Fundamentals of Electrical Circuits MODULE 1 Engr. Prince Sero Outline I. Course Description II. General Policies III. Units, Contact Hours, Requisites IV. Grading System V. Course Outline VI. References VII. Basic Concepts COURSE DESCRIPTION COURSE DESCRIPTION This course introduces the fundamental concepts, circuit laws, theorems, and techniques used in electrical circuit analysis and transient analysis, as well as its applications. The course covers circuit topologies and DC excitations, transient response, AC response, and polyphase circuits. The use of computer software for circuit simulation and design are emphasized to expose students to computer-based tools. General Policies General Policies • Attendance will be checked through a SEAT PLAN. You will have a freedom to choose your place good for the whole semester unless told otherwise. • Only missed major exams may be given a special make-up exam with valid reasons and upon presentation of related documents. Missed quizzes will be given a score of “0”. General Policies • Cheating will be automatically penalized with a final grade of “5.0”. • Going out of the class during exams is NOT ALLOWED. • Assignments and seat works have a weight equal to a quiz. NO LATE SUBMISSION policy is implemented. Units, Contact Hours, Requisites Units Lecture – 3 units Laboratory – 1 unit Hours per week Lecture – 3 hours/week Laboratory – 3 hours/week Pre-requisite Co-requisite Physics for Engineers ECEN2101 / ECEN2013 Grading System MIDTERM Lecture Quizzes (Q) Quizzes (Q) Midterm Exam (ME) Final Exam (FE) Midterm Grade (MGLec) Final Grade (FGLec) MIDTERM Laboratory FINALS FINALS Experiment Report (ER) Experiment Report (ER) Midterm Exam (ME) Final Exam/Project (FE) Midterm Grade (MGLec) Final Grade (FGLec) Grading System Course Outline Course Outline I. Circuit Topologies and DC Excitations • Introductory Concepts • Electrical Properties of Materials • Passive Elements • Network Laws and Theorems • Electric Circuit Theorems Course Outline II. Transient Response • RC Circuits • RL Circuits • RLC Circuits Course Outline III. AC Response and Polyphase Circuits • Reactance and Impedance • Introduction to Single-phase AC • AC Power Analysis • Sinusoidal Steady-State Analysis • Three-Phase Circuits • Transformers References References • Boylestad, Robert L. 2010. Introductory Circuit Analysis. New Jersey : Pearson Education, Inc. • Bird, John. 2010. Electrical Circuit Theory and Technology. Amsterdam: Elsevier • Dorf, Richard C. and Svoboda, James A. 2011. Introduction to Electric Circuits 7th edition. USA: John Wiley & Sons, Inc. • Edminister, J.A. 2011. Theory and Problems of Electric Circuits, Schaum’s Outline Series. New York, USA : McGraw-Hill Basic Concepts Systems of Units Quantity Basic Unit Symbol Length Meter m Mass Kilogram kg Time Second s Thermodynamic Temperature Kelvin K Electric Current Ampere A Amount of Substance Mole mol Luminous Intensity Candela cd Basic Concepts SI Unit Prefixes Prefix Multiplier Symbol Prefix Multiplier Symbol yotta x 1024 Y yocto x 10-24 y zetta x 1021 Z zepto x 10-21 z exa x 1018 E atto x 10-18 a peta x 1015 P femto x 10-15 f tera x 1012 T pico x 10-12 p giga x 109 G nano x 10-9 n mega x 106 M micro x 10-6 µ kilo x 103 k milli x 10-3 m hecto x 102 h centi x 10-2 c deka x 101 da deci x 10-1 d Basic Concepts Scientific Notation • It is the shifting of the decimal point either to the left or to the right of the given number until there is only one significant digit to the left of the decimal point and then multiplying the number with the appropriate power of 10 to retain its original value. • A way of expressing a number in terms of the power of 10. Example: 58, 000 meters = 5.8 x 104 m Basic Concepts Engineering Notation • It is an exponential format of specifying numbers in which the powers of 10 are limited to the multiples of three so that it corresponds to an S.I. prefix. • It is the application of decimal prefixes and their abbreviations to simplify language when dealing with very small or very large units. Example: 58, 000 meters = 58 km Basic Concepts Electric Circuit • A closed loop of pathway with electric charges or current flowing through it. • A basic electric circuit contains three components: the power supply, the load, and the wires. • Wires connect the power supply and the load. • Power supply is a device that supplies electrical energy to the load of the circuit. • Load is a device that is usually connected to the output terminal of an electric circuit. Basic Concepts Electric Circuit Basic Concepts Schematic Symbols Component Circuit Symbol DC Power Supply AC Power Supply Fixed Resistor Variable Resistor Basic Concepts Schematic Symbols Component Circuit Symbol Capacitor Inductor Switch Basic Concepts Electric Current • Electric current is measured by the amount of electric charge that flows past a given point at a certain time interval in an electric circuit. 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 = 𝐶ℎ𝑎𝑟𝑔𝑒 𝑇𝑖𝑚𝑒 𝐼= 𝑄 𝑇 • Electric current is also expressed by the derivative: 𝑑𝑞 𝑖= 𝑑𝑡 Basic Concepts Electric Current Similarly expressed as: 𝑡 𝑄 = න 𝑖 𝑑𝑡 𝑡0 Here, we represent current as i because there can be several types of current; that is, charge can vary with time in several ways. If the current does not change with time but remains constant, we call it direct current (DC). Otherwise, we call it alternating current (AC). Basic Concepts DIRECT CURRENT (DC) is a current ALTERNATING CURRENT (AC) is a that remains constant with time. current that varies sinusoidally with time. Basic Concepts Electric Current Quantity Quantity Symbol Unit Unit Symbol Charge Q Coulombs C Time t Seconds s Current I Amperes A 1 Coulomb = 6.25 x 1018 electrons, e1 electron = - 1.602 x 10-19 Coulomb, C Basic Concepts 1 Coulomb = 6.25 x 1018 electrons, e1 electron = - 1.602 x 10-19 Coulomb, C Electric Current 1 Ampere = 1 Coulomb / 1 second Basic Concepts Ammeter Ammeter is an instrument that can be used to measure current, and its symbol is It must be connected in series with the circuit to measure current, as shown in the figure. Basic Concepts Direction of Electric Current There are two methods to express the direction of electric current. Conventional Current Flow Electron Flow Basic Concepts Direction of Electric Current Conventional Current Flow The assumed direction of the flow of current, which is opposite from the electron flow, that is from the positive of the source to the negative of the source. Electron flow Actual flow of current since electrons are the moving charges therefore it moves from the negative of the source going to the positive of the source. Basic Concepts SAMPLE PROBLEMS Sample Problems 1. How much charge is represented by 4,600 electrons? Ans. -7.369 x 10-16 C 2. The total charge entering the terminal is given by q = 5t sin 4πt mC. Calculate the current at t = 0.5 s. Ans. 31.42 mA 3. Determine the total charge entering a terminal between t = 1 s and t = 2 s if the current passing the terminal is i = (3t2 – t ) A. Ans. 5.5 C 4. If in problem number 2, q = (10 – 10e-2t) mC, find the current at t = 1.0 s. Ans. 2.707 mA Basic Concepts Electric Voltage Voltage / Electromotive Force ( V or E ) • EMF is an electric pressure or force that is supplied by a voltage source, which causes electric current to flow in a circuit. • Voltage is responsible for the pushing and pulling of electrons or current through an electric circuit. • In a linear circuit of fixed resistance, if we increase the voltage, the current goes up, and similarly, if we decrease the voltage, the current goes down. Basic Concepts Potential Difference Potential difference/voltage is the amount of energy or work required to move electrons between two points and is expressed by the formula: 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 = 𝑊𝑜𝑟𝑘 𝐶ℎ𝑎𝑟𝑔𝑒 𝑉= 𝑊 𝑄 Voltage is also expressed by the derivative: 𝑑𝑤 𝑣= 𝑑𝑞 Basic Concepts Electric Voltage Quantity Quantity Symbol Unit Unit Symbol Voltage V Volt V Work (Energy) W Joule J Charge Q Coulomb C Basic Concepts Potential Difference Explained Basic Concepts Potential Difference Explained Assuming there are two water tanks A and B. Water will flow from tank A to B because tank A has a higher water level than tank B It is the water-level difference that produces the potential energy for tank A, and work is done when water flows from tank A to B. Basic Concepts Potential Difference Explained Basic Concepts Electric Voltage • Current will flow between two points in an electric circuit only when there is an electrical potential difference. • For example, if 1 J of energy is used to move a 1 C charge from point a to b, it will have a 1 V potential difference or voltage across two points. Basic Concepts Electric Voltage ”The charge will not move unless you apply the potential difference.” Voltage drop occurs when a voltage across a component when current flows from a higher potential point to a lower potential point. Voltage rise occurs when a voltage across a component when current flows from a lower potential point to a higher potential point. Basic Concepts Voltmeter Voltmeter is an instrument that can be used to measure voltage. Its symbol is The voltmeter should be connected in parallel with the circuit component to measure voltage. Basic Concepts Resistance Resistor • “Resists” the flow of electrical current. • The higher the value of resistance, the smaller the current will be. Resistance • The property of a material or circuit elements to oppose the flow of electrons. • Expressed in ohms (Ω). Basic Concepts Factors Affecting Resistance • • • • Length Cross-sectional Area Nature of the Material Temperature Basic Concepts Factors Affecting Resistance Cross-sectional area of the wire (A) The larger the diameter of the wire, the greater the cross-sectional area, the less the resistance in the wire and the more the flow of current. Length (L) The longer the wire, the more the resistance and the more the time taken for the current to flow. Basic Concepts Factors Affecting Resistance Resistivity (ρ) It is a measure for the opposition to flowing current through a material of wire, or how difficult it is for current to flow through a material. The different materials have different resistivity, i.e. more or less resistance in the materials. Temperature (T) Resistivity of a material is dependent upon the temperature surrounding the material. Resistivity increases with an increase in temperature for most materials. Basic Concepts Resistance Since, 𝑅∝ 𝐿 𝐴 𝜌𝐿 𝐴 Then, 𝑅= But, 𝑉 = 𝐴𝐿 ; Then, Therefore, 𝐿= 𝑅= where: ; 𝑉 𝑉 and 𝐴 = 𝐴 𝐿 𝜌𝑉 𝜌𝐿2 = 𝐴2 𝑉 ; 𝝆 = resistivity or specific resistance of a given material at a certain temperature (Ω-m) L = length (m) A = cross-sectional area (m2) V = volume (m3) For constant temperature only. Basic Concepts Resistivity of Copper at 20°C • Standard Annealed Copper 𝝆 = 1.7241 x 10-8 Ω - m 𝝆 = 1.7241 x 10-6 Ω - cm 𝝆 = 10.37 Ω - cmil / ft • Hard - Drawn Copper 𝝆 = 1.77 x 10-8 Ω - m 𝝆 = 1.77 x 10-6 Ω – cm 𝝆 = 10.65 Ω - cmil / ft Basic Concepts Mil (mil) A unit of length equivalent to one thousandth of an inch. 1 mil = 1 x 10-3 in Square mil (mil2) A cross sectional area of a square whose side is equivalent to 1 mil. Circular mil (cmil) A cross sectional area of a circle whose diameter is equivalent to 1 mil. 𝜋 1 𝑐𝑚𝑖𝑙 = 𝑠𝑞𝑢𝑎𝑟𝑒 𝑚𝑖𝑙 4 𝐴𝑟𝑒𝑎 𝑖𝑛 𝑐𝑚𝑖𝑙 = 𝐷2 = 𝐷1 2 𝑥 106 where: D = diameter in mils D1 = diameter in inch Basic Concepts END Basic Concepts SAMPLE PROBLEMS Sample Problems 1. Calculate the voltage required to accelerate an electron to a kinetic energy of 8x10-15 Joules? 2. A car battery supplies a current of 50A to the starter motor. How much charge passes through the starter in half a minute? 3. A positively charged dielectric has a charge of 2 coulombs. If 12.5x1018 free electrons are added to it, what will be the net charge on the said dielectric? 4. A cloud of 2.5x1019 electrons move past a given point every two seconds. How much is the intensity of the electron flow? Sample Problems 5. A conductor has an area of 40,000 circular mils. What is the diameter of this conductor in inches? 6. What is the area in circular mils (CM) of a conductor whose diameter is 0.25 inch? 7. Determine the resistance of the copper wire with a length of 10 meters and a cross sectional of 4 cm by 4 cm. 8. A copper wire has a diameter of 2 inches and a length of 20 feet. What is the resistance of the wire? 9. An electric conductor 1 m long with a cross sectional area of 1 mm2 has a resistance of 0.017 Ω, what is the resistance of a 50 m wire of the same material with a cross-sectional of 0.25 mm2?