EE 42 Lecture 11Spring 2005Ideal wires, Ideal device models, Ideal circuits Ideal models for circuit elements Wires Currents and Voltages Joints Resistors Voltage sources Current sources.EE 42 Lecture 12Spring 2005Cast of Characters Fundamental quantities Charge Current Voltage Power Fundamental concern Current-Voltage Relationship Fundamental elements Resistor Voltage Source Current SourceEE 42 Lecture 13Spring 2005Charge You are already familiar with the idea of chargefrom 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 10-19C1 electron = -1.6 x 10-19C1 C is a whole lot of protons!6.25 x 1018protons in 1 C.EE 42 Lecture 14Spring 2005Electric Field We 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 15Spring 2005Voltage It 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 16Spring 2005Voltage Conventions Voltage 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 17Spring 2005Voltage Conventions: Notation We 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, VFredis 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”).+|VFredabEE 42 Lecture 18Spring 2005Examples1.5V1.5V9VABCDWhat is VAD?Find V1and 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 19Spring 2005Voltage Conventions: Ground Many 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 Vaa+−zVz+−EE 42 Lecture 110Spring 2005Current: Moving Charge An 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 s Even though it is usually (negative) electrons that do the moving, current is defined as the flow of positive charge.dtdqi =EE 42 Lecture 111Spring 2005Water Model for Electric CurrentSince we can’t see electric charges moving in a wire, it is helpful to use the analogy between water flow and charge flow: electric currentflowing in a wire is like water flowing in a pipe.Electric charge (coulombs) is like quantity of water (gallons)Current flow (coulombs per second – amperes) is likewater flow rate past a point (gallons per second)EE 42 Lecture 112Spring 2005Schematic Symbol and Water Model of DC VoltageSource (assumes gravity acting downward)+−+−EE 42 Lecture 113Spring 2005Current Reference Direction Current 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 114Spring 2005Resistance Current flow results from the ability of electrons to break awayfrom atoms and move around in a solid. In some materials such as metals, mobile electrons exist and can move around where an electric field exists to drive them– in such materials the resistance for current flow is low, and these are called good conductors of electricity. In other materials, very few mobile electrons exist and less current flows in the same electric field. These materials are said to have a higher resistance and be poorer conductors. Resistance, measured in ohms (Ω), indicates how much voltage is necessary to create a certain amount of current.EE 42 Lecture 115Spring 2005Resistor (top left), its Schematic Symbol (top right),and Two Water Models of a ResistorSpongeConstrictionEE 42 Lecture 116Spring 2005Power Power 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 with 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
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