Fundamentals of Electrical Circuits PDF

ELEN 20044 ENGR. RONALD FERNANDO ENGR. MARK KERVIN NATIVIDAD  CMPE 20044 FUNDAMENTALS OF ELECTRICAL CIRCUIT Introduction Electric circuit and electromagnetic theory are...

ELEN 20044 ENGR. RONALD FERNANDO ENGR. MARK KERVIN NATIVIDAD  CMPE 20044 FUNDAMENTALS OF ELECTRICAL CIRCUIT Introduction Electric circuit and electromagnetic theory are the two fundamental theories upon which all branches of electrical engineering are constructed based on electric circuit theory: ▪ Power ▪ Electronics ▪ Electric Machines ▪ Communications ▪ Control ▪ Instrumentation The basic electric circuit theory course is the most important course not only for an Electrical engineering students but students taking up Electronics Engineering and Computer Engineering, and always an excellent starting point for a beginning student in this field of education. This instructional material is not for the study of various uses and applications of circuits but rather major concern is the analysis of the circuits, meaning a study of the behavior of the circuit: How does it respond to a given input? How do the interconnected elements and devices in the circuit interact? LESSON 1 – DC Electric Current Learning Objectives After successful completion of this lesson, you should be able to: ▪ Learn the standard System of units ▪ Define the SI units used by Electric Current ▪ Learn the fundamentals of Electric current ▪ Define the term Electric Current ▪ Identify the types of Electric Circuits ▪ Learn the fundamentals of Electric resistance ▪ Identify the variables of Electric resistance ▪ Interpret the basic circuit concepts, such as voltage, current, power, energy, etc. ▪ Identify the components of Electric circuits ▪ Discuss the types of electric circuits ▪ Differentiate between Independent and Dependent sources 2|Page  CMPE 20044 Course Materials: Watch: ▪ Electrical Circuits: The Basic (https://www.youtube.com/watch?v=k7aPL5cnYsM) ▪ How Electricity Works - Working Principles (https://www.youtube.com/watch?v=mc979OhitAg) ▪ Basic Electricity – What is an Amp? (https://www.youtube.com/watch?v=8gvJzrjwjds) Read: ▪ Alexander and Sadiku, “Fundamentals of Electric Circuits”, 4th Ed., McGraw Hill, ▪ Hayt, Kemmerly, and Durbin, “Engineering Circuit Analysis”, 7th Ed., McGraw Hill, 2017. Before defining different concepts such as charge, current, voltage, circuit elements, power, and energy it must first establish a system of units that will be used throughout the text. System of Units As engineers, measurable quantities are very important. Measurement, however, must be communicated in a standard language that all professionals can understand, irrespective of the country where the measurement is conducted. Such measurement language is the International System of Units, SI (Système Internationale). In 1960, General Conference on Weights and Measures, CGPM (Conférence générale des poids et mesures) adopted this standard of measurement. Table 1a is the redefinition of SI base units in 2019. Table 1a SI base units of a typical physical quantities Quantity Unit Physical Quantity Unit Symbol Symbol Time t second s Length L meter m Mass m kilogram kg Electric Current I Ampere A Thermodynamic Temp T Kelvin K Charge Q Coulomb C Luminous Intensity 𝑙𝑣 candela cd Plane Angle θ radian rad Solid Angle Ω steradian sr 3|Page  CMPE 20044 Table 1b Typical SI derived units Quantity Unit Physical Quantity Unit Symbol Symbol Force F Newton N Power P Watt W Energy W or En Joule J Resistance R Ohm Ω One great advantage of the SI unit is that it uses prefixes based on the power of 10 to relate larger and smaller units to the basic unit. SI prefixes, their symbols and corresponding powers is shown in Table 1c. Table 1c SI prefixes, their symbols and corresponding powers Multiplier Prefix Symbol Multiplier Prefix Symbol 𝟏𝟎𝟏𝟖 exa E 10−1 deci d 𝟏𝟎𝟏𝟓 peta P 10−2 centi c 𝟏𝟎𝟏𝟐 tera T 10−3 milli m 𝟏𝟎𝟗 giga G 10−6 micro µ 𝟏𝟎𝟔 mega M 10−9 nano n 𝟏𝟎𝟑 Kilo k 10−12 pico p 𝟏𝟎𝟐 hector h 10−15 fempto f 𝟏𝟎𝟏 deka da 10−18 atto a Charge and Current Charge, Q is an electrical property of the atomic particles of which matter consists, measured in coulombs (C) Coulomb, C is the SI unit of charge and the quantity symbol is Q for a constant charge and q for a charge that varies with time. 4|Page  CMPE 20044 Things to be considered on electric charge: 1. The coulomb is a large unit for charges. 1 𝑐𝑜𝑢𝑙𝑜𝑚𝑏 = 6.24 𝑥 1018 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 1 𝐶 = 6.24 𝑥 1018 𝑒 − o realistic or laboratory values of charges are on the order of pC, nC, or μC. o the smallest unit of charge is electrons, 𝑒 − which is equal to 1.602 𝑥 10−19 𝐶𝑜𝑢𝑙𝑜𝑚𝑏, 𝐶 2. According to experimental observations, the only charges that occur in nature are integral multiples of the electronic charge. 1 𝑒 − = −1.602 𝑥 10−19 𝐶 3. The law of conservation of charge states that charge can neither be created nor destroyed, only transferred. Thus, the algebraic sum of the electric charges in a system does not change. Electric Charge is the most basic quantity in an electric circuit. It must have either negative or positive polarity, labeled -Q or +Q, with an excess of either electrons or protons. A neutral condition is considered zero charge. Kinds of Electric Charge 1. POSITIVE charge – carried by sub-atomic particles called proton, 𝑝+ 2. NEGATIVE charge – carried by sub-atomic particles called electron, 𝑒 − o charges produce forces on each other: Charges of the same sign repel each other, but charges of the opposite sign attract each other Electric Current, I ▪ the movement of electric charge ▪ the rate at which free electrons can be made to drift through a material in a particular direction ▪ It is the continuous and uniform flow (called a drift) of electrons (the negative particles of an atom) around a circuit that are being “pushed” by the voltage source. ▪ If a steady flow of 1 C of charge passes a given point in a conductor in 1 s, the resulting current is 1 A. Ampere, A – the SI unit of current and the quantity symbol is I for a constant current and i for a time varying current. It was named after Andre-Marie Ampere in 1775 – 1836, a French mathematician and Physicist. Two Common Types of Current 1. A direct current (dc), I is a current that remains constant with time and does not change with time, but remains constant 2. An alternating current (ac), i is a current that varies sinusoidally with time. Andre-Marie Ampere 5|Page  CMPE 20044 Figure 1.1 Types of Current (a) direct current, dc (b) alternating current, ac 𝑄 𝐶𝑜𝑢𝑙𝑜𝑚𝑏 𝐼= 𝐴𝑚𝑝𝑒𝑟𝑒 = 𝑡 𝑠𝑒𝑐𝑜𝑛𝑑 Where, I is the current in Ampere, A Q the electric charge in Coulomb, C t the time in second, s Example 1. Find the current flow through a Light Emitting Diode from a steady movement of (a) 100 𝑚𝐶 in 4 𝑠, (b) 4 𝑥 1012 electrons in an hour, and (c) 15 𝐶 in 2 𝑚𝑖𝑛 Solution: 𝑄 100 𝑚𝐶 a) 𝐼 = 𝑡 = 4 𝑠 = 25 𝑚𝐴 1𝐶 (4 𝑥 1017 𝑒 )( ) 6.24 𝑥 1018 𝑒 b) 𝐼 = 3600 𝑠 = 17.8 𝜇𝐴 (1 𝐻)( ) 1𝐻 15 𝐶 c) 𝐼 = (2 min 𝑥 60 𝑠/min ) = 125 𝑚𝐴 2. How much charge in coulomb is represented by 12,500 electrons? 1𝐶 Solution: (12,500 𝑒 ) (6.24𝑥1018 𝑒) = 2 𝑥 10−15 𝐶 = 2 𝑓𝐶 In a circuit diagram in Figure 1.2, each I (or i) usually has an associated arrow to indicate the current reference direction. current reference I Copper Conductor Figure 1.2 Associated arrow to indicate the current reference direction 6|Page  CMPE 20044 This arrow specifies the direction of positive current flow, but not necessarily the direction of actual flow. If, after calculations, I is found to be positive, then actual current flow is in the direction of the arrow. But if I is negative, current flow is in the opposite direction. Voltage, V or potential difference (pd) or electromotive force (emf) ▪ the energy required to move a unit charge through an element, measured in volt (V) and was named in honor of Alessandro Antonio Volta (1745 – 1827), an Italian physicist, who invented the electric battery ▪ the potential energy of an electrical supply stored in the form of an electrical charge. ▪ the difference in voltage levels between two points in a circuit. Note: emf is a cause and p.d. is an effect. Alessandro Antonio Volta In general, 𝑊 𝐽𝑜𝑢𝑙𝑒 𝑛𝑒𝑤𝑡𝑜𝑛 − 𝑚𝑒𝑡𝑒𝑟 𝑉= 𝑉𝑜𝑙𝑡 = = 𝑄 𝐶𝑜𝑢𝑙𝑜𝑚𝑏 𝐶𝑜𝑢𝑙𝑜𝑚𝑏 Where: V is the voltage in Volt, V W or 𝐸𝑛 is the work or energy and the SI unit is in Joule, J Q is the electric charge in Coulomb, C Current and voltage are the two basic variables in electric circuits. The common term signal is used for an electric quantity such as a current or a voltage (or even electromagnetic wave) when it is used for conveying information. Like electric current, a constant voltage is called a dc voltage and is represented by V, whereas a sinusoidally time-varying voltage is called an ac voltage and is represented by v. Direct Current, dc voltage is commonly produced by a battery Alternating Current, ac voltage is produced by an electric generator x x 10 V -10 V y y (a) (b) Figure 1.3 Equivalent representations of two equal dc voltage 𝑉𝑥𝑦 : (a) point x is 10 V above point y, (b) point x is -10 V above point y. 7|Page  CMPE 20044 Power, P - the rate at which something either absorbs or produces/expending energy within the circuit. - the quantity symbol is P for constant power and p for time-varying power. If 1 Joule of work is either absorbed or delivered at a constant rate in 1 second, the corresponding power is 1 Watt. Watt, W is the SI unit of power in honor of James Watt, a Scottish inventor, mechanical engineer, and chemist who also developed the concept of horsepower. James Watt (1736–1819) Horsepower, hp is another unit of measurement of power, or the rate at which work is done, usually with reference to the output of engines or motors. The use of horsepower in the EU (European Union) is permitted only as a supplementary unit. Two common definition of Horsepower a. Mechanical Horsepower (or imperial Horsepower) = 745.7 Watts ≈ ¾ kW b. Metric Horsepower = 735.5 Watts In general, 𝑊 𝑜𝑟 𝐸𝑛 𝐽𝑜𝑢𝑙𝑒 𝑃= Watts = 𝑡 𝑠𝑒𝑐𝑜𝑛𝑑 𝐸𝑛 = 𝑃 ∙ 𝑡 𝐽𝑜𝑢𝑙𝑒 = watts ∙ 𝑠𝑒𝑐𝑜𝑛𝑑 Joule, J is the SI unit of Energy, 𝐸𝑛 or Work, W. The power absorbed by an electric component is the product of voltage and current if the current reference arrow is into the positively referenced terminal 𝑃 = 𝑉𝐼 Watts = 𝑉𝑜𝑙𝑡 𝑥 𝐴𝑚𝑝𝑒𝑟𝑒 If the calculated P is positive (+) with either formula, the component actually absorbs power. But if P is negative (-), the component produces power, it is a source of electric energy. 1 Joule = 1 watt-second → SI unit of Energy Example: 1. Convert 1 Wh to Joule 𝐸𝑛 = 𝑉𝑄 3600s 1 Wh 𝑥 = 3600 Ws = 3600 J But, 1h 1 Wh = 3600 J 𝑄 = 1 𝐶 = 6.24 𝑥 1018 𝑒 2. How many electron-volt, 𝑒𝑉 are Assume that V = 1V there in 1 Joule Therefore, Solution: 𝐸𝑛 = 6.24 𝑥 1018 𝑒𝑉 𝑄 𝐸𝑛 = 𝑃 ∙ 𝑡 = 𝑉 ∙ 𝐼 ∙ 𝑡 = 𝑉 ∙ ∙ 𝑡 𝑡 8|Page  CMPE 20044 Circuit Elements Two Types of Elements in an Electric Circuit 1. Passive element - an electrical component that does not generate power, but instead dissipates, stores, and/or releases it. Ex. Resistors, Capacitors, Inductors, etc. 2. Active element – an electrical component capable of generating energy and hence the ability to electrically control the flow of charge. Ex. generators, batteries, and operational amplifiers Most important active elements are voltage or current sources that generally deliver power to the circuit connected to them. Two kinds of sources 1. Ideal Independent Source - an active element that provides a specified voltage or current that is completely independent of other circuit elements. Figure 1.4 shows the symbols for independent sources. 2. Ideal Dependent (or controlled) Source - an active element in which the source quantity is controlled by another voltage or current. Figure 1.5 shows the symbols for dependent sources. (a) (b) (c) Figure 1.4. Symbol for independent sources: (a) for constant or time-varying voltage, (b) for constant voltage, direct current (c) for current source (a) Dependent Current Source (b) Dependent Voltage Source Figure 1.5. Symbol for Dependent Sources Dependent sources shown above are being controlled by a voltage or current of some element in the circuit, and the source can be voltage or current, so that four possible types of dependent source will be the result. 9|Page  CMPE 20044 Types of Dependent Sources 1. Voltage-Controlled Voltage Source (VCVS) 2. Current-Controlled Voltage Source (CCVS) 3. Voltage-Controlled Current Source (VCCS) 4. Current-Controlled Current Source (CCCS) 𝑉𝐷 = µ𝑣1 𝑉𝐷 = r𝑖1 VCVS ICVS where: where: 𝑉𝐷 = dependent voltage source, V 𝑉𝐷 = dependent voltage source, V µ = voltage gain, dimensionless r = transresistance, Ω 𝑣1 = voltage located elsewhere in the circuit, V 𝑖1 = current located elsewhere in the circuit, A 𝐼𝐷 = g𝑣1 𝐼𝐷 = 𝛽𝑖1 VCCS CCCS where: where: 𝐼𝐷 = dependent current source, A 𝐼𝐷 = dependent current source, A g = transconductance, S (siemens) or Ʊ (mho) 𝛽 = current gain, dimensionless 𝑣1 = voltage located elsewhere in the circuit, V 𝑖1 = current located elsewhere in the circuit, A Figure 1.6 Types of Dependent Sources 10 | P a g e  CMPE 20044 LESSON 2 - DC Electric Resistance Learning Objectives After successful completion of this lesson, you should be able to: Learn the fundamentals of Electric resistance Define the term Electric resistance Define the physical properties of resistance Define the SI units used by Electric resistance Identify the variables of Electric resistance Explain the difference between a potentiometer and a rheostat. Interpret the resistor color code to determine the resistance and tolerance of a resistor. Explain the significance of a resistor’s power rating. Resistance In general materials have a characteristic behavior of opposing the flow of electric charge. This physical property, or ability to oppose, limit or resist current, is known as resistance and the quantity symbol is 𝑅 and the SI unit is in ohm, Ω. The resistance of any material with a uniform cross- sectional area, 𝐴 depends on 𝐴 and its length, ℓ as shown in Fig. 2.1. We can represent the resistance of a material mathematically, ℓ 𝑚𝑒𝑡𝑒𝑟 𝑅=𝜌 𝑂ℎ𝑚 = 𝑜ℎ𝑚 ∙ 𝑚𝑒𝑡𝑒𝑟 𝐴 𝑚𝑒𝑡𝑒𝑟 2 Cross-sectional area A Where: 𝜌 = resistivity of the material in Ω∙m Material with ℓ = length of the material, m resistivity ρ A = its cross-cross sectional area in m2 Cross-sectional area A Relationship among Conductance Figure 2.1 Equivalent resistor 𝐴 𝑠𝑖𝑒𝑚𝑒𝑛 𝑚𝑒𝑡𝑒𝑟 2 and circuit symbol 𝐺=𝜎 𝑚ℎ𝑜 = · ℓ 𝑚𝑒𝑡𝑒𝑟 𝑚𝑒𝑡𝑒𝑟 Where: 𝜎 = (sigma) constant of proportionality and is the quantity symbol for conductivity in SI unit is siemens per meter, S/m A = its cross-cross sectional area in m2 ℓ = length of the material, m The resistance of a conductor of uniform cross-sectional area is directly proportional to the length of the conductor. For the same material and length, one conductor will have more resistance than another with a larger cross-sectional. That is, the resistance of a conductor is inversely proportional to the cross-sectional area of the conductor. 𝑅1 𝐿1 𝐴2 = = 𝑅2 𝐿2 𝐴1 11 | P a g e  CMPE 20044 Where: 𝑅1 and 𝑅2 are the resistances of conductors with lengths 𝐿1 and 𝐿2 and areas 𝐴1 and 𝐴2 Cross-sectional area of a wire is 𝜋𝑑2 𝐴= 4 𝜋𝑑22⁄ 𝑅1 𝐴2 4 𝑅1 𝑑22 since = = therefore, = 𝑅2 𝐴1 𝜋𝑑12⁄ 𝑅2 𝑑12 4 Hence, the resistance of a conductor varies inversely as the square of the diameter. Cross-sectional area in terms of circular mil, cmil. Use 𝐴 = 𝑑2 where: 𝑑 is the diameter in mil and A is the cross-sectional area in cmil. Note that, 1 𝑚𝑖𝑙 = 0.001 𝑖𝑛𝑐ℎ = 0.00254 𝑐𝑚 Convert the cmil unit to in2 𝜋𝑑2 𝐴 = 𝜋𝑟 2 = 4 Since, 1 mil = 0.001 inch 𝜋(0.001 𝑖𝑛)2 1𝑐𝑚𝑖𝑙 = 4 𝜋 𝑥 10−6 2 1𝑐𝑚𝑖𝑙 = 𝑖𝑛 4 Or 2 4 𝑥 106 1 𝑖𝑛 = 𝑐𝑚𝑖𝑙 𝜋 Standard Wire Gauge The gauge number specifies the size of round wire in terms of its diameter and cross-sectional circular area. Things to remember about wire gauge: 1. As the gauge number increase from 1 to 40, the diameter and circular area decrease. Higher gauge numbers indicate thinner sizes. 2. The circular area doubles for every three gauge sizes. A number 10 wire has approximately twice the area of number 13 wire. 3. The higher the gauge number and the thinner the wire, the greater the resistance of the wire for any given length. A #22 AWG the maximum current the wire can carry without overheating is 0.5 to 1 Ampere A #14 AWG, about 5 to 15 Ampere The circuit element, shown in figure 2.1, used to model the current-resisting behavior of a material is the resistor. 12 | P a g e  CMPE 20044 Table 2.1 Resistivity of common materials Resistivity, Resistivity, Material ρ (Ω∙m) @ Usage Material ρ (Ω∙m) @ Usage 20°C 20°C Silver 1.64 𝑥 10−8 Conductor Carbon 4.00 𝑥 10−5 Semiconductor Copper 1.72 𝑥 10−8 Conductor Germanium 47.0 𝑥 10−2 Semiconductor Aluminum 2.80 𝑥 10−8 Conductor Silicon 2.50 𝑥 103 Semiconductor Gold 2.45 𝑥 10−8 Conductor Paper 1.00 𝑥 1010 Insulator Iron 12.3 𝑥 10−8 Conductor Mica 5.00 𝑥 1011 Insulator Constantan 49.0 𝑥 10−8 Conductor Glass 1.00 𝑥 1012 Insulator Nichrome 100 𝑥 10−8 Conductor Teflon 3.00 𝑥 1012 Insulator Electric Resistance or Resistance, R of an element denotes its ability to resist the flow of electric current and the SI unit is in ohms, Ω. Sometimes kilo-ohms ( kΩ = 1 𝑥 103 Ω ) and Mega-ohms (MΩ = 1 𝑥 106 Ω ). Note that resistance cannot be negative in value. - It is the opposition to the passage of an electric current through a conductor. - is this property of materials that opposes or resists the movement of electrons and makes it necessary to apply a voltage to cause current to flow. The SI unit of electrical resistance is measured in Ohms (Ω). Its inverse quantity is electrical conductance, G and is measured in Siemens (S) or mhos (℧). 1 𝑅= 𝐺 It is the capacity of a material to resist or prevent the flow of current or, more specifically, the flow of electric charge within a circuit. The circuit element which does this perfectly is called the “Resistor”. Conductance is the ability of an element to conduct electric current and is measured in mhos (℧) or siemens (S). Figure 2.2 Different types of resistor IEC (International Electrotechnical Commission) Symbol - Standard electrical symbols also known as IEC 60617 (British Standard BS 3939) used to represent various devices including 13 | P a g e  CMPE 20044 resistors, pilot lights, relays, timers and so on. Founded in 1906, it is the world's leading organization for the preparation and publication of International Standards for all electrical, electronic and related technologies. These are known collectively as “electrotechnology”. IEEE (Institute of Electrical and Electronics Engineers) - describes itself as "the world's largest technical professional society -- promoting the development and application of electrotechnology and allied sciences for the benefit of humanity, the advancement of the profession, and the well-being of our members." It fosters the development of standards that often become national and international standards. The organization publishes a number of journals, has many local chapters, and several large societies in special areas, such as the IEEE Computer Society. Types of Resistor 1. Linear Resistor – an element that obeys Ohm’s law and has a constant resistance, thus its current-voltage characteristic is illustrated figure a. 2. Nonlinear Resistor – an element that does not obey Ohm’s law. Its resistance varies with current. Its i-v characteristic is typically shown in figure b. Figure a Figure b Figure 2.3 Linear and nonlinear Resistor Current-voltage characteristics Rheostat is a variable Resistance, R with two terminals connected in series with a load. The purpose is to vary the amount of current. 14 | P a g e  CMPE 20044 Potentiometer, a pot for short, has three terminals. The fixed maximum R across the two ends is connected across a voltage source. Then the variable arm is used to vary the voltage division between the center terminal and the ends. Light Dependent Resistor (LDR) or a photoresistor is a component that is sensitive to light. When light falls upon it then the resistance changes. Values of the resistance of the LDR may change over many orders of magnitude the value of the resistance falling as the level of light increases. Resistor Power Absorption - power absorbed by a linear resistor in terms of its resistance, 𝑃 = 𝑉𝐼 = (𝐼𝑅)𝐼 = 𝐼 2 𝑅 or 𝑉 𝑉2 𝑃 = 𝑉𝐼 = 𝑉 ( ) = 𝑅 𝑅 Every resistor has a power rating, also called power rating or wattage rating, that is the maximum power that the resistor can absorb without overheating to a destructive temperature. Two things to be considered about resistance power dissipation: 1. The power dissipated in a resistor is a nonlinear function of either current or voltage. 2. Since 𝑅 and 𝐺 are positive quantities, the power dissipated in a resistor is always positive. Thus, a resistor always absorbs power from the circuit. This confirms the idea that a resistor is a passive element, incapable of generating energy. Example 1. A soldering gun draws 1.5 A at 230 V. Find its resistance. 2. The essential component of a toaster is an electrical element (heating element with resistance) that converts electrical energy to heat energy. How much current is drawn by a toaster with resistance 25 Ω at 110 V? 15 | P a g e  CMPE 20044 Nominal Values and Tolerances Printed resistance values provided by the manufacturer on resistor casings either in numerical form or in a color code are only nominal values: They are only approximately equal to the actual resistances. The possible percentage variation of resistance about the nominal value is called the tolerance. The popular carbon-composition resistors have tolerances of ±20, ±10, and ± 5 percent, which means that the actual resistances can vary from the nominal values by as much as ±20, ±10, and ± 5 percent of the nominal values. Color Code The most popular resistance color code has nominal resistance values and tolerances indicated by the colors of either three, four or five bands around the resistor casing, as shown in Fig. 2.3. Four band color Five band color code code Figure 2.4 Four and Five bands Resistors Table 2.2 Four and Five band Resistors Band A and B Band A and B (1st and 2nd Band C Band D (1st and 2nd Band C Band D Color Color Significant (Multiplier) (Tolerance) Significant (Multiplier) (Tolerance) Figure) Figure) Black 0 1 𝑥 100 - Violet 7 1 𝑥 107 ±0.1% Brown 1 1 𝑥 101 ±1% Gray 8 1 𝑥 108 - Red 2 1 𝑥 102 ±2% White 9 1 𝑥 109 - Orange 3 1 𝑥 103 - Gold - 1 𝑥 10−1 ±5% Yellow 4 1 𝑥 104 - Silver - 1 𝑥 10−2 ±10% Green 5 1 𝑥 105 ±0.5% No Color - - ±20% Blue 6 1 𝑥 106 ±0.25% For five bands color code, bands A, B, and C represents the 1st, 2nd, and 3rd significant digit and bands D and E represents the multiplier and tolerance respectively. Likewise, the colors brown, red, green, blue, and violet represent the following tolerances: ±1%, ±2%, ±0.5%, ±0.25% and ±0.1% respectively. 16 | P a g e  CMPE 20044 Example: Give the equivalent nominal value and tolerance of the following color codes 1. Red, Orange, Red, Silver 2 3 𝑥 102 = 23 𝑥 100 Ω ± 10% = 2,200 Ω ± 10% = 2.2 kΩ ± 10% → answer 2. Green, Brown, Black 5 1 𝑥 100 = 51 𝑥 1 Ω ± 20% = 51 Ω ± 20% → answer 3. Yellow, Red, Green, Red, Green 4 2 5 𝑥 102 = 425 𝑥 100 Ω ± 0.5% = 42,500 Ω ± 0.5% = 42.5 kΩ ± 0.5% → answer 4. Brown, Blue, Violet, Silver, Blue 1 6 7 𝑥 10−2 = 167 𝑥 0.01 Ω ± 0.25% = 1.67 Ω ± 0.25% → answer 17 | P a g e  CMPE 20044 LESSON 3 - DC Electric Circuit Learning Objectives After successful completion of this lesson, you should be able to: Discuss basic elements of a simple electric circuits Differentiate electron flow and conventional flow of current Discuss basic Ohm’s Law Determine the importance of the internal resistance of voltage and current sources DC electric circuit or network is an interconnection of electrical elements linked together in a closed path so that an electric current may flow continuously. We use this in communicating or transferring energy from one point to another. - a path for transmitting electric current which includes a device that gives energy to the charged particles constituting the current. Three Basic Elements of a Simple Electric Circuit a) Source: a battery, dc or ac power supply, etc. b) Load: a lamp or bulb, appliances, etc. c) Path or connecting wires: conducting materials that can carry or allow electric charge to flow freely such as conductor wire, copper clad board, d) Control Device: switch, circuit breaker or any device that are capable of allowing or hindering any movement of charge within the circuit Load Path Figure 3.1b Equivalent Schematic Diagram Control Source Device Figure 3.1a Simple Electric Circuit 18 | P a g e  CMPE 20044 Types of Current Flow or direction 1. Conventional Current Flow - movement of the positive charge (holes) around a closed circuit flowing from the positive terminal of the battery, through the circuit and returns to the negative terminal of the battery. The arrows shown on symbols for components such as diodes and transistors point in the direction of conventional current flow. Figure 3.2a 2. Electron Flow - is opposite to the direction of the conventional current flow being negative to positive. Electrons that flow from the negative terminal of the battery and return back to the positive terminal of the battery. In the entire discussion we will be using conventional current Figure 3.2b flow. Ohm’s Law states that the amount of current, I is directly proportional to the voltage, V and inversely proportional to the resistance, R. 𝐼∝𝑉 Mathematically, 𝑉 𝐼= =𝑉∙𝐺 𝑅 Where: 1 𝑜𝑟 𝐺 → constant of proportionality in siemen, S or mho, Ʊ 𝑅 Georg Simon Ohm (1787–1854) is a German physicist who, in 1826, experimentally determined the most basic law relating voltage and current for a resistor. To honor him, the unit of resistance was named the ohm. Georg Simon Ohm Ohm’s Law Formula Wheel 19 | P a g e  CMPE 20044 Open and Short Circuits 1. Open Circuit is a circuit element with resistance approaching infinity. This means that it has zero current flow through it for any finite voltage across it. On a circuit diagram it is indicated by two terminals not connected to anything. (a) 2. Short circuit - is a circuit element with resistance approaching zero. It is the opposite of an open circuit. It has zero voltage across it for any finite current flow through it. On a circuit diagram a short circuit is designated by an ideal conducting wire with zero resistance. (b) Internal Resistance – it is the electrical resistance inside batteries and power supplies in series that can limit the potential difference that can be supplied to an external load. Every practical voltage or current source has an internal resistance that adversely affects the operation the source. For any load except an open circuit, a voltage source has a loss of voltage across its internal resistance. And except for a short-circuit load, a current source has a loss of current through its internal resistance. Practical Voltage Source In a practical voltage source the internal Internal resistance has almost the same effect as a resistor Resistance in series with an ideal voltage source, as shown in Fig. a. (Components in series carry the same Ideal current.) voltage Terminals source (a) Practical Current Source In a practical current source the internal resistance has almost the same effect as a resistor in parallel with an ideal current source, as shown in Ideal Fig. b. (Components in parallel have the same current Internal Resistance Terminals voltage across them.) source (b) 20 | P a g e