Introduction to Electric Circuits PDF

Introduction to Electric Circuits PART 1 1️⃣ INTRODUCTION Electrical elements may be connected together to form a circuit. Engineers use electric circuit to solve problems tha...

Introduction to Electric Circuits PART 1 1️⃣ INTRODUCTION Electrical elements may be connected together to form a circuit. Engineers use electric circuit to solve problems that are important to modern society. In particular: 1. Electric circuits are used in the generation, transmission, and consumption of electric power and energy. 2. Electric circuits are used in the encoding, decoding, storage, retrieval, transmission, and processing of information. The behavior of an electric circuit depends on the behaviors of the individual circuit elements that comprise the circuit. Of course, different types of circuit elements behave differently. The equations that describe the behaviors of the various types of circuit elements are called the constitutive equations. Frequently, the constitutive equations describe a relationship between the current and voltage of the element. Ohm’s law is a well-known example of a constitutive equation and you will learn about it on Circuit Elements section. Introduction to Electric Circuits 1  2️⃣ OBJECTIVES After completion of this course, you should be able to: ❖ Represent the current and voltage of an electric circuit element, paying particular attention to the reference direction of the current and to the reference direction or polarity of the voltage. ❖ Calculate the power and energy supplied or received by a circuit element. ❖ Use the passive convention to determine whether the product of the current and voltage of a circuit element is the power supplied by that element or the power received by the element. ❖ Use scientific notation to represent electrical quantities with a wide range of magnitudes. ❖ Investigate the behavior of several common types of circuit element. Introduction to Electric Circuits 2  3️⃣ ELECTRIC CIRCUIT VARIABLES Mobility and flexibility are two outstanding characteristics of electricity when compared with other power sources. Electrical energy can be moved to any point along a couple of wires and can also be converted to light, heat, and motion. An electrical circuit or electric network is an interconnection of electrical elements linked together in a closed path so that an electric current may flow continuously. You should always remember that theoretically, current would not be able to flow if the path is incomplete. Figure 1.1 shows a simple electric circuit which consists of three elements: battery, wires, and a lamp. Figure 1.2 shows a simple circuit diagram of Figure 1.1, representing the lamp as a load resistor. You will see here that each element may be represented by a general two- terminal electrical element, as shown in Figure 1.3 VOLTAGE The voltage across an element is the work (energy) required to move a unit positive charge from the negative terminal to the positive terminal. The unit of voltage is the volt, V. 1 𝑉=1 𝐽/𝐶 (Joule/Coulomb) Introduction to Electric Circuits 3  Figure 1.4 shows the notation we use to describe a voltage. There are two parts to this notation: a value (perhaps represented by a variable name) and an assigned direction. The value of a voltage may be positive or negative. The direction of a voltage is given by its polarities (+,-). As a matter of vocabulary, we say that a voltage exists across an element. It shows that there are two ways to label the voltage across an element. The voltage 𝑣𝑏𝑎 is proportional to the work required to move a positive charge from terminal a to terminal b. On the other hand, the voltage 𝑣𝑎𝑏 is proportional to the work required to move a positive charge from terminal b to terminal a. We sometimes read 𝑣𝑏𝑎 as “the voltage at terminal b with respect to terminal a.” Similarly, 𝑣𝑎𝑏 can be read as “the voltage at terminal a with respect to terminal b.” Alternatively, we sometimes say that 𝑣𝑏𝑎 is the voltage drop from terminal a to terminal b. The voltages 𝑣𝑎𝑏 and 𝑣𝑏𝑎 are similar but different. They have the same magnitude but different polarities. This means that vab = −vba Introduction to Electric Circuits 4  CURRENT Electron drift constitutes an electric current flow. When a conducting wire (consisting of several atoms) is connected to a battery (a source of electromotive force), the charges are compelled to move; positive charges move in one direction while negative charges move in the opposite direction. This motion of charges creates an electric current. You can simply say that current is the flow of electrons. You might have previously encountered circuit analysis and have observed that in solving unknown circuit parameters, you assume that current flows from the positive terminal of the voltage source, going to the network, and then back to the negative terminal. Does this mean that positive charges move through the circuit? The answer is no. Benjamin Franklin, an American scientist, and inventor introduced this convention (i.e., current is the net flow of positive charges) and it is universally accepted and used. Charge (𝑸) is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). It is the quantity that is responsible for the electric phenomena. 1C = 6.24x101 8e− . Electric Current is the time rate of flow of electric charge past a given point and can be expressed as 𝑖=𝑑𝑞/𝑑𝑡, measured in amperes (𝐴). 1 𝐴=1 𝐶/𝑠 (coulomb per second). Figure 1.5 shows the notation that we use to describe a current. There are two parts to this notation: a value (perhaps represented by a variable name) and an assigned direction. As a matter of vocabulary, we say that a current exists in or through an element. It also shows that there are two ways to assign the direction of the current through an element. The current 𝑖1 is the Introduction to Electric Circuits 5  rate of flow of electric charge from terminal a to terminal b. On the other hand, the current 𝑖2 is the flow of electric charge from terminal b to terminal a. The currents 𝑖1 and 𝑖2 are similar but different. They are the same magnitude but have different directions. Therefore, 𝒊𝟐=−𝒊𝟏 We always associate an arrow with a current to denote its direction. A complete description of current requires both a value (which can be positive or negative) and a direction (indicated by an arrow). We can represent a current flowing through an element by a constant 𝑰 if it is constant, meaning, time does not affect its magnitude. Figure 1.6 shows a constant current. This type is called direct current (dc). A direct current (dc) is a current that remains constant with time. Introduction to Electric Circuits 6  Note: throughout this course, we use a lowercase letter to denote a variable that is a function of time and uppercase letter to represent a constant. Time-dependent currents, denoted by 𝒊, take many forms. Among them is the other type of current that is in widespread use today and takes the form of a sinusoid, called alternating current (ac). Figure 1.7 shows a sinusoidal current. An alternating current (ac) is a current that varies sinusoidally with time. From the first equation, we obtain ELECTRON DRIFT VELOCITY Although all the free electrons in a conductor begin moving almost instantaneously upon the application of an electric pressure, their actual velocity, or drift, is exceedingly slow; this depends upon the current density in the given conductor (i.e., the number of amperes per unit of cross-sectional area). Introduction to Electric Circuits 7  It is seen that contrary to the common but mistaken view, the electron drift velocity is rather very slow and is independent of the current flowing and the area of the conductor. POWER AND ENERGY The power and energy delivered to an element are of great importance. For example, the useful output of an electric lightbulb can be expressed in terms of power. We know that a 300-watt bulb delivers more light than a 100-watt bulb. Introduction to Electric Circuits 8  Power is the time rate of supplying or receiving energy, measured in watts. 1 𝑊=1 𝐽/𝑠 (joule per second) From Eq. 1.5, we see that the power is simply the product of the voltage across an element times the current through the element. The power has units of watts. Two circuit variables are assigned to each element of a circuit: a voltage and a current. Figure 1.8 shows that there are two different ways to arrange the direction of the current and the polarity of the voltage: ❖ In Figure 1.8a, the current is directed from the + toward the - of the voltage polarity. When the current enters the circuit element at the + terminal of the voltage and exits at the - terminal, the voltage and current are said to “adhere to the passive convention.” In the passive convention, the voltage pushes a positive charge in the direction indicated by the current. Accordingly, the power calculated by multiplying the element voltage by the element current (i.e., 𝑝=𝑣𝑖) is the power received by the element. (This power is sometimes Introduction to Electric Circuits 9  called “the power absorbed by the element” or “the power dissipated by the element.”) The power received by an element can be either positive or negative. This will depend on the values of the element voltage and current. ❖ In Figure 1.8b, the current is directed from the - toward the + of the voltage polarity. Here, the passive convention has not been used. Instead, the current enters the circuit element at the - terminal of the voltage and exits at the + terminal. In this case, the voltage pushes a positive charge in the direction opposite to the direction indicated by the current. Accordingly, when the element voltage and current do not adhere to the passive convention, the power calculated by multiplying the element voltage by the element current is the power supplied by the element. The power supplied by an element can be either positive or negative, depending on the values of the element voltage and current. Passive Sign Convention is satisfied when the current enters through the positive terminal of an element and 𝑝=+𝑣𝑖. If the current enters through the negative terminal, 𝑝=−𝑣𝑖. The power received and the power supplied by an element are related by: Introduction to Electric Circuits 10 Introduction to Electric Circuits 11  4️⃣ SUMMARY Current is the flow of electrons but as a convention, which is recognized and used worldwide, we assume that current is the net flow of positive charges when solving circuit parameters. The energy available to cause charge to move through the element is indicated by the voltage across it. You can solve for power “delivered to” or “received by” the circuit using the equation 𝑝=𝑣∙𝑖 and the passive sign convention is used when calculating it. The SI units are used by today’s engineers and scientists. Using decimal prefixes, you may simply express electrical quantities with a wide range of magnitudes. PART 2 Introduction to Electric Circuits 12 Introduction to Electric Circuits 13 Introduction to Electric Circuits 14 Introduction to Electric Circuits 15 Introduction to Electric Circuits 16 Introduction to Electric Circuits 17