EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross Lecture 2 Cast of Characters Basic quantities Charge Current Voltage Power Basic elements Resistor Voltage Source Current Source Capacitor Inductor EECS 40 Spring 2003 Lecture 2 CHARGE Most 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 RELATIONSHIP EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross MOVING CHARGE Measuring Charge Charge is measured in Coulombs An electron has charge 1 6 x 10 19 C Charge flow Current Charge storage Energy Definition of Current 1 Ampere flow of 1 Coulomb per second i A dq C where q is the charge in Coulombs dt S and t is the time in seconds Current is defined as flow of positive charge EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross VOLTAGE Voltage is the difference in electric potential between two points a Vab b 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 or draw a and indicating polarity Vx EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross REFERENCE DIRECTIONS A question like Find the current or Find the voltage is always accompanied by a definition of the direction V I In this example if the current turned out to be 1mA but flowing to the left we would merely say I 1mA 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 EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross SIGN CONVENTIONS Suppose you have an unlabelled battery and you measure its voltage with a digital voltmeter It will tell you magnitude and sign of the voltage a 1 401 DVM b b DVM a With this circuit you are measuring Va Vb or Vab DVM indicates 1 401 so Va Vb by 1 401 V Which is the positive battery terminal Note that we have used ground Now you symbol for reference node on make a DVM Often it is labeled C or change common What would this circuit measure EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross SIGN CONVENTIONS Example 1 B A C 1 5V 1 5V D 9V What is VAD Find V1 and Vx Example 2 B A 1 5V C 1 5V D 9V V1 VX EECS 40 Spring 2003 Lecture 2 POWER IN ELECTRIC CIRCUITS Power Transfer of energy per unit time Joules per second Watts In falling through a potential drop V 0 a positive charge q gains energy Potential energy change qV for each charge q Power P V dq dt VI P V I Volt Amps Volts Coulombs sec Joules sec Watts Circuit 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 element EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W 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 I This box represents the rest of the circuit Here I and V are associated V Circuit element 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 EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EXAMPLES OF CALCULATING POWER Find the power absorbed by each element a 0 5 mA b Element Element Element 2V 3 mA 3V Element c 2 5 mA 1V 1V EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross RESISTOR I With the associated current and voltage relationship shown we get Ohm s law v R V IR where R is the resistance in Ohms In reality R is never negative resistor always absorbs power If you know resistor current you know resistor voltage and vice versa EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross WIRE AND AIR In class we will mostly assume that wire is a perfect conductor In reality wire does have a very small resistance Wire No voltage drop all points on wire at same potential Current does flow defined by other circuit elements We will also assume that air is a perfect insulator no arcing Air No current flow May carry voltage defined by other circuit elements There can be a nonzero voltage over a hole in a circuit EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross IDEAL VOLTAGE SOURCE Symbol The ideal voltage source explicitly defines the voltage between its terminals Vs Constant DC voltage source Vs 5 V Time Varying voltage source Vs 10 sin t V The ideal voltage source has known voltage but unknown current The current through the voltage source is defined by the rest of the circuit to which the source is attached You cannot assume that the current is zero EECS 40 Spring 2003 Lecture 2 W G Oldham and S Ross REALISTIC VOLTAGE SOURCE Rs Vs IRs a In reality the voltage across a voltage source decreases slightly as more current is drawn Real voltage sources can be thought …
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