UNIT 1 DEFINITION AND UNITS 2023.pdf

DFT 10013 ELECTRICAL PRINCIPLES UNIT 1.0: DEFINITION AND UNITS LECTURER: CHE HASMIZI BIN CHE DERAMAN SUB UNIT 1.1 Introduction to electrical quantities 1.2 Current and charge 1.3 Voltage, Energy and Power. 1.4 Passive and A...

DFT 10013 ELECTRICAL PRINCIPLES UNIT 1.0: DEFINITION AND UNITS LECTURER: CHE HASMIZI BIN CHE DERAMAN SUB UNIT 1.1 Introduction to electrical quantities 1.2 Current and charge 1.3 Voltage, Energy and Power. 1.4 Passive and Active Components 1.5 Resistors  After completing the unit, students should be able to:  1. Identify electrical quantities and units. (C1)  2. Use scientific notation / metric prefix to express large and small quantities. (C3)  3. Define the electrical charge and electrical current. (C1)  4. Define voltage, energy, power and their relationship. (C1)  5. Explain and identify passive and active elements. (C2)  6. Describe basic types of resistors. (C2)  7. Identify resistance by colour code or labelling. (C1) 1.1 Introduction to electrical quantities 1. Identify electrical quantities and units. What is the SI Unit? SI unit (Système International) is an international system of measurements that are used universally in technical and scientific research to avoid the confusion with the units. Having a standard unit system is important because it helps the entire world to understand the measurements in one set of unit systems.  Following is the table with base SI units: Sl. No. Name of the Quantity SI Unit SI Unit Symbol 1. Length (l) Meter m 2. Mass (M) Kilogram kg 3. Time (T) Second s 4. Electric current (I) Ampere A 5. Thermodynamic temperature (Θ) Kelvin K 6. Amount of substance (N) Mole mol 7. Luminous intensity (J) Candela cd Electrical quantities and units Electrical Measuring Symbol Description Parameter Unit Unit of Electrical Potential Voltage Volt V or E V=I×R Unit of Electrical Current Current Ampere I or i I =V ÷ R Unit of DC Resistance Resistance Ohm R or Ω R =V ÷ I Reciprocal of Resistance Conductance Siemen G or ℧ G=1÷R Unit of Capacitance Capacitance Farad C C = Q ÷V Unit of Electrical Charge Charge Coulomb Q Q = C ×V Unit of Inductance Inductance Henry L or H VL = -L(di/dt) Unit of Power Power Watts W P = V × I or I2 × R Unit of AC Resistance Impedance Ohm Z Z2 = R2 + X2 Unit of Frequency Frequency Hertz Hz ƒ = 1 ÷T 2. Use scientific notation / metric prefix to express large and small quantities Scientific notation Provides a convenient method to represent large and small numbers and to perform calculations involving such numbers. In scientific notation, a quantity is expressed as a product of a number between 1 and 10 and a power of ten. For example, the quantity 150,000 is expressed in scientific notation as 1.5 * 105 , and the quantity 0.00022 is expressed as 2.2 * 10-4.  Multiples and Sub-multiples There is a huge range of values encountered in electrical and electronic engineering between a maximum value and a minimum value of a standard electrical unit. For example, resistance can be lower than 0.01Ω or higher than 1,000,000Ω. By using multiples and submultiple’s of the standard unit we can avoid having to write too many zero’s to define the position of the decimal point The table below gives their names and abbreviations Prefix Symbol Multiplier Power of Ten Tera T 1,000,000,000,000 1012 Giga G 1,000,000,000 109 Mega M 1,000,000 106 kilo k 1,000 103 none none 1 100 centi c 1/100 10-2 milli m 1/1,000 10-3 micro µ 1/1,000,000 10-6 nano n 1/1,000,000,000 10-9 pico p 1/1,000,000,000,000 10-12 Powers of Ten The power of ten is expressed as an exponent of the base 10 in each case (10x). An exponent is a number to which a base number is raised. It indicates the number of places that the decimal point is moved to the right or left to produce the decimal number. For a positive power of ten, move the decimal point to the right to get the equivalent decimal number. For example, for an exponent of 4, For a negative the power of ten, move the decimal point to the left to get the equivalent decimal number. For example, for an exponent of -4, EXAMPLE 1 Express each number in scientific notation (a) 200 (b) 5,000 (c) 85,000 (d) 3,000,000  Solution  In each case, move the decimal point an appropriate number of places to the left to determine the positive power of ten.  Notice that the result is always a number between 1 and 10 times a power of ten Express 4,750 in scientific notation.  EXAMPLE 2  Express each number in scientific notation. (a) 0.2 (b) 0.005 (c) 0.00063 (d) 0.000015  Solution  In each case, move the decimal point an appropriate number of places to the right to determine the negative power of ten. Express 0.00738 in scientific notation.  EXAMPLE 3  Express each of the following as a regular decimal number: Solution  Move the decimal point to the right or left a number of places indicated by the positive or the negative power of ten, respectively. Express 9.12 x 103 as a regular decimal number. Tutorial 1 1. Scientific notation uses powers of ten. (True or False) 2. Express 100 as a power of ten. 3. Express the following numbers in scientific notation: (a) 4,350 (b) 12,010 (c) 29,000,000 4. Express the following numbers in scientific notation: (a) 0.760 (b) 0.00025 (c) 0.000000597  Engineering Notation Engineering notation is similar to scientific notation. However, in engineering notation a number can have from one to three digits to the left of the decimal point and the power-of-ten exponent must be a multiple of three. For example, the number 33,000 expressed in engineering notation is 33 x 103. In scientific notation, it is expressed as 3.3 x 104. As another example, the number 0.045 expressed in engineering notation is 45 x 10-3. In scientific notation, it is expressed as 4.5 x 10-2. EXAMPLE 4 Express the following numbers in engineering notation: (a) 82,000 (b) 243,000 (c) 1,956,000 Solution  In engineering notation,  Related Problem Express 36,000,000,000 in engineering notation. EXAMPLE 5 Convert each of the following numbers to engineering notation: (a) 0.0022 (b) 0.000000047 (c) 0.00033  Solution  In engineering notation, Related Problem Express 0.0000000000056 in engineering notation  Metric Prefixes A metric prefix is an affix that precedes a measured quantity and represents a multiple or power of 10 multiple of the quantity. In engineering notation metric prefixes represent each of the most commonly used powers of ten in electronics and electrical work. Metric prefixes are used only with numbers that have a unit of measure, such as volts, amperes, and ohms, and precede the unit symbol. For example, 0.025 amperes can be expressed in engineering notation as 25 x 10-3 A. This quantity expressed using a metric prefix is 25 mA, which is read 25 milliamps. Note that the metric prefix milli has replaced 10-3. As another example, 10,000,000 ohms can be expressed as 10 x 106 Ω. This quantity expressed using a metric prefix is 10 MΩ, which is read 10 megohms. The metric prefix mega has replaced 106. Common metric prefixes used in electronics and electrical work with their symbols and corresponding powers of ten and values EXAMPLE 6 Express each quantity using a metric prefix: (a) 50,000 V (b) 5,000,000 Ω (c) 0.000036 A Solution Related Problem Express using metric prefixes: (a) 56,000 Ω (b) 0.000470 A Calculator tip  Tutorial 2 1. Express the following numbers in engineering notation: (a) 0.0056 (b) 0.0000000283 (c) 950,000 (d) 375,000,000,000 2. List the metric prefix for each of the following powers of ten: 106 , 103 , 10-3 , 10-6 , 10-9 , and 10-12 3. Use an appropriate metric prefix to express 0.000001 A. 4. Use an appropriate metric prefix to express 250,000 W.  Metric Unit Conversions  The following rules apply to metric unit conversions: 1. When converting from a larger unit to a smaller unit, move the decimal point to the right. 2. When converting from a smaller unit to a larger unit, move the decimal point to the left. 3. Determine the number of places to move the decimal point by finding the difference in the powers of ten of the units being converted. For example, when converting from milliamperes (mA) to microamperes (µA), move the decimal point three places to the right because there is a three-place difference between the two units (mA is 10-3 A and uA is 10-6 A). Notice that when the unit is made smaller, the number is made larger by a corresponding amount and vice versa.  EXAMPLE 7  Convert 0.15 milliampere (0.15 mA) to microamperes (µA).  Solution Move the decimal point three places to the right. Related Problem : Convert 1 mA to microamperes. EXAMPLE 8  Convert 4,500 microvolts (4,500 uV) to millivolts (mV). Solution Move the decimal point three places to the left Related Problem : Convert 1,000 mV to microvolts. Tutorial 3 1. Convert 5,000 nanoamperes (5,000 nA) to microamperes (uA). 2. Convert 893 nA to microamperes. 3. Convert 47,000 picofarads (47,000 pF) to microfarads (uF). 4. Convert 10,000 pF to microfarads. 5. Convert 0.00022 microfarad (0.00022 uF) to picofarads (pF). 6. Convert 0.0022 uF to picofarads 7. Convert 1,800 kilohms (1,800 kΩ) to megohms (MΩ). 8. Convert 2.2 kΩ to megohms. 9. Add 15 mA and 8,000 mA and express the sum in milliamperes. 10. Add 2,873 mA to 10,000 uA; express the sum in milliamperes 11. Convert 0.01 MV to kilovolts (kV). 12.Convert 250,000 pA to milliamperes (mA). 13. Add 0.05 MW and 75 kW and express the result in kW. 14. Add 50 mV and 25,000 uV and express the result in mV. 15. Which is larger: 2000 pF or 0.02 μF?  1.2 Current and charge  Define the electrical charge and electrical current CHARGE Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). The charge e on an electron is negative and equal in magnitude to 1.602×10−19 C, while a proton carries a positive charge of the same magnitude as the electron. The presence of equal numbers of protons and electrons leaves an atom neutrally charged The following points should be noted about electric charge: 1. The coulomb is a large unit for charges. In 1 C of charge, there are 1/(1.602 × 10−19) = 6.24 × 1018 electrons. 2. According to experimental observations, the only charges that occur in nature are integral multiples of the electronic charge e = −1.602 × 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 current due to flow of electronic charge in a conductor.  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 electric current. It is conventional to take the current flow as the movement of positive charges, that is, opposite to the flow of negative charges,  CURRENT  Electric current is the time rate of change of charge, measured in amperes (A) where current is measured in amperes (A), and 1 ampere = 1 coulomb/second The charge transferred between time t0 and t is obtained by integrating both sides There can be several types of current; that is, charge can vary with time in several ways that may be represented by different kinds of mathematical functions.  If the current does not change with time, but remains constant, we call it a direct current (dc) A direct current (dc) is a current that remains constant with time By convention the symbol I is used to represent such a constant current. Dc voltage sources can be divided into three broad categories: (1) batteries (chemical action), (2) generators (electromechanical), and (3) power supplies (rectification). A time-varying current is represented by the symbol i. A common form of time-varying current is the sinusoidal current or alternating current (ac) An alternating current (ac) is a current that varies sinusoidally with time.  EXAMPLE 9  How much charge is represented by 4,600 electrons?  Solution: Each electron has −1.602 × 10−19 C. Hence 4,600 electrons will have : =−1.602 × 10−19 C/electron × 4,600 electrons = −7.369 × 10−16 C EXERCISE 1 Calculate the amount of charge represented by two million protons. Answer: +3.204 × 10−13 C EXERCISE 2 A conductor has a constant current of five amperes. How many electrons pass a fixed point on the conductor in one minute? Answer:  EXAMPLE 10  If 840 coulombs of charge pass through the imaginary plane during a time interval of 2 minutes, what is the current? Solution : Convert t to seconds. Thus,  EXAMPLE 11  The charge flowing through the imaginary surface is 0.16 C every 64 ms. Determine the current in amperes Solution:  EXAMPLE 12  Determine the time required for 4 x 1016 electrons to pass through the imaginary surface if the current is 5 mA. Solution: Determine Q: Determine t:  Tutorial 4 1. What is the current in amperes if 9 coulombs of charge flow past a point in an electric circuit in 3 seconds? Answer: 3 Amperes 2. A circuit has a current of 5 amperes. How long does it take for one coulomb to pass a given point in the circuit? Answer: 0.2 seconds 3. If a current of 5 A flows for 2 minutes, find the quantity of electricity transferred Answer:. Q=600 C 1.3 Voltage, Energy and Power.  4. Define voltage, energy, power and their relationship. Voltage To move the electron in a conductor in a particular direction requires some work or energy transfer. This work is performed by an external electromotive force (emf), typically represented by the battery.  Voltage  This emf is also known as voltage or potential difference.  The voltage between two points a and b in an electric circuit is the energy (or work) needed to move a unit charge from a to b; mathematically, where w is energy in joules (J) and q is charge in coulombs (C). The voltage or simply v is measured in volts (V). Voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V).  The voltage across an element (represented by a rectangular block) connected to points a and b.  The plus (+) and minus (-) signs are used to define reference direction or voltage polarity.  The Vab can be interpreted in two ways: 1. Point a is at a potential of Vab volts higher than point b, or 2. The potential at point a with respect to point b is Vab.  EXAMPLE 13  An energy source forces a constant current of 2 A for 10 s to flow through a light bulb. If 2.3 kJ is given off in the form of light and heat energy, calculate the voltage drop across the bulb Solution:  EXAMPLE 14  To move charge q from point a to point b requires -30 J. Find the voltage drop if: (a) q=6 C, (b) q=-3 C  Answer: Answer: (a) -5V, (b) 10 V  EXAMPLE 15  Find the potential difference between two points in an electrical system if 60 J of energy are expended by a charge of 20 C between these two points. Solution:  EXAMPLE 16  Determine the energy expended moving a charge of 50 µC through a potential difference of 6 V. Solution:  Tutorial 5 1. If it takes 35 J of energy to move a charge of 5 C from one point to another, what is the voltage between the two points? Answer : 7 V  2. The voltage between two points is 19 V. How much energy is required to move 67 1018 electrons from one point to the other? Answer : 204 J  3. The potential difference between two points is 140 mV. If 280 mJ of work are required to move a charge Q from one point to the other, what is Q? Answer : 2 mC  Power  Power is the time rate of expending or absorbing energy, measured in watts (W). where p is power in watts (W), w is energy in joules (J), and t is time in seconds (s) or p is a time varying quantity and is called the instantaneous power. Thus, the power absorbed or supplied by an element is the product of the voltage across the element and the current through it. +p : power is being delivered to element or (+sign) : power is absorbed by the element -p : power is being supplied by the element (-sign)  How to know the power have + or - signs?  Current direction and voltage polarity play a major role in determining the sign of power  By the Passive Sign Convention: +p : current enters through the + polarity of the voltage (p = +vi or vi > 0 implies that the element is absorbing power). -p : current enters through the - polarity of the voltage (p = -vi or vi < 0 the element is releasing or supplying power).  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. Reference polarities for power using the passive sign convention: (a) absorbing power, (b) supplying power EXAMPLE 17  Calculate the power consumed in the circuit Solution: EXAMPLE 18  What voltage is required to deliver 2 amperes of current at 200 watts? Solution:  EXAMPLE 19  How much current does a 100-watt, 120- volt light bulb use? Solution Tutorial 6  1. Define power as it relates to electricity.  2. What unit is used to measure power?  3. Calculate the missing value:  a. P = ?, E = 12 V, I = 1 A  b. P = 1000 W, E = ?, I = 10 A  c. P = 150 W, E = 120 V, I = ?  d. P =? ,E = 30 V, I = 40 mA  e. P = 1 W, E = ?, I = 10 mA  f. P = 12.3 W, E = 30 V, I = ?  Energy  Energy, w is the capacity to do work, measured in joules (J).  The Law of Conservation of Energy: The algebraic sum of power in the circuit at any instant of time must be zero.  The total power supplied to the circuit must balance the total power absorbed.  From equation p=vi, the energy absorbed or supplied by an element from time t0 to time t is;  The electric power utility companies measure energy in watt-hours (Wh), where:  EXAMPLE 20  How much energy does a 100-W electric bulb consume in two hours? Solution:  EXAMPLE 21  A stove element draws 15 A when connected to a 240-V line. How long does it take to consume 180 kJ? Answer: 50 s.  1.4 Passive and Active Components 5. Explain and identify passive and active elements. (C2)  An active element is capable of generating energy while a passive element is not.  Examples of passive elements are resistors, capacitors, and inductors.  Typical active elements include generators, batteries, and operational amplifiers.  Active Elements  The most important active elements are voltage or current sources that generally deliver power to the circuit connected to them.  There are two kinds of sources: independent and dependent sources  An ideal independent voltage source delivers to the circuit whatever current is necessary to maintain its terminal voltage.  Physical sources such as batteries and generators may be regarded as approximations to ideal voltage sources Symbols for independent voltage sources: (a) used for constant or time- varying voltage (b) used for constant voltage (dc)  An ideal independent current source is an active element that provides a specified current completely independent of the voltage across the source.  The current source delivers to the circuit whatever voltage is necessary to maintain the designated current.  The symbol for an independent current source is displayed in Fig, where the arrow indicates the direction of current, i. Symbol for independent current source.  Dependent sources are usually designated by diamond-shaped symbols.  Since the control of the dependent source is achieved by a voltage or current of some other element in the circuit, and the source can be voltage or current, it follows that there are four possible types of dependent sources, namely: 1. A voltage-controlled voltage source (VCVS). 2. A current-controlled voltage source (CCVS). 3. A voltage-controlled current source (VCCS). 4. A current-controlled current source (CCCS).  Symbols for: a) dependent voltage source, b) dependent current source  Dependent sources are useful in modeling elements such as transistors, operational amplifiers, and integrated circuits.  An example of a current-controlled voltage source is shown on the right-hand side of Fig., where the voltage of the voltage source depends on the current i through element C.  The value of the dependent voltage source is 10i V (and not 10i A) because it is a voltage source.  The key idea to keep in mind is that a voltage source comes with polarities (+ -) in its symbol, while a current source comes with an arrow, irrespective of what it depends on The source on the right- hand side is a current- controlled voltage source EXAMPLE 24  Calculate the power supplied or absorbed by each element Solution: Apply the sign convention for power  For P1, the 5-A current is out of the positive terminal (or into the negative terminal); hence, P1 = - 20(5) = - 100 W Supplied power  For P2 and P3, the current flows into the positive terminal of the element in each case P2 = 12(5) = 60 W Absorbed power P3 = 8(6) = 48 W Absorbed power  For P4, the voltage is 8 V (positive at the top), the same as the voltage for P3 since both the passive element and the dependent source are connected to the same terminals.  (Remember that voltage is always measured across an element in a circuit.) Since the current flows out of the positive terminal, P4 = 8(0.2I) = 8(-0.2 x 5) = - 8 W Supplied power  The 20-V independent voltage source and 0.2I dependent current source are supplying power to the rest of the network, while the two passive elements are absorbing power. P1 + P2 + P3 + P4 = -100 + 60 + 48 - 8 = 0 (The total power supplied equals the total power absorbed) EXAMPLE 22  Compute the power absorbed or supplied by each component of the circuit in Fig. Answer: 1.5 Resistors  6. Describe basic types of resistors. (C2)  What is a resistor?  A passive two-terminal electrical component that implements electrical resistance as a circuit element.  In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. Types of resistors 7. Identify resistance by color code or labelling. (C1) Resistor Color Codes END OF SUB TOPIC