TEL102 — Introduction to Electrical Engineering: Lecture Note

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Course code: TEL 102 Course title: Introduction to Electrical Engineering Course credit load: 2 Units Series 1: Electrical Circuit Fundamentals, Electrostatics, and Circuit Theorems • Part 1.1: Electrical Circuit Fundamentals and Quantities o Sub Part 1.1.1: Electrical quantities and their units o Sub Part 1.1.2: Direct current and alternating current signals o Sub Part 1.1.3: Root-mean-square, average, and instantaneous values • Part 1.2: Electrostatics and Capacitance o Sub Part 1.2.1: Electrostatics and the capacitor o Sub Part 1.2.2: Capacitance of an isolated sphere and a parallel plate capacitor o Sub Part 1.2.3: Capacitors in series and in parallel • Part 1.3: Basic Electrical Laws o Sub Part 1.3.1: Ohm's Law o Sub Part 1.3.2: Kirchhoff's Laws o Sub Part 1.3.3: The Superposition Theorem • Part 1.4: Network Theorems and Transformations o Sub Part 1.4.1: Thevenin's Theorem o Sub Part 1.4.2: Delta-Star transformation o Sub Part 1.4.3: Star-Delta transformation Introduction Every device that runs on electricity, from a simple torchlight to a national power grid, depends on the same underlying principles: quantities that can be measured and expressed in standard units, charge that can be stored and released, and laws that govern how current and voltage

behave in a network of components. This Series lays that essential foundation for the rest of the course. The aim of this Series is to equip you with a sound understanding of basic electrical quantities, electrostatics and capacitance, and the fundamental laws and theorems used to analyse electrical circuits. We shall commence this Series by examining the fundamental electrical quantities, direct and alternating current signals, and the root-mean-square, average, and instantaneous values of an alternating quantity. Next, we will consider electrostatics and capacitance, including the capacitance of isolated spheres, parallel plate capacitors, and capacitors connected in series and in parallel. Following that, our attention turns to the basic laws of Ohm and Kirchhoff and the Superposition Theorem. Finally, we will conclude by examining Thevenin's Theorem and the delta-star and star-delta transformations used to simplify electrical networks. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: define the fundamental electrical quantities and state their SI units, • SLO 1.2: calculate the root-mean-square, average, and instantaneous values of an alternating quantity, • SLO 1.3: calculate the capacitance of an isolated sphere and a parallel plate capacitor, • SLO 1.4: calculate the equivalent capacitance of capacitors connected in series and in parallel, • SLO 1.5: apply Ohm's Law and Kirchhoff's Laws to solve electrical circuits, • SLO 1.6: apply the Superposition Theorem to analyse electrical circuits, • SLO 1.7: apply Thevenin's Theorem to simplify and solve electrical networks, • SLO 1.8: perform Delta-Star and Star-Delta transformations on electrical networks. 1.1 Electrical Circuit Fundamentals and Quantities 1.1.1 Electrical quantities and their units An electrical quantity is any physical property associated with electric charge or its effects that can be measured, such as current, voltage, resistance, power, and energy, and each is expressed

in a specific SI unit: current in amperes (A), potential difference in volts (V), resistance in ohms (Ω), power in watts (W), and energy in joules (J), providing the common language in which all subsequent circuit analysis in this course is expressed. Electric current is the rate of flow of electric charge past a point in a circuit, defined as I = Q/t, where Q is the charge in coulombs and t is the time in seconds, while electromotive force (EMF) is the total energy supplied by a source, such as a battery or generator, to drive current around a circuit, distinguished from potential difference, which is the energy used or dissipated between two points in the external circuit, a distinction of direct relevance whenever internal resistance is taken into account. Worked example: A current of 5 A flows through a conductor for 20 seconds, so the charge transferred is Q = It = 5 × 20 = 100 C, illustrating the direct relationship between current, charge, and time. Fill in the blank: Electric current is measured in the SI unit called the ________. The energy supplied by a source to drive current around a circuit is called the ________. 1.1.2 Direct current and alternating current signals Direct current (DC) is an electric current that flows in one direction only, with a magnitude that may be constant or varying but never reverses polarity, typical sources being batteries and DC generators, and is the form of supply assumed in most basic circuit analysis before the effects of time-varying signals are introduced. Alternating current (AC) is an electric current that periodically reverses direction and varies continuously in magnitude, typically following a sinusoidal waveform described by i(t) = Im sin(ωt), where Im is the maximum (peak) value, ω is the angular frequency in radians per second, and t is time, and is the form in which electrical power is generated, transmitted, and distributed in practice, making its properties of direct engineering importance. Worked example: A domestic AC supply with a peak voltage of 325 V has instantaneous value v = 325 sin(ωt); at the instant when ωt = 30°, v = 325 sin(30°) = 162.5 V, showing how the sinusoidal equation gives the voltage at any point in the cycle. Fill in the blank: A current that flows in one direction only is called ________ current. A sinusoidal current is described by the equation i(t) = Im sin(________). 1.1.3 Root-mean-square, average, and instantaneous values The instantaneous value of an alternating quantity is its magnitude at a particular instant in time, denoted by lower-case letters such as i or v, while the maximum (peak) value, denoted Im or Vm, is the highest instantaneous value reached during a complete cycle. The root-mean-square (RMS) value of an alternating current is the value of direct current that would produce the same heating effect in a given resistance, calculated for a sinusoidal

waveform as Irms = Im/√2 (approximately 0.707 Im), while the average value over a half-cycle is Iav = 2Im/π (approximately 0.637 Im); the form factor is the ratio of the RMS value to the average value (approximately 1.11 for a pure sine wave), and the crest factor is the ratio of the maximum value to the RMS value (approximately 1.414 for a pure sine wave), with equipment ratings invariably expressed in RMS values since these correspond directly to equivalent heating or working capacity. Worked example: A 230 V AC mains supply is quoted as an RMS value, so its peak value is Vm = Vrms × √2 = 230 × 1.414 = 325.2 V, and its average value is Vav = 0.637 × 325.2 = 207.1 V, figures that recur throughout this course. Fill in the blank: The RMS value of a sinusoidal current is related to its maximum value by Irms = Im/________. The ratio of the RMS value to the average value of a waveform is called the ________ factor. Figure 1.1: Graphical comparison of AC and DC signal waveforms with marked RMS and average levels. Pilot questions 1.1 1. Define electric current and state its SI unit. (Linked to SLO 1.1) 2. Distinguish between electromotive force and potential difference. (Linked to SLO 1.1) 3. Distinguish between direct current and alternating current. (Linked to SLO 1.2)

4. Calculate the RMS value of a sinusoidal current with a peak value of 10 A. (Linked to SLO 1.2) 5. Explain the significance of the form factor and crest factor of a waveform. (Linked to SLO 1.2) 1.2 Electrostatics and Capacitance 1.2.1 Electrostatics and the capacitor Electrostatics is the branch of electricity concerned with electric charges at rest and the fields and forces they produce, underpinning the behaviour of devices such as capacitors that store energy in an electric field rather than through the flow of current. A capacitor is a passive electrical component consisting of two conducting plates separated by an insulating material known as a dielectric, capable of storing electric charge and energy when a potential difference is applied across its plates, with capacitance, measured in farads (F), defined as the ratio of the charge stored to the potential difference applied, C = Q/V. Worked example: A capacitor stores a charge of 2 mC when a potential difference of 100 V is applied across it, giving a capacitance of C = Q/V = 0.002/100 = 20 µF, the standard method used to determine capacitance from measured charge and voltage. Fill in the blank: The branch of electricity concerned with charges at rest is called ________. Capacitance is measured in the SI unit called the ________. 1.2.2 Capacitance of an isolated sphere and a parallel plate capacitor The capacitance of an isolated sphere of radius r, situated in a medium of absolute permittivity ε, is given by C = 4πεr, showing that capacitance increases with both the physical size of the conductor and the permittivity of the surrounding medium. The capacitance of a parallel plate capacitor, consisting of two plates of area A separated by a distance d, is given by C = εA/d, where ε is

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