This document discusses basic circuit laws including Ohm's law, Kirchhoff's laws, and techniques for analyzing circuits. It defines key circuit elements and relationships. Ohm's law defines the relationship between voltage, current, and resistance. Kirchhoff's laws allow the use of nodes, loops, and branches to simplify circuit analysis. Resistors can be analyzed individually and in series and parallel combinations using these fundamental laws and techniques. Examples are provided to demonstrate applying the laws to calculate current, voltage, power, and equivalent resistances in various circuits.
This document contains 25 questions about electrical concepts such as series and parallel circuits, resistance, current, power, and more. The questions cover topics like calculating equivalent resistance and current in different circuit configurations, determining time to boil water using heating coils in series vs parallel, and finding drift velocity of electrons and temperature coefficient of resistance for various materials.
This document provides conceptual problems and questions about solids and the theory of conduction. It includes:
1. Questions about how energy is lost by electrons colliding with ions and how this appears as Joule heat.
2. Questions about the resistivity of brass and copper at low temperatures being due to residual resistance from impurities.
3. Problems involving calculating contact potentials between different metals using their work functions.
4. Additional conceptual questions about properties of conductors, insulators, semiconductors and how doping affects conduction.
This document contains physics examination papers from 2008-2012 administered by the Central Board of Secondary Education (CBSE) in Delhi, India. It lists the contents which include CBSE examination papers from Delhi and All India in those years, as well as foreign papers. A sample paper from the 2008 Delhi exam is then provided, consisting of 30 multiple choice questions testing concepts in physics.
This document contains an unsolved physics test paper from 2010 with multiple choice and numerical questions covering topics like circuits, mechanics, waves, optics, and thermodynamics. The questions range from single answer to multiple answer types. Paragraphs provide contexts for related questions. The test assesses understanding of fundamental physics concepts and calculations.
This document discusses electric circuits and direct current. It contains conceptual problems, picture problems, and determine the concept problems related to topics like Ohm's law, resistors, capacitors, Kirchhoff's laws, and more. Some key points:
- Resistors dissipate more power when connected in series compared to parallel due to their higher equivalent resistance in series.
- The time it takes for the charge on a capacitor to reduce to half its initial value when discharging through a resistor can be calculated using the RC time constant.
- Kirchhoff's laws apply to all circuits as they are statements about the conservation of energy and charge in circuits.
- Applying concepts like Ohm's
The document is the question paper for a CBSE Board Examination for Physics (Theory).
[1] It contains 30 questions ranging from very short answer to long answer questions. [2] The questions cover various topics in Physics including electromagnetism, optics, semiconductor properties, and magnetic materials. [3] Instructions are provided on how to attempt the paper and the marking scheme for different types of questions.
This document discusses the application of the superposition theorem to resistive DC circuits with multiple independent voltage and current sources. It begins with an introduction to the superposition theorem and its basis in the linear and additive properties of circuits. Examples are then provided to demonstrate how to use the superposition theorem to find branch currents and voltages. The key steps are to consider each source independently while replacing all other sources with their internal resistances, calculate the contribution of each source, and sum the individual contributions. Limitations of the superposition theorem for non-linear circuits and power calculations are also noted. The document concludes with practice problems testing the reader's understanding of applying the superposition theorem.
This document provides information about electrical generators and DC motors. It discusses:
1. The principle of electrical generators, which convert mechanical energy into electrical energy by inducing voltage in conductors moving through a magnetic field according to Faraday's law of induction.
2. Key parts of generators including a magnetic field and conductors that move to cut the magnetic flux.
3. Types of DC generators including separately excited, shunt wound, series wound, and compound wound generators and their characteristics.
4. The principle of DC motors, which convert electrical energy into mechanical energy by applying a current to a conductor in a magnetic field, producing motion. DC motors can function interchangeably as motors or generators.
5
This document contains 25 questions about electrical concepts such as series and parallel circuits, resistance, current, power, and more. The questions cover topics like calculating equivalent resistance and current in different circuit configurations, determining time to boil water using heating coils in series vs parallel, and finding drift velocity of electrons and temperature coefficient of resistance for various materials.
This document provides conceptual problems and questions about solids and the theory of conduction. It includes:
1. Questions about how energy is lost by electrons colliding with ions and how this appears as Joule heat.
2. Questions about the resistivity of brass and copper at low temperatures being due to residual resistance from impurities.
3. Problems involving calculating contact potentials between different metals using their work functions.
4. Additional conceptual questions about properties of conductors, insulators, semiconductors and how doping affects conduction.
This document contains physics examination papers from 2008-2012 administered by the Central Board of Secondary Education (CBSE) in Delhi, India. It lists the contents which include CBSE examination papers from Delhi and All India in those years, as well as foreign papers. A sample paper from the 2008 Delhi exam is then provided, consisting of 30 multiple choice questions testing concepts in physics.
This document contains an unsolved physics test paper from 2010 with multiple choice and numerical questions covering topics like circuits, mechanics, waves, optics, and thermodynamics. The questions range from single answer to multiple answer types. Paragraphs provide contexts for related questions. The test assesses understanding of fundamental physics concepts and calculations.
This document discusses electric circuits and direct current. It contains conceptual problems, picture problems, and determine the concept problems related to topics like Ohm's law, resistors, capacitors, Kirchhoff's laws, and more. Some key points:
- Resistors dissipate more power when connected in series compared to parallel due to their higher equivalent resistance in series.
- The time it takes for the charge on a capacitor to reduce to half its initial value when discharging through a resistor can be calculated using the RC time constant.
- Kirchhoff's laws apply to all circuits as they are statements about the conservation of energy and charge in circuits.
- Applying concepts like Ohm's
The document is the question paper for a CBSE Board Examination for Physics (Theory).
[1] It contains 30 questions ranging from very short answer to long answer questions. [2] The questions cover various topics in Physics including electromagnetism, optics, semiconductor properties, and magnetic materials. [3] Instructions are provided on how to attempt the paper and the marking scheme for different types of questions.
This document discusses the application of the superposition theorem to resistive DC circuits with multiple independent voltage and current sources. It begins with an introduction to the superposition theorem and its basis in the linear and additive properties of circuits. Examples are then provided to demonstrate how to use the superposition theorem to find branch currents and voltages. The key steps are to consider each source independently while replacing all other sources with their internal resistances, calculate the contribution of each source, and sum the individual contributions. Limitations of the superposition theorem for non-linear circuits and power calculations are also noted. The document concludes with practice problems testing the reader's understanding of applying the superposition theorem.
This document provides information about electrical generators and DC motors. It discusses:
1. The principle of electrical generators, which convert mechanical energy into electrical energy by inducing voltage in conductors moving through a magnetic field according to Faraday's law of induction.
2. Key parts of generators including a magnetic field and conductors that move to cut the magnetic flux.
3. Types of DC generators including separately excited, shunt wound, series wound, and compound wound generators and their characteristics.
4. The principle of DC motors, which convert electrical energy into mechanical energy by applying a current to a conductor in a magnetic field, producing motion. DC motors can function interchangeably as motors or generators.
5
This document contains a series of questions and problems related to basic electrical concepts such as charge, current, voltage, power, energy, Ohm's law, Kirchhoff's laws, and resistor networks. The questions cover topics like calculating charge, current, power, and energy in circuits; applying Kirchhoff's laws to determine voltages and currents; analyzing series and parallel resistor networks; and using techniques like star-delta transformations. Solutions are provided for some of the example circuit analysis problems. The document appears to be from a textbook or class on basic electrical and electronic engineering concepts.
This document provides an introduction to basic electrical concepts including charge, current, voltage, power, energy, and circuit elements. It defines the international system of units used in electrical engineering. Key concepts covered include defining the ampere as the unit of current representing the flow of electric charge, defining voltage as the work required to move a unit of charge from one point to another, and defining power as the rate at which energy is transferred. Circuit analysis techniques are introduced for studying the behavior of electric circuits.
1. The document discusses concepts related to molecules, including:
- Polar vs non-polar molecules based on dipole moments
- Ionic vs covalent bonding mechanisms
- Quantum numbers related to molecular rotation and vibration
- Estimating properties like bond lengths using concepts like potential energy
2. It works through conceptual problems calculating properties like ionization energies, bond energies, quantum numbers, and percentages of ionic character in bonds.
3. The problems involve setting up and solving equations related to molecular structure, energies, and quantum mechanics.
This document contains a set of practice problems related to sinusoidal signals, phasors, and AC power analysis. It begins with definitions of terms like sinusoids, phasors, resistance, inductance, capacitance, and impedance. It then presents 35 problems involving concepts like phasor representations of signals, phase relationships between voltage and current in different circuit elements, power calculations, RMS values, and power factors. The document spans 24 pages and provides the questions, blank spaces for solutions, and sometimes diagrams related to circuit analysis.
This document contains 8 questions related to network analysis for an examination. The questions cover a range of topics including circuit analysis using Kirchhoff's laws, impedance matching, transient response of RLC circuits, network theorems such as Thevenin's theorem and Norton's theorem, and filter design problems. Solutions to the questions are not provided. The document appears to be an exam paper from a B.Tech program with sets of questions on network analysis as the subject.
The document discusses a workshop organized by KV Andrews Ganj to prepare sample higher-order thinking (HOT) questions for Class XII Physics. [1] A two-day workshop was held in July 2008 with 10 Physics teachers from various KVs participating. [2] The teachers worked to computerize chapter-wise sample HOT questions for CBSE Class XII Physics. [3] The principal expresses that this material will help students and teachers perform better in board exams, while noting that teachers can prepare additional questions to improve student competency.
The document is a study guide containing questions and problems related to electrical engineering topics like single-phase and three-phase AC circuits. Some key points covered include:
- The advantages of three-phase systems over single-phase, such as using less material for the same power output.
- Calculating values like impedance, current, power, and power factor in RLC circuits connected to AC power sources.
- Analyzing phasor diagrams for series RLC circuits.
- Determining line and phase voltages and currents in wye-delta and delta-wye connected three-phase systems.
This document contains solutions to physics problems from the 12th CBSE exam. It discusses topics like Lenz's law, electric fields, the photoelectric effect, atomic spectra of hydrogen, rectifiers, and more. The solutions are presented in point form and range from short explanations to longer derivations. Overall, the document provides concise answers and working steps to multiple conceptual and numerical problems in 12th grade physics.
This document summarizes an experiment to verify Broglie's relations, which state that the wavelength of an electron is inversely proportional to its momentum or kinetic energy. The experiment measured the radii of diffraction rings produced when electrons struck a graphite target. Plotting the inverse square root of voltage against radii produced linear relationships, confirming Broglie's prediction and demonstrating the wave-particle duality of electrons. While limited data points could be improved, measurement precision was high. The results substantiated the de Broglie hypothesis relating electron wavelength to momentum.
(1) The document contains the details of a Physics exam including instructions, questions, and solutions.
(2) It provides short answer and long answer questions on topics in Physics ranging from electromagnetism to semiconductor devices.
(3) The questions assess knowledge of concepts like Lenz's law, photoelectric effect, atomic structure, capacitors, diodes, and transistor amplifiers.
Cbse class 12 physics sample paper 02 (for 2014)mycbseguide
The document provides a sample physics question paper for Class 12 with 29 questions ranging from 1 to 5 marks. It includes questions from various topics in physics like electromagnetism, optics, modern physics, semiconductor devices, communication systems, and electrical circuits. The paper tests concepts, calculations, principles, diagrams, and applications of concepts across different areas of the physics syllabus. It provides guidelines for time, marks distribution and instructions for answering the questions.
1. The document contains a physics exam paper with 32 multiple choice questions covering topics in optics, mechanics, electricity, magnetism, atomic physics, and nuclear physics.
2. For each question, 4 possible answers are provided labelled a, b, c, or d and the correct answer must be identified.
3. The questions cover calculating magnification of a telescope, properties of lenses, diffraction patterns, interference, blackbody radiation, units of work, projectile motion, satellite communications, centrifugal force, vector calculations, friction, planetary rotation, bullet velocity, magnetic fields, electric fields, circuits, self-inductance, electromagnetic induction, magnetic moments, particle wavelengths, photoelectric effect, nuclear scattering, atomic
This document contains an unsolved physics exam from 1990 containing multiple choice and fill-in-the-blank questions testing concepts in mechanics, waves, electricity, and magnetism. The exam is divided into three sections. Section I contains 6 multiple choice questions. Section II contains 4 fill-in-the-blank questions requiring numeric or one-word answers. Section III asks the reader to match 3 physical quantities with their appropriate units from a list of choices. The document provides context for summarizing a past physics exam, but does not include answers to the questions.
Solution of problems of chapter 2 for simple resistiv circuitsMôstafâ Araby
This document outlines 15 practice problems from Chapter 2 on simple resistive circuits. The problems cover various circuit analysis techniques including Kirchhoff's Current and Voltage Laws, series and parallel resistor combinations, nodal analysis, and power calculations. The goal is to help students learn and practice analyzing circuits to solve for values like current, voltage, power, and equivalent resistance.
The document provides instructions for a CBSE board exam for Physics (Theory). It notes there are 29 questions total, ranging from 1 to 5 marks each. Questions 1-8 are very short answer, 9-16 are 2 marks, 17-25 are 3 marks, and 27-29 are 5 marks. The exam allows 3 hours and is out of 70 total marks. It provides various instructions, constants to use, and the structure of the exam.
This document summarizes Chapter 1 from the textbook "Electrical Engineering: Principles and Applications" by Allan R. Hambley. It includes sample exercises and problems from Chapter 1 on topics like charge, current, voltage, power, energy, circuits, and circuit analysis techniques. The chapter introduces fundamental concepts of electrical engineering.
This document contains conceptual physics problems and their solutions related to magnetic fields. Some key points:
- Problem 1 discusses how electrons moving perpendicular to a magnetic field will follow a circular path due to the magnetic force.
- Problem 12 determines that an electron will be deflected upward when passing through a magnetic field, due to the direction of the magnetic force on electrons being opposite that of positive charges.
- Problem 22 calculates the magnetic force acting on a segment of wire using the cross product relationship between the magnetic field, the wire orientation, and the current in the wire.
This document provides errata for problems in the textbook "Electronics, 2nd ed. by Allan R. Hambley". It lists over 70 problems and provides corrections to errors in equations, values, figures, and problem statements. The corrections range from minor typos and mathematical errors to missing details in problem descriptions. The goal is to resolve inaccuracies in the textbook solutions to improve learning and understanding of circuit analysis concepts.
1) The document discusses various concepts related to electric current and direct current circuits, including resistance, resistivity, Ohm's law, temperature dependence of resistance, and drift velocity of electrons.
2) It provides examples and conceptual problems involving calculating resistance, current, power, drift velocity, and other quantities using relationships like Ohm's law, relationships between resistance and resistivity, and how resistance changes with temperature.
3) Sample problems include calculating the resistance of wires with different lengths and gauges, the drift speed of electrons in copper wires carrying different currents, the potential difference required across a wire to produce a given current, and the temperature at which a copper wire's resistance would be 10% greater than at 20
BEF 12403 - Week 7 - Linearity and Superposition Principles.pptLiewChiaPing
This document discusses linear circuits and techniques for analyzing them, including linearity principle, superposition theorem, and source transformations. It provides examples of using linearity principle to find unknown voltages and currents when an independent source is applied to a linear network. It also provides examples of using superposition theorem to solve for unknowns in a linear circuit with multiple independent sources by considering each source individually.
This document provides an introduction to analyzing DC resistive circuits that contain nonlinear elements using load-line analysis. It defines linear and nonlinear voltage-current characteristics and explains how load-line analysis can be used to determine the operating point of a circuit when a nonlinear element is present. Load-line analysis graphs the characteristic curves of the nonlinear element and equivalent circuit to find their intersection point, which represents the operating point. The document provides examples of using both graphical load-line analysis and analytical methods to solve circuits with nonlinear elements like diodes and thermistors.
This document contains a series of questions and problems related to basic electrical concepts such as charge, current, voltage, power, energy, Ohm's law, Kirchhoff's laws, and resistor networks. The questions cover topics like calculating charge, current, power, and energy in circuits; applying Kirchhoff's laws to determine voltages and currents; analyzing series and parallel resistor networks; and using techniques like star-delta transformations. Solutions are provided for some of the example circuit analysis problems. The document appears to be from a textbook or class on basic electrical and electronic engineering concepts.
This document provides an introduction to basic electrical concepts including charge, current, voltage, power, energy, and circuit elements. It defines the international system of units used in electrical engineering. Key concepts covered include defining the ampere as the unit of current representing the flow of electric charge, defining voltage as the work required to move a unit of charge from one point to another, and defining power as the rate at which energy is transferred. Circuit analysis techniques are introduced for studying the behavior of electric circuits.
1. The document discusses concepts related to molecules, including:
- Polar vs non-polar molecules based on dipole moments
- Ionic vs covalent bonding mechanisms
- Quantum numbers related to molecular rotation and vibration
- Estimating properties like bond lengths using concepts like potential energy
2. It works through conceptual problems calculating properties like ionization energies, bond energies, quantum numbers, and percentages of ionic character in bonds.
3. The problems involve setting up and solving equations related to molecular structure, energies, and quantum mechanics.
This document contains a set of practice problems related to sinusoidal signals, phasors, and AC power analysis. It begins with definitions of terms like sinusoids, phasors, resistance, inductance, capacitance, and impedance. It then presents 35 problems involving concepts like phasor representations of signals, phase relationships between voltage and current in different circuit elements, power calculations, RMS values, and power factors. The document spans 24 pages and provides the questions, blank spaces for solutions, and sometimes diagrams related to circuit analysis.
This document contains 8 questions related to network analysis for an examination. The questions cover a range of topics including circuit analysis using Kirchhoff's laws, impedance matching, transient response of RLC circuits, network theorems such as Thevenin's theorem and Norton's theorem, and filter design problems. Solutions to the questions are not provided. The document appears to be an exam paper from a B.Tech program with sets of questions on network analysis as the subject.
The document discusses a workshop organized by KV Andrews Ganj to prepare sample higher-order thinking (HOT) questions for Class XII Physics. [1] A two-day workshop was held in July 2008 with 10 Physics teachers from various KVs participating. [2] The teachers worked to computerize chapter-wise sample HOT questions for CBSE Class XII Physics. [3] The principal expresses that this material will help students and teachers perform better in board exams, while noting that teachers can prepare additional questions to improve student competency.
The document is a study guide containing questions and problems related to electrical engineering topics like single-phase and three-phase AC circuits. Some key points covered include:
- The advantages of three-phase systems over single-phase, such as using less material for the same power output.
- Calculating values like impedance, current, power, and power factor in RLC circuits connected to AC power sources.
- Analyzing phasor diagrams for series RLC circuits.
- Determining line and phase voltages and currents in wye-delta and delta-wye connected three-phase systems.
This document contains solutions to physics problems from the 12th CBSE exam. It discusses topics like Lenz's law, electric fields, the photoelectric effect, atomic spectra of hydrogen, rectifiers, and more. The solutions are presented in point form and range from short explanations to longer derivations. Overall, the document provides concise answers and working steps to multiple conceptual and numerical problems in 12th grade physics.
This document summarizes an experiment to verify Broglie's relations, which state that the wavelength of an electron is inversely proportional to its momentum or kinetic energy. The experiment measured the radii of diffraction rings produced when electrons struck a graphite target. Plotting the inverse square root of voltage against radii produced linear relationships, confirming Broglie's prediction and demonstrating the wave-particle duality of electrons. While limited data points could be improved, measurement precision was high. The results substantiated the de Broglie hypothesis relating electron wavelength to momentum.
(1) The document contains the details of a Physics exam including instructions, questions, and solutions.
(2) It provides short answer and long answer questions on topics in Physics ranging from electromagnetism to semiconductor devices.
(3) The questions assess knowledge of concepts like Lenz's law, photoelectric effect, atomic structure, capacitors, diodes, and transistor amplifiers.
Cbse class 12 physics sample paper 02 (for 2014)mycbseguide
The document provides a sample physics question paper for Class 12 with 29 questions ranging from 1 to 5 marks. It includes questions from various topics in physics like electromagnetism, optics, modern physics, semiconductor devices, communication systems, and electrical circuits. The paper tests concepts, calculations, principles, diagrams, and applications of concepts across different areas of the physics syllabus. It provides guidelines for time, marks distribution and instructions for answering the questions.
1. The document contains a physics exam paper with 32 multiple choice questions covering topics in optics, mechanics, electricity, magnetism, atomic physics, and nuclear physics.
2. For each question, 4 possible answers are provided labelled a, b, c, or d and the correct answer must be identified.
3. The questions cover calculating magnification of a telescope, properties of lenses, diffraction patterns, interference, blackbody radiation, units of work, projectile motion, satellite communications, centrifugal force, vector calculations, friction, planetary rotation, bullet velocity, magnetic fields, electric fields, circuits, self-inductance, electromagnetic induction, magnetic moments, particle wavelengths, photoelectric effect, nuclear scattering, atomic
This document contains an unsolved physics exam from 1990 containing multiple choice and fill-in-the-blank questions testing concepts in mechanics, waves, electricity, and magnetism. The exam is divided into three sections. Section I contains 6 multiple choice questions. Section II contains 4 fill-in-the-blank questions requiring numeric or one-word answers. Section III asks the reader to match 3 physical quantities with their appropriate units from a list of choices. The document provides context for summarizing a past physics exam, but does not include answers to the questions.
Solution of problems of chapter 2 for simple resistiv circuitsMôstafâ Araby
This document outlines 15 practice problems from Chapter 2 on simple resistive circuits. The problems cover various circuit analysis techniques including Kirchhoff's Current and Voltage Laws, series and parallel resistor combinations, nodal analysis, and power calculations. The goal is to help students learn and practice analyzing circuits to solve for values like current, voltage, power, and equivalent resistance.
The document provides instructions for a CBSE board exam for Physics (Theory). It notes there are 29 questions total, ranging from 1 to 5 marks each. Questions 1-8 are very short answer, 9-16 are 2 marks, 17-25 are 3 marks, and 27-29 are 5 marks. The exam allows 3 hours and is out of 70 total marks. It provides various instructions, constants to use, and the structure of the exam.
This document summarizes Chapter 1 from the textbook "Electrical Engineering: Principles and Applications" by Allan R. Hambley. It includes sample exercises and problems from Chapter 1 on topics like charge, current, voltage, power, energy, circuits, and circuit analysis techniques. The chapter introduces fundamental concepts of electrical engineering.
This document contains conceptual physics problems and their solutions related to magnetic fields. Some key points:
- Problem 1 discusses how electrons moving perpendicular to a magnetic field will follow a circular path due to the magnetic force.
- Problem 12 determines that an electron will be deflected upward when passing through a magnetic field, due to the direction of the magnetic force on electrons being opposite that of positive charges.
- Problem 22 calculates the magnetic force acting on a segment of wire using the cross product relationship between the magnetic field, the wire orientation, and the current in the wire.
This document provides errata for problems in the textbook "Electronics, 2nd ed. by Allan R. Hambley". It lists over 70 problems and provides corrections to errors in equations, values, figures, and problem statements. The corrections range from minor typos and mathematical errors to missing details in problem descriptions. The goal is to resolve inaccuracies in the textbook solutions to improve learning and understanding of circuit analysis concepts.
1) The document discusses various concepts related to electric current and direct current circuits, including resistance, resistivity, Ohm's law, temperature dependence of resistance, and drift velocity of electrons.
2) It provides examples and conceptual problems involving calculating resistance, current, power, drift velocity, and other quantities using relationships like Ohm's law, relationships between resistance and resistivity, and how resistance changes with temperature.
3) Sample problems include calculating the resistance of wires with different lengths and gauges, the drift speed of electrons in copper wires carrying different currents, the potential difference required across a wire to produce a given current, and the temperature at which a copper wire's resistance would be 10% greater than at 20
BEF 12403 - Week 7 - Linearity and Superposition Principles.pptLiewChiaPing
This document discusses linear circuits and techniques for analyzing them, including linearity principle, superposition theorem, and source transformations. It provides examples of using linearity principle to find unknown voltages and currents when an independent source is applied to a linear network. It also provides examples of using superposition theorem to solve for unknowns in a linear circuit with multiple independent sources by considering each source individually.
This document provides an introduction to analyzing DC resistive circuits that contain nonlinear elements using load-line analysis. It defines linear and nonlinear voltage-current characteristics and explains how load-line analysis can be used to determine the operating point of a circuit when a nonlinear element is present. Load-line analysis graphs the characteristic curves of the nonlinear element and equivalent circuit to find their intersection point, which represents the operating point. The document provides examples of using both graphical load-line analysis and analytical methods to solve circuits with nonlinear elements like diodes and thermistors.
The document discusses network duality and constructing dual networks. It defines duality as a principle where circuit equations and theorems remain the same except that certain element properties are interchanged, such as voltage and current, resistance and conductance, and capacitance and inductance. A table shows common dual pairs. The document provides steps for constructing a dual network graphically by placing nodes at the centers of meshes and replacing elements with their duals. Examples demonstrate this process and verifying dual circuits.
This lab report summarizes experiments conducted to study Ohm's Law and circuit behavior. The experiments involved measuring currents and voltages in circuits with single and dual power supplies connected to various resistor configurations. The results showed that resistance decreases in parallel circuits as predicted by Ohm's Law. Kirchhoff's Laws and the conservation of energy were also verified. Overall, the experimental findings supported the theoretical understanding of how voltage, current and resistance relate in electrical circuits.
This document reports on an electrical engineering lab experiment involving the superposition principle and Thevenin's theorem. The experiment used resistors, power supplies, and multimeters to measure voltages and currents in circuits. For the superposition principle part, measurements were taken with individual and combined sources and compared. For Thevenin's theorem, voltage and current across a variable load resistor were measured and recorded in a table to determine the equivalent resistance and voltage of the original circuit.
Microelectronic circuits and devices: chapter onemuhabaw amare
This document discusses diode models and characteristics. It introduces the ideal diode model and its voltage-current relationship. It then discusses more realistic models that account for the diode's finite voltage drop of around 0.7V. The document explains how to determine the diode constants like the emission coefficient and leakage current by analyzing voltage-current curves. It also discusses how temperature affects the diode's leakage current and voltage characteristics.
This document discusses series and parallel resistor circuits. It defines series and parallel connections and provides the formulas for calculating total resistance. In series circuits, the total resistance equals the sum of the individual resistances. In parallel circuits, the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances. The document also discusses series-parallel circuits and provides methods for simplifying them. It introduces delta-wye transformations, which allow converting between a delta and wye configuration to simplify circuit analysis. An example uses a delta-to-wye transformation to find the current and power drawn by a circuit.
- The reciprocity theorem states that the current in one branch of a linear network due to a voltage source in another branch is equal to the current that would flow in the second branch if the voltage source was placed there instead.
- To verify the theorem, the problem calculates the current in one branch with the voltage source in the other branch, and then vice versa, showing the currents are equal.
- The transfer resistance between the two branches can also be determined using the reciprocity theorem.
02 Basic Electrical Electronics and Instrumentation Engineering.pdfBasavaRajeshwari2
The document provides information about electrical circuits and instrumentation engineering including:
1. Questions and answers related to basic electrical concepts like Ohm's law, Kirchhoff's laws, series and parallel circuits, network analysis methods.
2. Definitions of terms used in AC circuits like impedance, resonance, real power, reactive power, apparent power.
3. Relationships and calculations related to 3-phase systems including line and phase quantities.
4. Brief descriptions of different types of wiring used for houses and industrial applications. Materials commonly used for wiring are also mentioned.
Basic Electrical Engineering Module 1 Part 1Divya15121983
This document provides an overview of basic electrical engineering concepts including Ohm's Law, series and parallel circuits, and Kirchhoff's Laws. It defines Ohm's Law as stating that current is directly proportional to voltage and inversely proportional to resistance. Kirchhoff's Current Law and Voltage Law are introduced as the principles that the algebraic sum of currents at a junction is zero and the algebraic sum of voltages around a closed loop is also zero. An example circuit problem is worked through using these laws to solve for unknown currents.
This document introduces second-order circuits, which contain two energy storage elements (ESLs) such as capacitors or inductors. Examples include RLC, RL, and RC circuits. Analyzing second-order circuits involves determining initial conditions such as voltage and current values as well as their derivatives. Two examples are provided to demonstrate how to find the initial conditions, transient responses, and final steady-state values for simple RLC circuits when components are switched or sources are changed. The document focuses on source-free circuits initially to examine natural responses before adding independent sources to analyze both transient and steady-state behavior.
1. Kirchhoff's current law states that at any node, the algebraic sum of currents entering and leaving the node equals zero. It is based on the principle of conservation of charge.
2. Kirchhoff's voltage law states that the algebraic sum of voltages around any closed loop in a circuit equals zero. It is based on the principle of conservation of energy.
3. The power balance equation states that the algebraic sum of power absorbed by all components in an electrical network equals zero. It is based on the principle of conservation of energy.
This document contains a 35-page exam on electrical circuit analysis techniques including nodal analysis, mesh analysis, Thevenin's theorem, Norton's theorem, and maximum power transfer theorem. It includes 37 practice problems of varying difficulty, asking students to use these analysis methods to solve circuits, determine equivalent circuits, calculate voltages, currents, power, and efficiency. The document provides circuit diagrams, explanations of analysis steps, and spaces for students to show their work and solutions.
This document provides an overview of basic circuit laws including Ohm's law, Kirchhoff's laws, and analysis of series and parallel circuits. Ohm's law states that voltage across a resistor is proportional to current through the resistor. Kirchhoff's laws include the junction rule that the total current entering a node equals the total leaving, and the loop rule that the sum of all potential differences around a closed loop is zero. Series and parallel circuits are analyzed using concepts like equivalent resistance, voltage division, and current division. Examples are provided to demonstrate applying these circuit analysis techniques.
The document discusses Thévenin's theorem and how to derive the Thévenin equivalent circuit for a given network. It states that any two-terminal DC network can be replaced by an equivalent circuit of a voltage source and series resistor. It then provides the steps to calculate the Thévenin voltage (ETh) and resistance (RTh) by opening and shorting terminals. Three examples are worked through applying these steps to find the Thévenin equivalent circuits for various networks.
This document discusses loop analysis of resistive circuits using Kirchhoff's voltage law. It begins by introducing mesh or loop analysis and defining key terms. Loop analysis provides a general method for circuit analysis using KVL. Key steps include drawing the circuit without crossovers, labeling mesh currents clockwise, and writing mesh equations for each loop by inspecting the circuit. Loops are analyzed by writing KVL equations and solving the system of equations for the unknown currents. Several examples demonstrate applying these steps to solve for unknown voltages and currents.
1. The document describes an experiment on analyzing series resistor-capacitor circuits. The objective is to understand the relationship between voltage, current, and phase angle and to calculate the phase angle.
2. Key aspects of the series RC circuit are discussed, including how impedance is calculated as the sum of resistance and capacitive reactance. The voltage and current relationships show the current is in phase with voltage across the resistor but lags the voltage across the capacitor by 90 degrees.
3. The experiment involves measuring voltages and calculating phase angles for different capacitors in a series RC circuit. Results show the phase angle depends on the capacitor value, with smaller capacitors producing larger phase angles. Errors in measurements
1. Kirchhoff's laws (KCL and KVL) form the foundation for electric circuit analysis. KCL states that the algebraic sum of currents entering a node is zero, while KVL states that the algebraic sum of voltages around a closed loop is zero.
2. A node is the point of connection between two or more branches, while a loop is any closed path in a circuit without repeating nodes. Kirchhoff's laws can be applied to nodes, closed surfaces, and loops.
3. Ohm's law defines the relationship between current and voltage in a resistor as V=IR. Resistors can be connected in series or parallel, and equivalent resistances can be calculated using their individual
Ellen Burstyn: From Detroit Dreamer to Hollywood Legend | CIO Women MagazineCIOWomenMagazine
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1. CHAPTER 2 Basic LawsCHAPTER 2 Basic Laws
To determine the values of electrical
variables such as current, voltage and
power in a given circuit requires
understanding some fundamental laws for
examples; Ohm’s law and Kirchhoff’s laws
to analyze the circuit. In addition, some
techniques must be used together with
those fundamental laws.
2. 2.2 Ohm’s law
Materials in general have a
characteristic behavior of
resisting the flow of electric
charge which is known as
resistance (R). The resistance of
any material depends on cross –
sectional area A and its lengthl
l
al with resistivity ρ
R = ρ
A
l(Ohm)
ρ – resistivity of materials (ohm – mete
Good conductors low resistivity
insulators high resistivity
See
Tab
l2.
1
3. The circuit element used to
model the current - resisting
behavior of a material is the
resistor
Resistance of the resistor
Ohm’s law states that the
voltage V across a resistor is
directly proportional to the
current i flowing through the
resistor
iRviv =⇒α
Note : AVΩ /11 =
4. If current flows from a
higher potential to a lower
potentialiRv =
If current flows from a lower
potential to a higher potential
iRv −=
fect conductor
short - circuit
∠∞∠R0
open - circuit
6. The reciprocal of resistance
R, known as conductance and
denoted by G
G =I
R = i
v
mho
Or Siemens (S)
G
i
GvpGvi
2
2
, ===
7. Example 2.2 In the circuit shown in Fig.2.8, calculate the
current i , the conductance G, and the power p.
Solution: The Voltage across the resistor is the same as
the source voltage (30 V) because the resistor and the
voltage source are connected to the same pair of terminals.
Hence, the current is
10. 2.3 Nodes, Branches and Loops
A branch represents a single
element such as a voltage source
or a resistorA Node is the point of
connection between two or more
branches
A Loop is any closed path in
the circuit formed by starting at
a node, passing through a set of
nodes, and returning to starting
node without passing through
11. Two or more elements are in
series if they exclusively share a
single node and consequent by
carry the same currentTwo or more elements are in
parallel if they exclusively
connected to the same two
nodes and consequent by have
12. Example 2.4 Determine the number
of branches and node in the circuit
show in Fig.2.12. Identify which
elements are in series and which are
in parallel.
Solution: Since there are four
elements in the circuit, the circuit
has four branches: 10 V, 5 Ω, 6 Ω,
and 2 A. The circuit has three nodes
as identified in Fig. 2.13. The 5 Ω
resistor is in series with the 10-V
voltage source because the same
current would flow in both. The 6-Ω
resistor is in parallel with the 2-A
current source because both are
connected to the same nodes 2 and
13.
14. 2.4 Kirchhoff’s laws
Kirchhoff’s current law (KCL)
states that the algebraic sum of
currents entering a node is zero0
1
=∑
=
N
n
ni
0)()( 54321 =−+++−+ iiiii
52431 iiiii +=++
enteringleaving
15. A simple application of KCL is
combining current sources in
parallel. The combined or equivalent
current source can be found by
applying KCL to node aIT = I1-I2+I3
IS = I1-I2+I3
IT
b
I1
I2 I3
IT
a
b
16. Kirchhoff’s voltage law (KVL) states
that the algebraic sum of all voltages
around a loop is zero
-v1+v2+v3-v4+v5 = 0
v2+v3+v5 = v1+v4
When voltage sources are connected
in series, KVL can be applied to
obtain the total voltage
17. 5 For the circuit in Fig.2.21 (a), find voltag
Solution: To find v1 and v2, we apply
Ohm’s law and Kirchhoff’s voltage
law. Assume that current i flow
through the loop as shown in Fig.
2.21(b). From Ohm’s law,v1 =2i , v2=-3i (2.5.1)
18. Applying KVL around the loop gives
-20+v1-v2=0 (2.5.2)
stituting Eq. (2.5.1) into Eq. (2.5.2), we ob
-20+2i+3i=0 or 5i=20
i =4 A
Substituting i in Eq. (2.5.1) finally gives
v1= 8 V , v2=-12 V
19. 6 Determine v0 and i in the circuit shown in
Solution: We apply KVL around the loop as shown in
Fig.2.23(b). The result is
-12+4i+2v0-4+6i = 0 (2.6.1)
Applying Ohm’s law to the 6-Ω resistor gives
v0 = -6i (2.6.2)
21. Example 2.8 Find the current and
voltage in the circuit show in Fig.
2.27(a)
e apply Ohm’s law and Kirchhoff’s law. By
v1 = 8i1, v2=3i2, v3 = 6i3 (2
22. resistor are related by Ohm’s law as
show, we are really looking for three
thing: (v1, v2, v3) or (i1, i2, i3). At
node a, KCL gives
i1- i2- i3 = 0
(2.8.2)
Applying KVL to loop as in Fig.
2.27(b),
-30 + v1 + v2 = 0
ess this in terms of i1 and i2 as in Fig. (2.81
-30 + 8i1 + 3i2 = 0
23. ( )
8
i330
i 2
1
−
= (2.8.3)
Applying KVL to loop 2,
-v2 + v3 = 0
v3 = v2
(2.8.4)
as expected since the two resistors
are in parallel. We express v1 and v2 in
term of i1 and i2 as in Eq. (2.8.1).Eq.
(2.8.4) becomes
24. 6 i3 = 3 i2
2
2
3
i
i =
tuting Eqs. (2.8.3) and (2.8.5) into (2.8.2)
0
28
330 2
2
2
=−−
− i
i
i
or i2 = 2 A. From the value of i2 ,
we now use Eqs. (2.8.1) to (2.8.5) to
obtain
i1 = 3 A, i3 = 1 A, v1 = 24 V, v2 =
6 V, v3 = 6 V.
25. 2.5 Series Resistors and
Voltage divisionv1 =
i
R
1
v2 =
i
R
2
-v+v1+v2
= 0v = v1+v2 = i
(R1+R2)v = i
R
eq
Req = R1 +
R2
...
N resistors in series then,
Req = R1 + R2+
…RN =
Rn Σ
N
n=1
26. ine the voltage across each resistor
v1
v
iR
1
i
(R1
+R2
)
= v1
R1+R2
R1v=
,
v2 = R1+R2
R2v
Vn= Rn
R1+R2+…+Rn
V
27. 2.6 Parallel resistors and
current divisionv = i1R1 = i2R2
i1
=
R
1
v i2
=
R
2
v,
at node a ;i = i1+ i2
1
Req
= R
1
1
R
2
1+
R1
R1
R2
R2
+
=1
Req
i
R
1
v
R
2
v+ v
R1
1
R2
1 +== v
Req
=
R1+R2
R1R2
=Req.
.
.1 = R2 then Req = R1
/2
สำำหรับ R 2 ตัวต่อ ขนำน
For N resistors1
R
e
=
R
1
1 + R
2
1
R
N
1+…+
If R = R1 = R2 = … = RN Req =R
N
28. It is more often to use
conductance rather than
resistance when dealing with
resistors in parallel.
Geq = G1 + G2 + G3 + … + GN
Given the total current i enter
node a, how do use obtain
current i1 and i2v = i Req = iR1R2
R1+R2
i1= R
1
v
R
1
=
R1R2
R1+R2
i iR2
R1+R2
=
=i2 iR1
R1+R2
Current divider
er current flow through the smaller resista
29. e 2.9 Find Req for the circuit shown in Fig.
Solution: To get Req , we combine
resistors in series and in parallel. The
6-Ω and 3-Ω resistors are in parallel, so
equivalent resistance is
Ω=
+
=ΩΩ 2
36
36
3//6
x
30. is
1Ω+5Ω = 6Ω
Thus the circuit in Fig. 2.34 is
reduced to that in Fig. 2.35(a). In Fig.
2.35(a), we notice that the two 2-Ω
resistors are in series, so the equivalent
resistance is
2Ω + 2Ω = 4Ω
This 4-Ω resistor is now in parallel
with the 6-Ω resistor in Fig. 2.35(a);
31. Ω=
+
=ΩΩ 4.2
64
64
6//4
x
The circuit in Fig. 2.35(a) is now
replaced with that in Fig. 2.35(b). In Fig.
2.35(b), the three resistors are in series.
Hence, the equivalent resistance for the
circuit is Ω=Ω+Ω+Ω= 4.1484.24Req
32. Example 2.10 Calculate the
equivalent resistance Rab in the circuit
in Fig. 2.37.
Solution: The 3-Ω and 6-Ω resistors are
in parallel because they are connected
to the same two nodes c and b. Their
combined resistance is
Ω=
+
=ΩΩ 2
63
63
6//3
x
33. Similarly, the 12-Ω and 4- Ω resistors are
in parallel since they are connected to
the same two nodes d and b. Hence
Ω=
+
=ΩΩ 3
412
412
4//12
x
Also the 1-Ω and 5-Ω resistors are in
series; hence, their equivalent
resistance is Ω=Ω+Ω 651With these three combinations, we can
replace the circuit in Fig. 2.37 with
that in Fig. 2.38(a). In Fig.2.38(a),3-Ω
in parallel with 6-Ω gives 2-Ω, as
calculated in Eq. (2.10.1). This 2-Ω
34. equivalent resistance is now in series
with the 1-Ω resistance to give a
combined resistance of 1Ω + 2Ω
=3Ω . Thus, we replace the circuit in
Fig. 2.38(a) with that in Fig. 2.38(b).
In Fig. 2.38(b), we combine the 2-Ω
and 3-Ω resistors in parallel to getΩ=
+
=ΩΩ 2.1
32
32
3//2
x
Ω resistor is in series with the 10-Ω resistor
Rab = 10 + 1.2 = 11.2 Ω
35.
36. Example 2.12 Find iO and vO in the
circuit shown in Fig. 2.42(a). Calculate
the power dissipated in the 3-Ω resistor.
Solution: The 6-Ω and 3-Ω resistors
are parallel, so their combined
resistance isΩ=
+
=ΩΩ 2
36
36
3//6
xThus our circuit reduces to that
shown in Fig. 2.42(b). Notice that vO is
not affected by the combination of the
resistors because the resistors are in
parallel and therefore have the same
voltage vO. From Fig. 2.42(b), we can
obtain vO in two ways. One way is to
37. Ai 2
24
12
=
+
=
and hence, vO = 2i = 2x2 = 4 V. Another
way is to apply voltage division, since
the 12 V in Fig. 2.42(b) is divided
between the 4-Ω and 2-Ω resistors.
Hence, VVvO 4)12(
42
2
=
+
=
Similarly, iO can be obtained in two way.
One approach is to apply Ohm’s law to
the 3-Ω resistor in Fig. 2.42(a) now that
we know vO; thus,
38. 43 == OO iv
AiO
3
4
=
Another approach is to apply current
division to the circuit in Fig. 2.42(a)
now that we know I, by writing
AAiiO
3
4
)2(
3
2
36
6
==
+
=
ower dissipated in the 3-Ω resistor is
Wivp OOO 333.5
3
4
4 =
==
39.
40. Example 2.13 For the circuit shown in
Fig. 2.44(a), determine: (a) the voltage
vO, (b) the power supplied by the
current source, (c) the power absorbed
by each resistor.
Solution: (a) The 6-kΩ and 12-kΩ
resistors are in series so that their
combined value is 6 + 12 = 18 kΩ .
Thus the circuit in Fig. 2.44(a)
reduces to that shown in Fig. 2.44(b).
We now apply the current division
41. mAmAi 20)30(
000,18000,9
000,18
1 =
+
=
mAmAi 10)30(
000,18000,9
000,9
2 =
+
=
Notice that the voltage across the
9-kΩ and 18-kΩ resistors are the
same, and vO = 9,000i1 = 18,000i2 =
180 V, as expected.
(b) Power supplied by the
source is WmWivp OOO 4.5)30(180 ===
42. Power absorbed by the 12-kΩ resistor is
WxRiRiiivp 2.1)000,12()1010()( 232
222 ===== −
wer absorbed by the 6-kΩ resistor is
WxRip 6.0)000,6()1010( 232
2 === −
wer absorbed by the 9-kΩ resistor is
W
R
v
p O
6.3
000,9
)180( 22
===
WmWivp O 6.3)20(1801 ===
Notices that the power supplied (5.4W)
equals the power absorbed (1.2 + 0.6 +
3.6) = 5.4 W). This is one way of
43. 2.7 Wye – Delta
transformationsWhen the resistors are neither in
parallel nor in series. For example,
the bridge circuit, this circuit can
be simplified by using three –
terminal equivalent networks, wye
(y) and delta ( ) as will be shown
in Ex.2.15.
44. Delta to Wye
conversion
Wye to delta
= Ra =
R1R2 + R2R3 + R3R1
R1
Rc =R1R2 + R2R3 + R3R1
R3
Rb =R1R2 + R2R3 + R3R1
R2
Y and balance
wh
e
n
R1 = R2 = R3 = Ry
Ra = Rb = Rc = R
Ry = R or R = 3Ry
3
Rb Rc
Ra+Rb+Rc
Rc Ra
Ra+Rb+Rc
Ra Rb
Ra+Rb+Rc
2 =
3 =
45. Example 2.14 Convert the ∆ network in Fig. 2.50(a) to an
valent Y network.
ution: Using Eqs. (2.49) to (2.51), we obta
Ω==
++
=
++
= 50
50
250
151025
1025
1
x
RRR
RR
R
cba
cb
47. Example 2.15 Obtain the equivalent
resistance Rab for the circuit in Fig.
2.52 and use it to find current i.
48. Solution: In this circuit, there are two Y network and one ∆
network. Transforming just one of these will simplify the
circuit. If we convert the Y network comprising the 5-Ω, and
20-Ω resistors, we may select
Ω= 101R Ω= 202R Ω= 53R
s from Eqs. (2.53) to (2.55) we have
10
1055202010
1
133221 xxx
R
RRRRRR
Ra
++
=
++
=
Ω== 35
10
350
50. so that the equivalent circuit is shown
in Fig. 2.53(b). Hence, we find
Ω=
+
=+= 632.9
21292.17
21292.17
21//)5.10292.7(
x
Rab
A
R
v
i
ab
s
458.12
632.9
120
===
51. 2.8 Application
Lighting systems, such as in a
house, often consist of N lamps
connected either in parallel or in
series
2.8.1 Lighting
systems
52. Assuming that all the lamps are
identical and v0 is the power – line
voltage, the voltage across each
lamp is v0 for parallel connection
and v0/N for series connection.
The series connection is easy to
manufacture but is seldom used
in practice for two reasons. First,
it is less reliable. Second, it is
harder to maintain.
53. Potentiometer is a three – terminal
device that operates on the principle
of voltage division. It is essentially an
adjustable voltage divider. As a
voltage regulator, it is used as a
volume or level control on radios, TVs
and other devices.
2.8.2 Design of DC
Meters
Potentiometer
controlling
potential levels
Vout = Vbc = Vin
Rbc
Rac
Where Rac = Rab+Rbc
Thus, vout decreases
or increases as the
sliding contact of the
pot moves toward c
54. Another application where resistors
are used to control current flow is the
analog dc meters, ammeter, voltmeter
and ohmmeter. Each of these meter
employs the d’Arsonval meter
movement.
The movement
consists of a movable
iron – core coil mounted
on a pivot between the
poles of a permanent
magnet. When current
flows through the coil, it
creates torque which
55. Voltmete
rIt measures the voltage across a load
and is connected in parallel with the
element. It consists of a d’Arsonval
movement in series with a resistor whose
resistance Rm is deliberately made very
large to minimize the current drawn from
the circuit.
( )
m
fs
fs
n
nmfsfs
R
I
V
R
RRIV
−=
+=
56. Ammete
rIt measures the current through the
load and is connected in series with it.
It consists of a d’ Arsonaval movement
in parallel with a resistor whose
resistance Rm is deliberately made very
small to minimize the voltage drop
across it.
m
mfs
m
n
fs
mn
n
m
R
II
I
R
I
RR
R
I
−
=
+
=
58. ( )
( ) )1.....(....................m
m
x
mxm
RR
I
E
R
IRRRE
+−=
++=
The resistor R is selected such
that the meter gives a full-scale
deflection when Rx = 0
fsm II =
( ) )2........(....................fsm IRRE +=
Substitute eq. (2) in (1)
( )m
m
fs
x RR
I
I
R +
−= 1
59. connected to a 9-V battery as shown in
Fig. 2.56(a). Calculate: (a) the total
current supplied by the battery, (b) the
current through each bulb, (c) the
resistance of each bulb.
Solution: (a) The total power supplied
by battery is equal to the total power
absorbed by the bulbs, that is,
p = 15 + 10 + 20 = 45 W
Since p = VI, then the total current
60. A
V
p
I 5
9
45
===(b) The bulbs can be modeled as
resistors as shown in Fig. 2.56(b).
Since R1 (20-W bulb) is in parallel with
the battery as the series combination
of R2 and R3,
V1 = V2 + V3 = 9 V
The current through R1 isA
V
p
I 222.2
9
20
1
1
1 ===
61. current through the series combination of
AIII 778.2222.2512 =−=−=
(c) Since p = I2
R,
Ω=== 05.4
222.2
20
22
1
1
1
I
p
R
Ω=== 945.1
777.2
15
22
2
2
2
I
p
R
Ω=== 297.1
777.2
10
22
3
3
3
I
p
R
62. setup of Fig. 2.60, design a voltmeter
for the following multiple ranges:
(a) 0-1 V (b) 0-5 V (c) 0-50 V
(d) 0-100 V
Assume that the internal resistance
Rm = 2 kΩ and the full scale current
.100 AI fs µ=
Solution: We apply Eq. (2.60) and
assume that R1, R2, R3, and R4
correspond with ranges 0-1 V, 0-5 V,
0-50 V, and 0-100 V, respectively.
For range 0-1 V,
Ω=−=−= −
k
x
R 82000000,102000
10100
1
61
63. or range 0-5 V, Ω=−=−= −
k
x
R 482000000,502000
10100
5
62
or range 0-50 V, Ω=−=−= −
k
x
R 4982000000,5002000
10100
50
63
or range 0-100 V, Ω=−=−= −
k
x
R 9982000000,000,12000
10100
100
64
64. .9 Summary1. A resistor is a passive element
in which the voltage v across it
is proportional to the current i
through itiRv =;R is the resistance of the resistor
en circuit is a resistor with infinite resistan
2. Short circuit is a resistor with
zero resistance(R = 0)
3. The conductor G of a resistor is
the reciprocal of its resistance
R
G
1
=
65. 4. A branch is a single two-terminal
element in an electric circuit
A node is the point of connection
between two or more branches
A loop is a closed path in a
circuit5. KCL states that the sum of the
currents entering a node equals
the sum of currents leaving the
node6. KVL states that the voltage
around a closed path
algebraically sum to zero
66. Elements are in parallel if
they have the same voltage
across them8. When two resistors are in
series
7. Elements are in series if the
same current flows through
them
21 RRReq +=
21
21
GG
GG
Geq
+
=
9. The voltage division principle
for two resistors in series is
v
RR
R
vv
RR
R
v
21
2
2
21
1
1 ,
+
=
+
=
67. 10.When two resistors R1 and R2
are in parallel
21
21
21 , GGG
RR
RR
R eqeq +=
+
=
11.The current division principle
for two resistors in parallel is
i
RR
R
ii
RR
R
i
21
1
2
21
2
1 ,
+
=
+
=
12.Delta – to – Wye conversion
cba
ba
cba
ac
cba
cb
RRR
RR
R
RRR
RR
R
RRR
RR
R
++
=
++
=
++
= 321 ,,
68. 13.Wye – to – Delta conversion
3
133221
2
133221
1
133221
R
RRRRRR
R
R
RRRRRR
R
R
RRRRRR
R
c
b
a
++
=
++
=
++
=