time. Exceptions: clouds in thunderstorm, people on carpets in dry weather, plates of a charged capacitor…Microscopically, of course, matter is full of charges.The application of an electric field causes charges to drift, or move. Electrons will naturally move from lower electric potential to higher potential.The rate at which the charges move depends on the magnitude of the potential difference and the properties of the matter.CURRENT – VOLTAGE RELATIONSHIPEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossMOVING CHARGECharge flow ➠ Current Charge storage ➠ EnergyDefinition of Currentwhere q is the charge in Coulombs and t is the time in seconds==SCdtdq(A)isecondperCoulomb1offlow 1 AmpereCharge is measured in Coulombs. An electron has charge -1.6 x 10-19C.Measuring ChargeCurrent is defined as flow of positive charge!EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossVOLTAGEab+−Vab“Vab” means the potential at a minus the potential at b.Potential is always defined by two points.We can use the subscript convention above to define a voltage between two labeled points (e. g. a and b above),Voltage is the difference in electric potential between two points.+|Vxor draw a + and – indicating polarity.EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossREFERENCE DIRECTIONSA question like “Find the current” or “Find the voltage” is always accompanied by a definition of the direction: To solve circuits, you may need to specify reference directions for currents. But there is no need to guess the reference direction so that the answer comes out positive….Your guess won’t affect what the charge carriers are doing! In this example if the current turned out to be 1mA, but flowing to the left we would merely say I = -1mA.I+|VEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossSuppose you have an unlabelled battery and you measure its voltage with a digital voltmeter. It will tell you magnitude and sign of the voltage.SIGN CONVENTIONSWith this circuit, you are measuring(or ). DVM indicates −1.401, so by 1.401 V. Which is the positive battery terminal?−1.401DVM+abbVaV −abVbVaV < ?DVM+baNow you make a change. What would this circuit measure?Note that we have used “ground” symbol ( ) for reference node on DVM. Often it is labeled “C” or “common.”EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossSIGN CONVENTIONSExample 1+ ++1.5V1.5V9VABCDWhat is VAD?Example 2Find V1and Vx.+++1.5V1.5V 9VABCDV1VX++--EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossPOWER IN ELECTRIC CIRCUITSPower: Transfer of energy per unit time (Joules per second = Watts)In falling through a potential drop V>0, a positive charge q gains energyPotential energy change = qV for each charge qPower = P = V (dq/dt) = VIP = V × I Volt × Amps = Volts × Coulombs/sec = Joules/sec = WattsCircuit elements can absorb power from or release power to the circuit.How to keep the signs straight for absorbing and releasing power?Memorize our convention:+ Power ≡ absorbed into element− Power ≡ delivered from elementEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. Ross“ASSOCIATED REFERENCE DIRECTIONS”If an element is absorbing power, positive charge will flow from higher potential to lower potential—over a voltage drop.P = VI > 0 corresponds to the element absorbing power if the definitions of I and V are “associated”.How can a circuit element absorb power?By converting electrical energy into heat (resistors in toasters); light (light bulbs); acoustic energy (speakers); by storing energy (charging a battery).VThis box representsthe rest of the circuit ICircuit element+-Here, I and V are “associated”EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEXAMPLES OF CALCULATING POWERFind the power absorbed by each element. Element :Element :Element :Element : −+−+2V1 V−+abc3V−+1 V2.5 mA0.5 mA3 mAEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossRESISTOR−+vIRWith the “associated” currentand voltage relationship shown,we get Ohm’s law:V = I Rwhere R is the resistance in Ohms.In reality, R is never negative => resistor always absorbs powerIf you know resistor current, you know resistor voltageand vice-versa.EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossWIRE AND AIRIn class, we will mostly assume that wire is a perfect conductor.Wire: No voltage drop, all points on wire at same potentialCurrent does flow, defined by other circuit elementsIn reality, wire does have a very small resistance.We will also assume that air is a perfect insulator (no “arcing”).Air: No current flowMay carry voltage, defined by other circuit elementsThere can be a nonzero voltage over a “hole” in a circuit!EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossIDEAL VOLTAGE SOURCESymbol++++−−−−VsThe ideal voltage source explicitly definesthe voltage between its terminals.Constant (DC) voltage source: Vs= 5 VTime-Varying voltage source: Vs= 10 sin(t) VThe ideal voltage source has known voltage, but unknown current!The current through the voltage source is defined by the rest ofthe circuit to which the source is attached.You cannot assume that the current is zero!EECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossEECS 40 Spring 2003 Lecture 2W. G. Oldham and S. RossREALISTIC VOLTAGE SOURCERsVsba+_ IIn reality, the voltage across a voltage source
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