EGR 1980 Recitation Worksheet 1 Introduction to Circuit Analysis H Griffith 17 January 2014 Introduction In class we reviewed various concepts associated with the meaning and operations of rational numbers Recall that a rational number is simply any number than can be written as a ratio of two integers A more common term for a rational number is a fraction By reviewing the processes of reducing fractions to simplest form and ordering fractions we also reviewed the concepts of the least common multiple LCM and greatest common factor GCF Today we ll examine how these concepts can be used in the context of electrical circuit analysis Circuit Analysis Basics Circuit analysis is one of the most fundamental skills that you will develop as an engineer In circuit analysis electrical electronic systems are described by representing the various components of the system in terms of ideal circuit components Once the modeling has been complete the resulting electrical circuit is represented graphically in the form an electrical schematic For example consider devices such as hair dryers electric stove burners or electric candle warmers Each of these devices uses energy supplied to it by an electrical source of energy in order to generate heat for some useful purpose drying hair cooking food etc Note that most of these components also use the energy supplied by the source in order to achieve additional functionality such as providing appropriate air flow in a hair dryer providing electronic displays controls on a stove etc In each case the energy supplied by the electrical source which is converted to heat by the system is not maintained by the system ie it is lost to the surrounding environment Therefore we say that the system consumes the energy that was provided to it thereby serving as an electrical load In general electrical loads may also store energy in addition to consuming it However for purposes of introduction we will focus solely on those loads which translate supplied electrical energy into heat which is lost from the electrical system In circuit analysis any component of a system which consumes energy supplied to it is referred to as a resistor Schematically a resistor is represented as follows Note that the above figure consists of three parts 1 the schematic symbol for the resistor 2 the reference designator R1 and 3 the rated component value 1 Another important point which you should notice from the above schematic symbol is that a resistor has two distinct points of connection which are referred to as terminals or nodes It is these two terminals which allows for the wiring of complete circuits closed loops of components which support the continuous flow of electricity Although we will discuss this concept in more detail in upcoming weeks for now you should be familiar with the fact that the unit of electrical resistance is Ohms which is abbreviated by the capital Greek letter pronounced in English as omega Physically resistance describes how the flow of electrical charge ie electricity referred to as electrical current is impeded opposed by a particular component due to the imperfect conductivity It is important to note that all electronic systems convert some of the energy supplied to them by their source into heat regardless of whether or not that is their intention Therefore the electrical model of any system will contain resistance in order to account for this inefficiency You Try Think of an electronic system component which converts a large portion of the energy supplied to it to heat even though this is not the system devices intention Formation of Electrical Networks In practice it is common for a single electrical source to supply power to many different loads This may be achieved by configuring electrical loads in two configurations 1 series and 2 parallel In a series connection electricity flows continuously ie no branching between the two components A visual representation of a series connection of two resistors is shown in the schematic below Note that in the above configuration the two components are connected vertically in series However schematics may also show components connected in series in a horizontal configuration ie In both of the two above configurations the two electrical components are interconnected by a straight line between a terminal node of each component This is referred to by many different names in electricity such as an interconnection or jumper In circuit analysis we assume that any interconnection has a negligible effect on the overall resistance of the network Note that in a series connection of loads a break in the electrical connectivity between any components results in an incomplete circuit referred to as an open circuit which does not support the continuous flow of electricity A network containing a fault which results in an open circuit is said to have infinite resistance Using shorthand the series connection of two resistors is designated as the sum of their reference designators Therefore the above series connection may be represented in shorthand as R1 R2 As we will see later the appearance of the above shorthand notation is representative of one of the key properties of series networks In a parallel configuration all components are subjected to the same source of electricity more formally we say that all components in the configuration have the same voltage measured across their terminals We will define the concept of voltage and current more formally in next week s recitation worksheet Schematically a parallel connection is represented as follows note that both the vertical and horizontal configurations are shown Using shorthand the parallel connection of two resistors is designated by separating the reference designators by two vertical lines Therefore the above connection may be represented in shorthand as R1 R2 Note that in a parallel connection the various pathways by which electricity may travel is oftentimes referred to as a branch For example each of the above networks has two branches each consisting solely of a single resistive component One of the most fundamental concepts to understand about parallel networks is that the electricity flowing in each branch is NOT NECESSARILY the SAME in contrast for a series connection the electricity flowing in each component along the series connection IS THE SAME In fact the amount of electricity flowing in each particular branch is inversely related to the resistance of each