Circuit Analysis

8 Key excerpts on "Circuit Analysis"

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  eBook - PDF

  Electric Circuit Theory

  Applied Electricity and Electronics

  • R. Yorke, P. Hammond(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  CHAPTER 4 Circuit Analysis 4 . 0 I N T R O D U C T I O N The process of Circuit Analysis consists of determining the currents in, and potential differences across, all branches of a network or circuit. The data normally comprise all source voltages and/or currents and all branch resistances/impedances. Ohm's and Kirchhoff's Laws form the basis of all methods of analysis, either directly or in modified form, according to circumstances. Thus, in circuits containing only voltage sources, mesh or loop analysis is generally to be preferred to Kirchhoff's Laws themselves since fewer simultaneous equations result and, when only current sources are pres-ent, nodal analysis is generally best. In addition, many network theorems exist which, although not strictly falling within the above definition of Circuit Analysis, are nevertheless useful aids in the process. A few of these will be dealt with in this chapter. 4 . 1 N E T W O R K T E R M I N O L O G Y First a few definitions. (a) A branch of a circuit is that part of the circuit containing a single active or passive element. (b) A node is the point of interconnection of two or more branches. The junction of three or more branches is referred to as a principal node; a secondary node is the junction of two branches. 200 Circuit Analysis 201 (c) A planar network is one whose schematic may be drawn on a plane surface without branch crossings. (d) A non-planar network is one whose schematic may not be so drawn. (e) A loop is any closed path in a network which does not pass through any branch or node more than once. (f) A mesh is a loop which contains no other loops. It is defined only for planar networks. 4.2 KIRCHHOFF'S LAWS The reader is referred to section 1.3 for a statement of the laws, which are valid for both planar and non-planar networks. An unknown current is assigned to every branch and the first law applied at as many nodes as will provide independent equations.

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  eBook - ePub

  Electrical Engineering for Non-Electrical Engineers

  • S. Bobby Rauf(Author)
  • 2021(Publication Date)
  • River Publishers

    (Publisher)

  Chapter 2 DC Circuit Analysis and Basic Electronic Devices

  Introduction

  In this chapter, we will review three fundamental laws of physics and electrical engineering, namely (1) Ohm’s law, (2) Kirchhoff’s voltage law, and (3) Kirchhoff’s current law. These three laws are instrumental in performing basic Circuit Analysis. Laws serve a vital purpose in electrical engineering analysis and problem-solving in DC as well as AC domains. Most engineering problems entail determination of unknown values of key parameters under certain known circumstances or conditions. Laws allow us the opportunity to formulate equations that can be solved for values of unknown parameters. Solving for one unknown variable requires a minimum of one equation, solution for determination of the values of two unknown variables requires two equations, and so on. Therefore, laws afford us the opportunity to model an engineering problem or scenario in the form of set of equations that can be solved to adequately define and idengify unknowns. Similar to the three basic laws of static equilibrium, i.e., ΣFx = 0, ΣFy = 0, and ΣM = 0―laws that a civil or mechanical engineer might employ to solve for unknown forces in a static equilibrium beam or truss scenario ― the Ohm’s law, the Kirchhoff’s voltage law, and the Kirchhoff’s current law are used to solve for important electrical parameters like current, voltage, resistance, power, energy, reactance, impedance, reactance, etc. The latter three parameters are AC entities, discussed in greater detail in Chapter 3.

  In addition to the basic laws, important electrical circuit principles and circuit simplification techniques, such as voltage division and current division will be discussed and their application will be illustrated through sample problems in this chapter. Note that there are many other principles and methods that are at an electrical engineer’s disposal to solve or analyze complex circuits. For example, the conversion of Y load (or resistor) configuration to Delta

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  Essentials of Advanced Circuit Analysis

  A Systems Approach

  • Djafar K. Mynbaev(Author)
  • 2024(Publication Date)
  • Wiley

    (Publisher)

  This brief introduction explains why we start considering the Circuit Analysis with dc circuits: It enables us to introduce this analysis’s primary laws and methods straightforwardly, minimizing the mathematical complexity. 2.2 Nodal Analysis and Mesh Analysis Fundamentals of the Circuit Analysis at an introductory level have been given in Chapter 1. Specifically, that chapter discusses main electrical parameters (current and voltage; power and energy), passive components (resistors, capacitors, and inductors), series and parallel circuits, sources, and primary circuit laws (Ohm’s and Kirchhoff’s laws). It’s worth revisiting that chapter 2 Methods of DC Circuit Analysis 82 to understand the Chapter 2 material better. Reviewing the Circuit Analysis subsection in Section 1.5 that discusses the main what and why is particularly conducive. To recall, Circuit Analysis aims to find the voltages across and currents through each circuit com- ponent. Ohm’s and Kirchhoff’s laws enable us to do this, but employing them to analyze sophisti- cated circuits becomes a cumbersome and time-consuming procedure. This chapter introduces new approaches to and theorems of Circuit Analysis, of which this section presents two fundamen- tally important methods—nodal analysis and mesh analysis. The concept of both nodal and mesh analysis is to describe an electrical circuit not in terms of i v − equation of each component but using the equations describing the status of every node or every loop of the circuit. These equations introduce new circuit variables. They allow, of course, finding the needed voltages across and currents through all circuit elements. Such an approach simplifies the analysis of circuits, especially the sophisticated ones. No wonder the nodal and mesh methods are one of the most powerful tools in the modern Circuit Analysis.

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  Circuit Analysis with PSpice

  A Simplified Approach

  • Nassir H. Sabah(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  Part I Basic Concepts in Circuit Analysis 3 Objective and Overview This chapter introduces some basic notions on electric circuits before embarking on Circuit Analysis in the fol- lowing chapters. The chapter begins by explaining what electric circuits are, what they are used for, and what conservation laws they obey. The primary circuit variables of current and voltage are defined with reference to a useful and easy- to-follow, hydraulic analogy. The significance of direc- tion of current and polarity of voltage is emphasized because of the key roles these play in Circuit Analysis. The relation of current and voltage to power and energy is derived, and active and passive circuit elements are characterized by the way they handle energy. The three passive circuit parameters of resistance, capacitance, and inductance are justified as accounting for three basic attributes of the electromagnetic field, namely, energy dissipation and energy storage in the electric and magnetic fields. The chapter concludes with an exami- nation of the idealizations and approximations made in the circuits approach. 1.1 What Are Electric Circuits and What Are They Used For? Definition: An electric circuit is an interconnection of com- ponents that affect electric charges in some characteristic manner. An example is a battery connected to a heater through a switch, as illustrated diagrammatically in Figure 1.1. Figure 1.2 is the corresponding circuit dia- gram in terms of symbols for the three components. When the switch is in the closed position, as shown, it allows electric charges to flow through the heater. In doing so, the charges impart some of their energy to the heater, thereby generating heat and raising the temperature of the heater metal. The battery restores energy to the electric charges, thereby allowing them to flow continuously through the circuit. Opening the switch interrupts the flow of charges and turns off the heater.

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  Introduction to Electric Circuits

  • Richard C. Dorf, James A. Svoboda(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  The analysis of a circuit is concerned with the methodical study of a given circuit designed to obtain the magnitude and direction of one or more circuit variables, such as a current or voltage. The analysis process begins with a statement of the problem and usually includes a given circuit model. The goal is to determine the magnitude and direction of one or more circuit variables, and the final task is to verify that the proposed solution is indeed correct. Usually, the engineer first identifies what is known and the principles that will be used to determine the unknown variable. The problem-solving method that will be used throughout this book is shown in Figure 1.6-1. Generally, the problem statement is given. The analysis process then moves sequentially through the five steps shown in Figure 1.6-1. First, we describe the situation and the assumptions. We also record or review the circuit model that is provided. Second, we state the goals and requirements, and we Correct Incorrect State the problem. Describe the situation and the assumptions. State the goals and requirements. Generate a plan to obtain a solution of the problem. Act on the plan. Communicate the solution. Verify that the proposed solution is indeed correct. Problem Situation Goal Plan Act Verify Solution FIGURE 1.6-1 The problem-solving method. Circuit Analysis and Design 11 normally record the required circuit variable to be determined. The third step is to create a plan that will help obtain the solution of the problem. Typically, we record the principles and techniques that pertain to this problem. The fourth step is to act on the plan and carry out the steps described in the plan. The final step is to verify that the proposed solution is indeed correct. If it is correct, we communicate this solution by recording it in writing or by presenting it verbally.

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  Introduction to Renewable Power Systems and the Environment with R

  • Miguel F. Acevedo(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  3 Fundamentals of Direct Current Electric Circuits

  This chapter is one of several providing a very basic review of those major concepts of electrical circuits that we need in order to understand electrical power systems. In this chapter, we review basic electrical quantities and circuits, introducing Ohm’s law and the fundamentals of Circuit Analysis methods including Kirchhoff’s voltage and current laws, nodal and mesh analysis, and Thévenin and Norton theorems. In preparation for understanding power transfer, we cover modeling of voltage and current sources and the basics of maximum power transfer. In this chapter, we will focus on direct current (DC) circuits, and later, in Chapter 5 , we introduce alternating current (AC) circuits. This topic is expanded in Chapter 8 discussing AC Circuit Analysis and power calculation for AC circuits, and in Chapter 10 when we introduce transformers and three-phase circuits. Basic DC Circuit Analysis is covered in many textbooks used in introductory Circuit Analysis courses and can serve as supplementary material [1–3 ]. Reviews are also available in textbooks devoted to renewable energy [4 ,5 ].

  3.1 Basics of Electric Circuits

  3.1.1 Principles of Electrical Quantities

  Electrical charge is a fundamental property of matter that can both generate and interact with electromagnetic fields. Charge can be positive or negative; at the subatomic level, protons represent positive charge, whereas electrons have negative charge. The unit of charge is the coulomb or C, where 1 C is the equivalent charge of 6.2 × 1018 electrons. In a conductor, free electrons can flow and represent a movement of negative charge.

  Voltage is the potential energy difference between two points in an electric field, measured per unit charge. Being potential energy means it is available to perform the work of moving a unit charge against an electric field. Intuitively, voltage is the energy available to cause electrons to flow through a conductor. Its unit is volt or V, which is defined as joule/coulomb (J/C), and is named volt in honor of Alessandro Volta. In general, work and charge vary with time. Denoting charge by q , voltage by v , and work by w

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  Engineering Circuit Analysis

  • J. David Irwin, R. Mark Nelms, Amalendu Patnaik(Authors)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  EXPERIMENTS THAT HELP STUDENTS DEVELOP AN UNDERSTANDING OF LOOP AND NODAL TECHNIQUES FOR Circuit Analysis ARE: ■ Kirchhoff’s Laws: Prove Kirchhoff’s laws experimentally and the conservation of power from voltage and current measurements in simple circuits. ■ Mesh Current and Node Voltage Analyses: Build and ana- lyze a circuit using mesh current or node voltage analysis and examine the effect of multiple sources on a circuit parameter by accumulating the results of the individual sources using superposition. ■ Wheatstone Bridge: Predict the temperature using a Wheatstone bridge with a thermistor as the element in one leg of the bridge. Nodal and Loop Analysis Techniques CHAPTER 3 THE LEARNING GOALS FOR THIS CHAPTER ARE THAT STUDENTS SHOULD BE ABLE TO: ■ Calculate the branch currents and node voltages in circuits containing multiple nodes using KCL and Ohm’s law in nodal analysis. ■ Calculate the mesh currents and voltage drops and rises in circuits containing multiple loops using KVL and Ohm’s law in loop analysis. ■ Identify the most appropriate analysis technique that should be utilized to solve a particular problem. 89 3.1 Nodal Analysis In a nodal analysis, the variables in the circuit are selected to be the node voltages. The node voltages are defined with respect to a common point in the circuit. One node is selected as the reference node, and all other node voltages are defined with respect to that node. Quite often, this node is the one to which the largest number of branches are connected. It is commonly called ground because it is said to be at ground-zero potential, and it sometimes represents the chassis or ground line in a practical circuit. 90 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES + – 1 2 3 4 5 V a = 3 V I 1 I 3 I 5 I 2 I 4 12 V 6 kΩ 4 kΩ 3 kΩ 9 kΩ 9 kΩ 3 kΩ + − + − + − V S V 1 + − V 3 + − V 5 + − V b = — V 3 2 V c = — V 3 8 Figure 3.1 Circuit with known node voltages.

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  Fundamentals of Electrical Engineering, Part 1

  • S. B. Lal Seksena, Kaustuv Dasgupta(Authors)
  • 2017(Publication Date)
  • Cambridge University Press

    (Publisher)

  2.1 Introduction The seventeenth century was the century for theorization of electricity. The electrical technology became more and more advanced and complex. Direct current technology was dominating the new inventions. It was very necessary to mathematize the different parameters of these complex electrical connections and circuits. We had to develop a new mathematical model to calculate and determine the voltage, current power etc. of a circuit at different branches and nodes without measuring it directly. Some important theorems regarding electrical circuit were mutated during the last half of the century. These theorems work good with some constrain in the nature of the circuit. Before the semiconductor circuits or electronic circuits came into the picture these theorems were successfully used to determined different parameters of an electrical circuit. In this chapter let us find out and discuss about some of those electrical circuit theories. 2.2 Basic Concepts: Electric Circuit, Loop, Mesh etc. a. Electric circuit: An electric circuit or electric network is a combination of different electric components (discussed in the next topic) via loop and branches of conductors. b. Node: A node is a junction of an electric circuit where two or more circuit components are connected together. c. Branch: Branch is the part of the circuit which lies between two junctions or nodes in an electric circuit. d. Loop: Loop is the closed path in an electric circuit in which no element or node is connected more than once. e. Mesh: Mesh is such a loop that does not involve no other loop in it. So every mesh is a loop but all loops are not meshes. 2 ELECTRICAL CIRCUITS Prerequisite Knowledge Fundamental of Current Electricity Basic understanding of Electric Circuit Electrical Circuits 35 Let us understand the circuit and its nodes, branches, loops and meshes with a simple example of Wheatstone bridge circuit In Fig.

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