Basic Electricity & Electronics PDF

# Basic Electricity & Electronics ## Circuit Variables D. Ahmed Tohamy Electronics and Communications Department Faculty of Engineering Sphinx University ## Course Specifications | Assessment Method | Percentage | |---|---| | Final Exam | 40% | | Mid-term Exam | 20% | | Tutorial Quiz | 10% | | L...

# Basic Electricity & Electronics ## Circuit Variables D. Ahmed Tohamy Electronics and Communications Department Faculty of Engineering Sphinx University ## Course Specifications | Assessment Method | Percentage | |---|---| | Final Exam | 40% | | Mid-term Exam | 20% | | Tutorial Quiz | 10% | | Lecture Quiz | 10% | | Semester Work | 10% | ## List of References ### Essential Books * Christopher R Robertson, "Fundamental Electrical and Electronic Principles", 3rd edition, Nownes, 2008 * J. Irwin and R. Nelms, "Basic Engineering Circuit Analysis", 10th edition, Wiley, 2011 ### Recommended Books * J. W. Nilsson and Susam A. Riedel, "Electric Circuits", 8th edition, Pearson Prentice Hall, 2008. ## Anything in Common? * An electric circuit is a mathematical model that approximates the behavior of an actual electrical system. * Here, we use circuit theory, rather than electromagnetic field theory, to study a physical system represented by an electric circuit, based on the following three assumptions: * Electrical effects happen instantaneously throughout a system (lumped-parameter system) * The net charge on every component in the system is always zero * There is no magnetic coupling between the components in a system ## Problem Solving * Identify what's given and what's to be found. * Sketch a circuit diagram or other visual model. * Think of several solution methods and decide on a way of choosing among them. * Calculate a solution. * Use your creativity. * Test your solution. ## Balancing Power **Diagram:** A picture of a house with a simplified circuit drawn next to it * a and b: electrical source to the home. * c, d, and e: the wires that carry the electrical current from the source to the devices in the home requiring electrical power. * f, g, and h: lamps, televisions, hair dryers, refrigerators, and other devices that require power. ## The International System of Units | Quantity | Basic Unit | Symbol | |---|---|---| | Length | meter | m | | Mass | kilogram | Kg | | Time | second | s | | Electric current | ampere | A | | Thermodynamic temperature | kelvin | K | | Amount of sumbstance | mole | mol | | Luminous intensity | candela | cd | ## Derived Units in SI | Quantity | Unit Name (Symbol) | Formula | |---|---|---| | Frequency | hertz (Hz) | $s^{-1}$ | | Force | newton (N) | $kg. m/s^2$ | | Energy or work | joule (J) | $N.m$ | | Power | watt (W) | $J/s$ | | Electric charge | coulomb (C) | $A.s$ | | Electric potential | volt (V) | $J/C$ | | Electric resistance | ohm (Ω) | $V/A$ | | Electric conductance | siemens (S) | $A/V$ | | Electric capacitance | farad (F) | $C/V$ | | Magnetic flux | weber (Wb) | $V.s$ | | Inductance | henry (H) | $Wb/A$ | ## Standardized Prefixes to Signify Powers of 10 | Prefix | Symbol | Power | |---|---|---| | atto | a | $10^{-18}$ | | femto | f | $10^{-15}$ | | pico | p | $10^{-12}$ | | nano | n | $10^{-9}$ | | micro | μ | $10^{-6}$ | | milli | m | $10^{-3}$ | | centi | c | $10^{-2}$ | | deci | d | $10^{-1}$ | | deka | da | $10^{1}$ | | hecto | h | $10^{2}$ | | kilo | k | $10^{3}$ | | mega | M | $10^{6}$ | | giga | G | $10^{9}$ | | tera | T | $10^{12}$ | ## Example #1 * If a signal can travel in a cable at 80% of the speed of light, what length of cable, in inches, represents 1ns? **Solution:** $\frac{2.4 x 10^8 meters}{1 second} \times \frac{1 second}{10^9 nanoseconds} \times \frac{100 centimeters}{1 meter} \times \frac{1 inch}{2.54 centimeters} = \frac{(2.4 \times 10^8)(100)}{(10^9)(2.54)} = 9.45 inches/nanosecond$ ## Voltage and Current * The charge is bipolar, meaning that electrical effects are described in terms of positive and negative charges. * The electric charge exists in discrete quantities, which are integral multiples of the electronic charge, $1.6022 \times 10^{-19} C$. * Electrical effects are atributed to both the separation of charge (Voltage) and charges in motion (Current). ## Voltage * whenever positive and negative charges (q) are separated, energy (w) is expended. Voltage (v) is the energy per unit charge created by the separation. * w: the energy in joules (J) * q: the charge in coulombs (C) * v: the voltage in volts (V) * 1 V is the same as 1 J/C. * Mathematically, $v= \frac{dw}{dq}$ ## Signs of the Terminals **Diagram**: A simple circuit with one resistor and two terminals labeled 1 and 2. One side of the terminals has a + sign on it and the other has a - sign. An arrow labeled "i" is going from terminal 1 to terminal 2. * The placement of +sign in terminal 1 indicates that terminal 1 is v volts positive with respect to terminal 2. * Note: A voltage can exist between a pair of electrical terminals whether a current is flowing or not. ## Example #2 **Diagram**: Four different configurations of a 2 terminal circuit with plus and minus signs labeling the voltage. * (a, b) Terminal 2 is 5V positive with respect to terminal 1. * (c, d) Terminal 1 is 5V positive with respect to terminal 2. ## Notes * The plus-minus pair of algebraic signs does not indicate the actual polarity of the voltage but is simple part of a convention that enables us to talk unambiguously about the voltage across the terminal pair. * The definition of any voltage must include plus-minus sign pair. ## Current * The motion of charges forms the electric current in a wire. The current (i) has both a numerical value and a direction associated with it; it is a measure of the rate at which charge (q) is moving past a given reference point in a specified direction. * i: the current in amperes (A) * q: the charge in coulombs (C) * t: the time in seconds (s) * 1 A is the same as 1 C/s. * Mathematically, $i = \frac{dq}{dt}$ ## The Direction of Current Flow **Diagram:** Two diagrams, one of a box with positive ions and the other of negative ions, both showing the flow of charge. Arrows indicate the direction of flow and an electric field labeled "B" is drawn inside the box. * (a) Positive ions * (b) Negative ions ## Direction is Important! **Diagram:** Three different curved arrows labeled with "i(t)" above each one. The first arrow is pointing in the direction of the curve, the second arrow is pointing opposite the curve, and the third arrow is pointed in the direction of the curve. * We should pay close attention to that the arrow is a fundamental part of the definition of the current. ## DC and AC **Diagram:** Two graphs: The first graph shows a straight line. The second graph shows a sinusoidal wave. Both graphs are labeled on the Y axis with "i" and on the X axis with "t" * A direct current (dc) is a current that remains constant with time. * An alternating current (ac) is a current that reverses (changes) its direction with time (varies sinusoidally). ## Example #3 **Diagram:** A simplified circuit with one resistor and two terminals labeled 1 and 2. The side of the terminals with the + sign is labeled with a "v" and the side with the - sign is labeled with an "i". * No charge exists at the upper terminal of the element for t < 0. At t = 0, a 5 A current begins to flow into the upper terminal. * a) Derive the expression for the charge accumulating at the upper terminal of the element for t > 0. * b) If the current is stopped after 10 seconds, how much charge has accumulated at the upper terminal? **Solution:** * a) From the definition of current given in Eq. 1.2, the expression for charge accumulation due to current flow is $q(t) = \int_{0}^{t} i(x)dx$ Therefore, we have: * $q(t) = \int_{0}^{t} 5dx = 5x |_0^t = 5t - 5(0) = 5t$ C for $t \ge 0$ * b) The total charge that accumulates at the upper terminal in 10 seconds due to a 5 A current is 5(t) = 5(10) = 50 C. ## Notes **Diagram:** A simplified circuit with one resistor and two terminals labeled 1 and 2. The side of the terminals with the + sign is labeled with a "v" and the side with the - sign is labeled with an "i". * Whenever the reference direction for the current in an element is in the direction of the reference voltage drop across the element, use a positive sign in any expression that relates the voltage to the current. Otherwise, use a negative sign. ## Power and Energy * Power (p) is the time rate of expending or absorbing energy (w). * Mathematically, $p = \frac{dw}{dt} = \frac{dwdq}{dqdt}= vi$ * p: the power in watts (W) * w: the energy in joules (J) * t: the time in seconds (s) * q: the charge in coulombs (C) * v: the voltage in volts (V) * i: the current in amperes (A) ## Positive Sign Convention **Diagram:** Four different diagrams of circuits with labeled voltage, current, and power. * (a) p =vi * (b) p = -vi * (c) p = -vi * (d) p = vi * The algebraic sign of power is based on charge movement through voltage drops and rises. As positive charges move through a drop in voltage, they lose energy, and as they move through a rise in voltage, they gain energy. ## Example #4 **Diagram:** There are three circuits, labeled (a), (b), and (c). Each circuit has a resistor with labeled voltage and current. * If the power is positive (that is, if p > 0), power is being delivered to the circuit inside the box. If the power is negative (that is, if p < 0), power is being extracted from the circuit inside the box. * Compute the power absorbed by each part in the following: **Solution for the Example #4** * In (a), with +3 A flowing into the positive reference terminal, we compute: $P = (2 V) (3 A) = 6 W$ of the power absorbed by the element. * (b) shows a slightly different picture. Now we have a current of -3 A flowing into the positive reference terminal. However, the voltage as defined is negative. This gives us an absorbed power: $P = (-2 V) (-3 A) = 6 W$ * In (c), we again apply the passive sign convention rulers and compute an absorbed power: $P = (4 V) (-5 A) = -20 W $ Since we computed a negative absorbed power, this tells us that the element in the Figure is actually supplying +20 W (i.e., it's a source of energy). ## Balancing Power * The law of conservation of energy * Energy is the capacity to do work, measured in joules (J). * Mathematically, $ \sum{p = 0} $ * $w = \int_{t_0}^{t}pdt = \int_{t_0}^{t} vidt $ ## Example #5 **Diagram:** An 8 component circuit with labeled voltage, current, and power. * Compute the power absorbed by each element in the following circuit? # Example #5 answer **Diagram:** An 8 component circuit with labeled voltage, current, and power. * $P_a = v_a i_a = (120)(-10) = -1200 W$ * $P_b= - v_b i_b = -(120)(9) = -1080 W$ * $P_c = v_c i_c = (10)(10) = 100 W$ * $P_d = -v_d i_d = -(10)(1) = -10 W$ * $P_e = v_e i_e = (-10)(-9) = 90 W$ * $P_g = v_g i_g = (120)(4) = 480 W$ * $P_f = -v_f i_f = -(-100)(5) = 500 W$ * $P_h = v_h i_h = (-220)(-5) = 1100 W$ $P_{supplied} = P_a + P_b + P_d = -1200 - 1080 - 10 = -2290 W$ $P_{absorbed} = P_c + P_e + P_f + P_g + P_h = 100 + 90 + 500 + 480 + 1100 = 2270 W$ $P_{supplied} + P_{absorbed} = -2290 + 2270 = -20 W$ * **Something is wrong – if the values for voltage and current in this circuit are correct, the total power should be zero!** **Diagram:** An 8 component circuit with labeled voltage, current, and power. ## Summary * Voltage * Current * Ideal basic circuit element * Passive sign convention * Power