Course Lectures of Basics of Electrical Engineering Electrical Engineering Dept. First year Chapter One : Basic Concepts and Laws Instructor : Ali Abdulkareem Al-Hashimi Basics of Electrical Engineering Lectures University of Missan / College of Engineering 1.1 SI System of Units : 1.1.1 Basic Units: Quantity Basic unit Symbol Length Meter m Mass Kilogram Kg Time Second s or sec. Electric current Ampere A Temperature Degree Kelvin K Luminous intensity Candela cd 1.1.2 Some scientific notations : In many cases, the (SI) units are either too small or too large to use conveniently. Standard prefixes, correspond to the power of 10, are applied to the basic unit as shown in the table below. Prefix Symbol Pico p nano n micro milli m centi c deci d kilo k mega M giga G Examples: 1 Power Basics of Electrical Engineering Lectures University of Missan / College of Engineering 1.2 Charge and Current : The concept of electric charge is the most basic quantity in an electric circuit . We all experience the effect of electric charge when we try to remove our wool sweater and have it stick to our body or walk across a carpet and receive a shock. Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). We know from elementary physics that all matter is made of fundamental building blocks known as atoms and that each atom consists of electrons, protons, and neutrons. We also know that 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. When a conducting wire (consisting of several atoms) is connected to a battery, 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. Electric current is the rate of change of charge measured in amperes (A). It is conventional to take the current flow as the movement of positive charges, that is, opposite to the flow of negative charges, as shown below . The current (i) is mathematically expressed as : The transferred charge may be obtained by integrating both sides of the equation above, which is : ∫ A direct current (DC) is a current that remains constant with time. The symbol (I) is usually used to represent such a current. An alternating current (AC) is a current that is varying with time. The symbol (i) is usually used to represent such a current. 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering Ex: The total charge entering a terminal is given by q = (5t sin 4πt) mC. Calculate the current at t = 0.5 seconds . Solution: i = dq / dt = d/dt (5t sin 4πt) mC/s = (5 sin 4πt + 20πt cos 4πt) mA At t = 0.5, i = 5 sin 2π + 10π cos 2π = 0 + 10π = 31.42 mA Ex: Determine the total charge entering a terminal between t = 1 s and t = 2 s if the current passing the terminal is i = (3t 2 − t) A. Solution: ∫ ) ∫( ( )| 1.3 Voltage: The voltage (or potential difference) is the energy required to move a unit charge through an element, measured in volts (V) . figure below shows the polarity of voltage ( ) This means that the potential of point (a) is higher than that of point (b), or : Like electric current, a constant voltage is called a DC voltage and is represented by (V), whereas a time-varying voltage is called an AC voltage and is represented by (v). 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering The voltage (Vab) 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 ( ) is energy in joules (J) and (q) is charge in coulombs (C) . 1.4 Power and Energy : Power is the time rate of expending or absorbing energy, measured in watts (W). We write this relationship as : where p is power in watts (W), w is energy in joules (J), and t is time in seconds (s). We have : If the power has a + sign, power is being delivered to or absorbed by the element. If, on the other hand, the power has a − sign, power is being supplied by the element . absorbing power supplying power The energy absorbed or supplied by an element from time ( ) to time ( ) is given by : ∫ ∫ Energy is the capacity to do work, measured in joules (J). The electric power utility companies measure energy in watt-hours (Wh), where : 1 Wh = 3,600 J 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering Ex: Find the power delivered to an element at (t = 3 ms) if the current entering its positive terminal is (i = 5 cos 60πt A) and the voltage is : (a) v = 3i, (b) v = 3 di/dt . Solution: (a) The voltage is v = 3i = 15 cos 60πt ; hence, the power is p = vi = 75 cos2 60πt W At t = 3 ms, p = 75 cos2(60π × 3 × 10−3) = 75 cos2 0.18π = 53.48 W (b) We find the voltage and the power as v = 3 * (di / dt) = 3(−60π)5 sin 60πt = −900π sin 60πt V p = vi = −4500π sin 60πt cos 60πt W Ex: How much energy does a 100-W electric bulb consume in two hours? Solution: w = pt = 100 W× 2 h = 200 Wh and w = 200 Wh * 3600 J = 720 kJ 1.5 Electric Circuit Elements : An element is the basic building block of a circuit. An electric circuit is simply an interconnection of the elements. Circuit analysis is the process of determining voltages across (or the currents through) the elements of the circuit. There are two types of elements found in electric circuits: passive elements and active elements. A passive element is not capable of generating energy. Examples of passive elements are resistors, capacitors, and inductors. An active element is capable of generating energy. Typical active elements include generators, batteries, and operational amplifiers. 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 independent source is an active element that provides a specified voltage or current that is completely independent of other circuit variables. A dependent (or controlled) source is an active element in which the source quantity is controlled by another voltage or current. 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering Independent Sources Dependent Sources Ex: Calculate the power supplied or absorbed by each element in figure below . Solution: p1 = 20(−5) = −100 W Supplied power p2 = 12(5) = 60 W Absorbed power p3 = 8(6) = 48 W Absorbed power p4 = 8(−0.2I) = 8(−0.2 × 5) = −8 W Supplied power 1.5.1 Voltage Source: It is a device which supplies a fixed terminal voltage even though the current drain may vary. There are two kinds of it : Ideal and non-ideal. Ideal Non-ideal 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering 1.5.2 Current source: It is a device which supplies a constant current to the load even though there will be variations in the terminal voltage. Ideal Non-ideal 1.6 Basic Laws : 1.6.1 Ohm's Law : Ohm’s law states that the voltage (V) across a resistor is directly proportional to the current (I) flowing through the resistor. That is : ⇒ Where (R) is the resistance which denotes the ability of an element to resist the flow of an electric current. It is measured in ohms ( ) . The resistance of any material with a uniform cross-sectional area (A) depends on (A) and its length ( ), as shown in figure below. In mathematical form, where (ρ) is known as the resistivity of the material in ( ). Good conductors, such as copper and aluminum, have low resistivities, while insulators, such as mica and paper, have high resistivities. 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering A short circuit is a circuit element with resistance approaching zero. An open circuit is a circuit element with resistance approaching infinity. Short circuit Open circuit 1.6.2 Conductance : A useful quantity in circuit analysis is the reciprocal of resistance (R), known as (conductance) and denoted by (G) : The conductance is a measure of how well an element will conduct electric current. It is measured in mhos ( ) or siemens ( S ). and or Ex: In the circuit shown, calculate the current, the conductance, and the power. Solution: or ( ) 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering 1.6.3 Nodes, Branches, and Loops : A branch represents a single element such as a voltage source or a resistor. A node is the point of connection between two or more branches. A loop is any closed path in a circuit. Ex: Determine the number of branches, nodes, and loops in the circuit shown in figure below : solution: there are 4 branches, 3 nodes, and 2 loops. Notes : Two or more elements connected in series carry the same current. Two or more elements connected to the same two nodes are in parallel and carry the same voltage across them. 1.6.4 Kirchoff's laws : Kirchhoff’s Current Law (KCL): It states that the algebraic sum of currents entering a node (or a closed boundary) is zero, or : The sum of the currents entering a node is equal to the sum of the currents leaving the node. Mathematically : ∑ or ∑ Where ( ∑ ) are the currents entering the node, while ( 1 ) are the currents leaving the node. Basics of Electrical Engineering Lectures University of Missan / College of Engineering Ex: For the network shown, calculate the total current. Solution: By KCL Kirchhoff’s Voltage Law (KVL): It states that the algebraic sum of all voltages around a closed path(or loop) is zero. Mathematically, it is expressed as : ∑ Where (M) is the number of voltages in the loop, and ( ) is the ( Ex: For the circuit shown: If we go around the loop in clockwise direction, the equation becomes : If we go around the loop in counterclockwise direction, the equation becomes : Ex: For the circuit shown, find V1 & V2 . 1 ) voltage. Basics of Electrical Engineering Lectures University of Missan / College of Engineering Solution: V1 = 2I , V2 = 3I Applying KVL : ∑ 20 - V1 + V2 = 0 20 – 2I + 3I =0 5I = 20 ⇒I = 4 A V1 = 8 V , V2 = 12 V Ex: Determine (I) and (Vo) in the circuit shown . Solution: By KVL : By ohm's law : By substituting (I), we get : ( ) ⇒ and 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering Note: ( ( ) ) where (a) and (b) are constants. Ex: a) b) c) d) ( ) e) f) Tutorial : 1) Write the following quantities in a shorter form. a) 50000 W b) 0.0008 A c) 0.000003 F 2) The voltage (v) across an element and the current through it are : ( ) ( ) ( ) Calculate: a) Total charge in the element from t = 2 s to t = 4 s . b) The power in the element at t = 1 s . c) Is this element supplying or absorbing power ? 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering 3) Find (Vo) and (Io) in the circuit below. 4) Find the currents and voltages in the circuit below. 5) Find (I) and (Vab) in the circuit shown below. 6) Determine all the currents and voltages in the figure below. 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering Homeworks: 1) The current flowing through an element is : { Calculate the total charge from t = 0 s to t = 2 s [6.667 C] 2) The voltage across an element and the current through it are given by : ( ) ( ) ( ) Determine: a) Total charge between t = 0 and t = 2 s. b) The power c) The energy absorbed in 3 s. [80 mC, 15.6 kJ] 3) Find the power in each element in the circuit below . 4) Find the resistance of a lightbulb whose rated 60 W, 220 V. [806.6 Ω] 1 Basics of Electrical Engineering Lectures University of Missan / College of Engineering 5) Determine the voltages V1 to V4 shown in figure below. [- 4 V, - 6 V, 4 V, - 2 V] 6) For the circuit below, find (Vo) and the power in the controlled source . [-4.44 V, 98.75 W] 1