TEL303 — Electric Circuit Theory: Lecture Note

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This is the complete lecture note for TEL303 Electric Circuit Theory. You can read it online below, open it in the full viewer, or download the PDF for offline study. It pairs with the course's video lectures, so you can read and watch together.

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Course code: TEL 303 Course title: Electric Circuit Theory Course credit load: 2 Units Series 1: Basic Concepts, Basic Laws, and Methods of Circuit Analysis • Part 1.1: Basic Concepts o Sub Part 1.1.1: Introduction to Circuit Theory and Systems of Units o Sub Part 1.1.2: Charge and Current o Sub Part 1.1.3: Voltage, Power, Energy, and Circuit Elements • Part 1.2: Basic Laws o Sub Part 1.2.1: Ohm's Law o Sub Part 1.2.2: Nodes, Branches, Loops, and Kirchhoff's Laws o Sub Part 1.2.3: Series and Parallel Resistors: Voltage and Current Division, and Wye-Delta Transformations • Part 1.3: Nodal Analysis o Sub Part 1.3.1: Nodal Analysis o Sub Part 1.3.2: Nodal Analysis with Voltage Sources o Sub Part 1.3.3: Nodal Analysis by Inspection • Part 1.4: Mesh Analysis o Sub Part 1.4.1: Mesh Analysis o Sub Part 1.4.2: Mesh Analysis with Current Sources o Sub Part 1.4.3: Mesh Analysis by Inspection, and Nodal versus Mesh Analysis

Introduction This is the opening Series of TEL 303: Electric Circuit Theory. This Series lays the foundation for everything that follows in this course, introducing the basic quantities, units, and laws that govern every electric circuit, before moving on to the two systematic methods, nodal analysis and mesh analysis, used throughout the rest of this course to analyse circuits of any complexity. The aim of this Series is to equip you with a sound understanding of the basic concepts of charge, current, voltage, power, and energy; the basic laws of Ohm and Kirchhoff, together with series and parallel resistor simplification; and the systematic methods of nodal and mesh analysis. We shall commence this Series by examining the basic concepts and units used throughout circuit theory. Next, we will consider Ohm's law, Kirchhoff's laws, and the simplification of series and parallel resistor networks. Following that, our attention turns to nodal analysis, including circuits containing voltage sources. Finally, we will conclude by examining mesh analysis, including circuits containing current sources, and by comparing the two methods. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: identify basic circuit elements and quantities, and express them in standard SI units, • SLO 1.2: calculate the power absorbed or supplied by a circuit element using the passive sign convention, • SLO 1.3: apply Ohm's law and identify nodes, branches, and loops in a circuit, • SLO 1.4: apply Kirchhoff's current and voltage laws, and the voltage and current division principles, to resistive circuits, • SLO 1.5: analyse circuits using nodal analysis, • SLO 1.6: analyse circuits containing voltage sources using nodal analysis, and set up nodal equations by inspection, • SLO 1.7: analyse circuits using mesh analysis, including circuits containing current sources, • SLO 1.8: select and apply the appropriate method, nodal or mesh analysis, for a given circuit.

1.1 Basic Concepts 1.1.1 Introduction to Circuit Theory and Systems of Units Electric circuit theory provides the fundamental tools needed to analyse and design the electrical and electronic systems encountered throughout this course, treating a circuit as an interconnection of circuit elements joined together by conducting wires through which current may flow. These circuit elements are broadly classified as either active elements, such as voltage and current sources, which are capable of supplying energy to a circuit, or passive elements, such as resistors, capacitors, and inductors, which can only absorb or store energy. The International System of Units (SI), the standard system of units adopted throughout engineering and science, defines seven base units, including the metre (length), kilogram (mass), second (time), and ampere (electric current), from which every other electrical quantity used in this course, such as voltage, power, and energy, is obtained as a derived unit, and standard prefixes such as kilo, milli, and micro are used throughout to keep numerical values conveniently sized. Worked example: A resistor is specified as having a resistance of 4.7 kΩ, where the prefix 'kilo' (k), one of the SI standard prefixes, indicates a multiplying factor of 10³, so that 4.7 kΩ = 4700 Ω. Application: Consistent use of SI units and standard prefixes throughout circuit analysis and design is essential, since a numerical answer expressed in the wrong unit, or with the wrong prefix, is as much an error as an incorrect calculation. Fill in the blank: The SI system defines ________ base units, from which all other electrical quantities are derived. A resistance of 4.7 kΩ is equal to ________ Ω. 1.1.2 Charge and Current Electric charge is an intrinsic electrical property of matter, measured in coulombs (C), and is the most basic quantity in electric circuit theory, since every other electrical quantity may ultimately be defined in terms of it. Charge obeys the law of conservation of charge, meaning that charge can neither be created nor destroyed, only transferred from one place to another. Electric current is the time rate of change of charge passing through a given point in a circuit, i = dq/dt, measured in amperes (A), where one ampere corresponds to a charge flow of one coulomb per second. By convention, the direction of conventional current is taken as the direction in which positive charge would flow, even in conductors such as metals where the charge carriers are in fact negatively charged electrons. Worked example: A wire carries a constant current of 2 A. The charge that flows past a given point in 3 seconds is q = i × t = 2 × 3 = 6 C.

Application: Correctly relating current and charge through i = dq/dt is essential for analysing circuits containing capacitors, examined in a later Series of this course, in which the current depends directly on how quickly the stored charge is changing. Fill in the blank: Electric current is defined as the time rate of change of ________. A current of one ampere corresponds to a charge flow of one ________ per second. 1.1.3 Voltage, Power, Energy, and Circuit Elements Voltage (or potential difference) between two points in a circuit is the energy required to move a unit charge between those points, measured in volts (V), where one volt corresponds to one joule per coulomb. Voltage is always defined between two points, and is commonly established by an electromotive force, such as a battery, which maintains a fixed potential difference across its own terminals regardless of the current drawn from it, within its rated limits. Power, measured in watts (W), is the time rate of expending or absorbing energy, p = vi, and its sign, determined by the passive sign convention, indicates whether a given circuit element is absorbing or supplying power at any instant. Energy, measured in joules (J), is the integral of power over time, w = ∫p dt, and is the quantity an electricity consumer is ultimately billed for, usually expressed commercially in kilowatt-hours rather than joules. Worked example: A circuit element has a voltage of 10 V across it and a current of 2 A flowing into its positive terminal. Using the passive sign convention, the power absorbed is p = vi = 10 × 2 = 20 W. Application: Correctly applying the passive sign convention to determine whether a given circuit element is absorbing or supplying power is an essential check applied throughout circuit analysis, since the total power supplied in any circuit must always equal the total power absorbed. Fill in the blank: One volt corresponds to one joule per ________. A circuit element with current flowing into its positive terminal is, by the passive sign convention, ________ power.

Figure 1.1: The passive sign convention for a two-terminal circuit element. Pilot questions 1.1 1. Define electric charge and state its SI unit. (Linked to SLO 1.1) 2. State the relationship between current and charge. (Linked to SLO 1.1) 3. Calculate the charge that flows past a point in 4 seconds for a constant current of 3 A. (Linked to SLO 1.1) 4. State the passive sign convention. (Linked to SLO 1.2) 5. Calculate the power absorbed by a circuit element with a voltage of 5 V and a current of 4 A flowing into its positive terminal. (Linked to SLO 1.2) 1.2 Basic Laws 1.2.1 Ohm's Law Ohm's law states that the voltage across a resistor is directly proportional to the current flowing through it, v = iR, where R is the resistance, measured in ohms (Ω), a property that depends on a material's resistivity together with its physical length and cross-sectional area. A resistor that obeys Ohm's law over its entire operating range is described as linear, and every resistor considered in this course is assumed to behave in this ideal, linear manner. The reciprocal of resistance is conductance, G = 1/R, measured in siemens (S), providing an alternative and sometimes more convenient way of expressing a resistor's current-voltage

relationship, i = Gv. Two important limiting cases are worth noting: a short circuit corresponds to R = 0, while an open circuit corresponds to R = ∞, both of which arise frequently when analysing practical circuits. Worked example: A

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