This document provides an overview of AC circuit analysis and three-phase systems. It discusses:
1. The basics of AC circuits including sinusoidal waveforms, impedance, and Ohm's law for AC circuits.
2. Three-phase systems including how the three voltages are phase-shifted by 120 degrees, derivation of line voltages, and generation of three-phase voltages using a three-phase generator.
3. Different connections for three-phase systems including star, delta, 4-wire and 3-wire systems and the implications of each.
1) In purely resistive AC circuits, the current is in phase with the applied voltage. The power is given by the product of the rms current and voltage.
2) In purely inductive and capacitive circuits, the average power over a cycle is zero as the energy stored during one quarter cycle is returned during the next quarter cycle, so no net power is consumed.
3) Practical inductive circuits contain both inductance and resistance. The power consumed is given by the product of the current and voltage drop across the resistor, which are in phase. This power is known as the "true" power.
Here are the key steps to solve this problem:
1) Draw the circuit diagram showing R, L, C in series with the AC voltage source.
2) Write the impedance equation:
Z = √(R2 + (XL - XC)2)
3) Calculate the individual reactances:
XL = 2πfL
XC = 1/(2πfC)
4) Calculate the net reactance:
Xnet = XL - XC
5) Calculate the impedance Z by plugging values into the impedance equation.
6) Use Ohm's law to calculate the current:
Irms = Vrms/Z
Okay, let's think through this step-by-step:
* When just the resistor is connected, power is 1.000 W
* When the capacitor is added, power is 0.500 W
* When the inductor is added (without the capacitor), power is 0.250 W
* Power delivered is proportional to the square of the current. As impedance increases, current decreases.
* With just the resistor, impedance is lowest so current is highest and power is 1.000 W
* Adding the capacitor increases impedance, so current decreases and power is 0.500 W
* Adding the inductor further increases impedance, so current decreases more and power is 0.250 W
1) An AC circuit uses a power source that provides alternating current where the voltage varies sinusoidally over time.
2) In a purely resistive AC circuit, the current and voltage are in phase and their instantaneous values are proportional based on Ohm's law.
3) Capacitors and inductors introduce phase shifts in AC circuits - the current through a capacitor lags 90 degrees behind the voltage, while the current through an inductor leads the voltage by 90 degrees.
1. The document describes theorems for analyzing AC circuits, including superposition, Thevenin's, and Norton's theorems.
2. Superposition theorem states that the current in any element of a linear circuit with multiple independent sources is the algebraic sum of the currents produced by each source acting alone.
3. Thevenin's and Norton's theorems provide methods to reduce two-terminal AC circuits to equivalent circuits of a voltage source in series with an impedance or a current source in parallel with an impedance, respectively.
This document provides an overview of AC fundamentals including:
- Definitions of key terms like EMF, direct current, alternating current, sinusoid, angular velocity, frequency, time period, average value, effective value
- How electrical power is generated using alternating current
- Terminologies related to sinusoidal waveforms like instantaneous value, maximum value, phase difference
- Phasor representation of sinusoidal quantities using rotating vectors
- Properties of inductors and capacitors and their behavior in AC circuits
- Phasor algebra and representation of sinusoidal quantities using complex numbers
The document discusses sinusoidal waveforms, which are fundamental to alternating current. It defines key characteristics of sine waves such as amplitude, period, frequency, and how they are related. The document also covers how sinusoidal voltages are generated by AC generators and function generators. It describes methods for specifying the voltage value of sine waves, including peak, RMS, average and peak-to-peak values. Finally, it introduces phasors as a way to represent rotating vectors for analyzing AC circuits using trigonometry.
1) In purely resistive AC circuits, the current is in phase with the applied voltage. The power is given by the product of the rms current and voltage.
2) In purely inductive and capacitive circuits, the average power over a cycle is zero as the energy stored during one quarter cycle is returned during the next quarter cycle, so no net power is consumed.
3) Practical inductive circuits contain both inductance and resistance. The power consumed is given by the product of the current and voltage drop across the resistor, which are in phase. This power is known as the "true" power.
Here are the key steps to solve this problem:
1) Draw the circuit diagram showing R, L, C in series with the AC voltage source.
2) Write the impedance equation:
Z = √(R2 + (XL - XC)2)
3) Calculate the individual reactances:
XL = 2πfL
XC = 1/(2πfC)
4) Calculate the net reactance:
Xnet = XL - XC
5) Calculate the impedance Z by plugging values into the impedance equation.
6) Use Ohm's law to calculate the current:
Irms = Vrms/Z
Okay, let's think through this step-by-step:
* When just the resistor is connected, power is 1.000 W
* When the capacitor is added, power is 0.500 W
* When the inductor is added (without the capacitor), power is 0.250 W
* Power delivered is proportional to the square of the current. As impedance increases, current decreases.
* With just the resistor, impedance is lowest so current is highest and power is 1.000 W
* Adding the capacitor increases impedance, so current decreases and power is 0.500 W
* Adding the inductor further increases impedance, so current decreases more and power is 0.250 W
1) An AC circuit uses a power source that provides alternating current where the voltage varies sinusoidally over time.
2) In a purely resistive AC circuit, the current and voltage are in phase and their instantaneous values are proportional based on Ohm's law.
3) Capacitors and inductors introduce phase shifts in AC circuits - the current through a capacitor lags 90 degrees behind the voltage, while the current through an inductor leads the voltage by 90 degrees.
1. The document describes theorems for analyzing AC circuits, including superposition, Thevenin's, and Norton's theorems.
2. Superposition theorem states that the current in any element of a linear circuit with multiple independent sources is the algebraic sum of the currents produced by each source acting alone.
3. Thevenin's and Norton's theorems provide methods to reduce two-terminal AC circuits to equivalent circuits of a voltage source in series with an impedance or a current source in parallel with an impedance, respectively.
This document provides an overview of AC fundamentals including:
- Definitions of key terms like EMF, direct current, alternating current, sinusoid, angular velocity, frequency, time period, average value, effective value
- How electrical power is generated using alternating current
- Terminologies related to sinusoidal waveforms like instantaneous value, maximum value, phase difference
- Phasor representation of sinusoidal quantities using rotating vectors
- Properties of inductors and capacitors and their behavior in AC circuits
- Phasor algebra and representation of sinusoidal quantities using complex numbers
The document discusses sinusoidal waveforms, which are fundamental to alternating current. It defines key characteristics of sine waves such as amplitude, period, frequency, and how they are related. The document also covers how sinusoidal voltages are generated by AC generators and function generators. It describes methods for specifying the voltage value of sine waves, including peak, RMS, average and peak-to-peak values. Finally, it introduces phasors as a way to represent rotating vectors for analyzing AC circuits using trigonometry.
This document provides information about AC circuit analysis including:
1) AC current periodically reverses direction while DC flows in one direction. AC power is delivered to homes and businesses as a sine wave.
2) A simple generator consists of a coil rotating in a magnetic field, inducing a sinusoidal waveform. One cycle is produced per coil revolution.
3) The frequency of an AC generator output depends on the coil rotation speed and number of magnetic pole pairs. Higher speeds or more pole pairs increases frequency.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
The document discusses alternating current circuits and provides learning objectives and specific objectives about alternating current waveforms. It defines key terms like frequency, amplitude, average value, maximum value, and root mean square value. It explains how an alternator generates a sine wave alternating current through a rotating coil in a magnetic field. The current periodically changes direction with each half rotation of the coil.
AC circuits usually contain inductance or capacitance which cause reactance. Reactance is resistance to current flow due to these components and is measured in ohms. There are two types of reactance - inductive reactance XL and capacitive reactance XC. Phasor diagrams can represent alternating quantities, with the phase angle between voltage and current indicating whether a circuit is resistive, capacitive, or inductive.
This document provides an outline and overview of key concepts in alternating current (AC) circuits including:
1. AC sources and how AC voltage and current vary sinusoidally over time.
2. The behavior of resistors, inductors, and capacitors in AC circuits, including how their current and voltage are phase shifted.
3. Series RLC circuits and the concept of resonance where the current is at its maximum.
4. Power calculations in AC circuits and the power factor.
5. Transformers and how they are used for power transmission. Electrical filters are also discussed.
This document contains the syllabus and content outline for a course on Basic Electrical Engineering. It covers topics such as Ohm's Law, Kirchhoff's Laws, network analysis techniques including nodal analysis and mesh analysis, AC circuit analysis using phasors, series and parallel RLC circuits, network theorems, resonance, and fundamentals of electrical machines including transformers, induction motors, and DC motors. The course aims to provide students a strong foundation in core electrical engineering concepts and their practical applications.
1. The document discusses single phase AC circuits including definitions of terms like amplitude, time period, frequency, instantaneous value. It also discusses generation of sinusoidal AC voltage using a rotating coil.
2. Key concepts discussed include phasor representation, RMS and average values, form factor, phase difference, AC circuits with pure resistance and inductance. Instantaneous and average power calculations for resistive and inductive circuits are also presented.
3. Various waveforms, equations and phasor representations are used to explain these concepts for sinusoidal quantities in AC circuits.
This document summarizes key concepts about alternating current (AC) circuits including resistors, inductors, and capacitors in AC circuits. It discusses the RLC series circuit, power in AC circuits, and resonance. It also covers transformers and how they are used for power transmission by stepping voltages up or down. Resonance occurs at the resonance frequency when the inductive reactance equals the capacitive reactance in a RLC series circuit, resulting in maximum current. Transformers use magnetic induction to change AC voltages efficiently for applications like power distribution.
Alternating current (AC), is an electric current in which the flow of electric charge periodically reverses direction, whereas in direct current (DC, also dc), the flow of electric charge is only in one direction.
This document discusses alternating current (AC) circuits. It begins by describing how an alternating electromotive force (EMF) is generated using a coil rotating in a magnetic field. Equations are provided showing that both the induced EMF and current vary as sine functions. Common terms used in AC circuits like cycle, frequency, phase, and root mean square (RMS) value are defined. Phasor diagrams are introduced to represent AC quantities in terms of magnitude and direction. Derivations of average and RMS values are shown. Finally, a purely resistive AC circuit is analyzed, showing the current is in phase with voltage and both follow sine waves. Power calculations are also demonstrated.
Three-phase systems have multiple voltages or currents that are displaced in time by 120 degrees. They provide advantages over single-phase systems like higher power capacity, self-starting motors, and more constant power output.
A 3-phase generator produces 3 voltages displaced by 120 degrees through its winding configuration. The voltages can be connected in either a star or delta configuration. In a star connection, the winding ends meet at a central neutral point. In a delta connection, the windings are connected in a closed loop.
Power in a 3-phase circuit can be measured using either 3 wattmeters connected to each phase, or 2 wattmeters connected across different phase combinations to calculate total power.
This document provides a summary of a group presentation on series AC circuits. Group 11, consisting of Robiul Awal Robi, Abdul Wahid, and Abu Jauad Khan Aliv, will be presenting on R-L series circuits, R-C series circuits, and R-L-C series circuits. The document outlines the analysis of each circuit type, including equations for total voltage and phase angle. It also notes a special case where the inductor and capacitor impedances are equal, resulting in a purely resistive circuit with zero phase angle. Sources for the material are listed at the end.
This document defines key terms and concepts related to electrical circuits and networks. It discusses different types of circuits including linear/non-linear, bilateral/unilateral circuits. It also defines electrical networks and their components such as nodes, branches, loops and meshes. Finally, it covers important circuit analysis techniques including Ohm's law, Kirchhoff's laws, mesh analysis, nodal analysis and superposition theorem.
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
1. Alternating current (AC) electricity alternates direction periodically compared to direct current (DC) which flows in one direction. AC is generated by AC generators at frequencies like 50-60 Hz.
2. The root mean square (rms) value is used to quantify AC voltage and current as it represents the equivalent steady DC power. Rms current and voltage are defined using formulas involving averaging the square of the instantaneous values.
3. In AC circuits, elements have both resistance and reactance properties. Resistance is opposition to current from resistance. Reactance is opposition from inductance or capacitance. Capacitive and inductive reactance are defined using frequency and element values. Impedance combines resistance and
This Slide is made of many important information which are very easily discussed in this slide briefly. I hope, after watching this slide , you will get some analytical information on Alternative Current(AC).Actually, this slide was made for my University Presentation.
This document discusses alternating current (AC) generation and properties. It describes how an AC generator produces a sinusoidal waveform by inducing a voltage in its armature coils. The waveform cycles between positive and negative alternations, with its peak, peak-to-peak, and effective (RMS) values defined. It also covers the relationship between frequency and period, and introduces common nonsinusoidal waveforms like square, triangular, and sawtooth.
Engineering review on AC circuit steady state analysis. Presentation lecture for energy engineering class.
Course MS in Renewable Energy Engineering, Oregon institute of technology
This document discusses the history and characteristics of alternating current (AC). It explains that AC electricity is generated by an AC electric generator and flows first in one direction and then the other, unlike direct current. Some key advantages of AC are that it can be transformed between voltages and controlled by various circuit components. The document also covers concepts such as reactance, impedance, and phase relationships in AC circuits. It describes how AC behaves differently than DC in capacitors and inductors due to the changing current.
Calculations of a.c distributions methods & 3 phase unbalanced loads &...vishalgohel12195
This document presents information on calculations for AC distribution methods, three-phase unbalanced loads, four-wire star-connected unbalanced loads, and ground detectors. It discusses two methods for calculating AC distribution based on load power factors referred to the receiving end voltage or respective load voltages. It also describes different types of unbalanced three-phase loads including four-wire star-connected and delta-connected loads. Ground detectors are defined as devices used to detect ground faults on ungrounded AC systems.
The document summarizes an advanced grid connection workshop that took place on July 16th, 2013. The workshop covered various topics related to connecting renewable energy projects to the grid, including variation in grid voltage, rural grid infrastructure, larger grid connection projects, and the application process. It included exercises for participants to complete site surveys and applications. The workshop aimed to provide interactive learning and support for connecting wind and other renewable technology projects to the grid.
This document provides information about AC circuit analysis including:
1) AC current periodically reverses direction while DC flows in one direction. AC power is delivered to homes and businesses as a sine wave.
2) A simple generator consists of a coil rotating in a magnetic field, inducing a sinusoidal waveform. One cycle is produced per coil revolution.
3) The frequency of an AC generator output depends on the coil rotation speed and number of magnetic pole pairs. Higher speeds or more pole pairs increases frequency.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
The document discusses alternating current circuits and provides learning objectives and specific objectives about alternating current waveforms. It defines key terms like frequency, amplitude, average value, maximum value, and root mean square value. It explains how an alternator generates a sine wave alternating current through a rotating coil in a magnetic field. The current periodically changes direction with each half rotation of the coil.
AC circuits usually contain inductance or capacitance which cause reactance. Reactance is resistance to current flow due to these components and is measured in ohms. There are two types of reactance - inductive reactance XL and capacitive reactance XC. Phasor diagrams can represent alternating quantities, with the phase angle between voltage and current indicating whether a circuit is resistive, capacitive, or inductive.
This document provides an outline and overview of key concepts in alternating current (AC) circuits including:
1. AC sources and how AC voltage and current vary sinusoidally over time.
2. The behavior of resistors, inductors, and capacitors in AC circuits, including how their current and voltage are phase shifted.
3. Series RLC circuits and the concept of resonance where the current is at its maximum.
4. Power calculations in AC circuits and the power factor.
5. Transformers and how they are used for power transmission. Electrical filters are also discussed.
This document contains the syllabus and content outline for a course on Basic Electrical Engineering. It covers topics such as Ohm's Law, Kirchhoff's Laws, network analysis techniques including nodal analysis and mesh analysis, AC circuit analysis using phasors, series and parallel RLC circuits, network theorems, resonance, and fundamentals of electrical machines including transformers, induction motors, and DC motors. The course aims to provide students a strong foundation in core electrical engineering concepts and their practical applications.
1. The document discusses single phase AC circuits including definitions of terms like amplitude, time period, frequency, instantaneous value. It also discusses generation of sinusoidal AC voltage using a rotating coil.
2. Key concepts discussed include phasor representation, RMS and average values, form factor, phase difference, AC circuits with pure resistance and inductance. Instantaneous and average power calculations for resistive and inductive circuits are also presented.
3. Various waveforms, equations and phasor representations are used to explain these concepts for sinusoidal quantities in AC circuits.
This document summarizes key concepts about alternating current (AC) circuits including resistors, inductors, and capacitors in AC circuits. It discusses the RLC series circuit, power in AC circuits, and resonance. It also covers transformers and how they are used for power transmission by stepping voltages up or down. Resonance occurs at the resonance frequency when the inductive reactance equals the capacitive reactance in a RLC series circuit, resulting in maximum current. Transformers use magnetic induction to change AC voltages efficiently for applications like power distribution.
Alternating current (AC), is an electric current in which the flow of electric charge periodically reverses direction, whereas in direct current (DC, also dc), the flow of electric charge is only in one direction.
This document discusses alternating current (AC) circuits. It begins by describing how an alternating electromotive force (EMF) is generated using a coil rotating in a magnetic field. Equations are provided showing that both the induced EMF and current vary as sine functions. Common terms used in AC circuits like cycle, frequency, phase, and root mean square (RMS) value are defined. Phasor diagrams are introduced to represent AC quantities in terms of magnitude and direction. Derivations of average and RMS values are shown. Finally, a purely resistive AC circuit is analyzed, showing the current is in phase with voltage and both follow sine waves. Power calculations are also demonstrated.
Three-phase systems have multiple voltages or currents that are displaced in time by 120 degrees. They provide advantages over single-phase systems like higher power capacity, self-starting motors, and more constant power output.
A 3-phase generator produces 3 voltages displaced by 120 degrees through its winding configuration. The voltages can be connected in either a star or delta configuration. In a star connection, the winding ends meet at a central neutral point. In a delta connection, the windings are connected in a closed loop.
Power in a 3-phase circuit can be measured using either 3 wattmeters connected to each phase, or 2 wattmeters connected across different phase combinations to calculate total power.
This document provides a summary of a group presentation on series AC circuits. Group 11, consisting of Robiul Awal Robi, Abdul Wahid, and Abu Jauad Khan Aliv, will be presenting on R-L series circuits, R-C series circuits, and R-L-C series circuits. The document outlines the analysis of each circuit type, including equations for total voltage and phase angle. It also notes a special case where the inductor and capacitor impedances are equal, resulting in a purely resistive circuit with zero phase angle. Sources for the material are listed at the end.
This document defines key terms and concepts related to electrical circuits and networks. It discusses different types of circuits including linear/non-linear, bilateral/unilateral circuits. It also defines electrical networks and their components such as nodes, branches, loops and meshes. Finally, it covers important circuit analysis techniques including Ohm's law, Kirchhoff's laws, mesh analysis, nodal analysis and superposition theorem.
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
1. Alternating current (AC) electricity alternates direction periodically compared to direct current (DC) which flows in one direction. AC is generated by AC generators at frequencies like 50-60 Hz.
2. The root mean square (rms) value is used to quantify AC voltage and current as it represents the equivalent steady DC power. Rms current and voltage are defined using formulas involving averaging the square of the instantaneous values.
3. In AC circuits, elements have both resistance and reactance properties. Resistance is opposition to current from resistance. Reactance is opposition from inductance or capacitance. Capacitive and inductive reactance are defined using frequency and element values. Impedance combines resistance and
This Slide is made of many important information which are very easily discussed in this slide briefly. I hope, after watching this slide , you will get some analytical information on Alternative Current(AC).Actually, this slide was made for my University Presentation.
This document discusses alternating current (AC) generation and properties. It describes how an AC generator produces a sinusoidal waveform by inducing a voltage in its armature coils. The waveform cycles between positive and negative alternations, with its peak, peak-to-peak, and effective (RMS) values defined. It also covers the relationship between frequency and period, and introduces common nonsinusoidal waveforms like square, triangular, and sawtooth.
Engineering review on AC circuit steady state analysis. Presentation lecture for energy engineering class.
Course MS in Renewable Energy Engineering, Oregon institute of technology
This document discusses the history and characteristics of alternating current (AC). It explains that AC electricity is generated by an AC electric generator and flows first in one direction and then the other, unlike direct current. Some key advantages of AC are that it can be transformed between voltages and controlled by various circuit components. The document also covers concepts such as reactance, impedance, and phase relationships in AC circuits. It describes how AC behaves differently than DC in capacitors and inductors due to the changing current.
Calculations of a.c distributions methods & 3 phase unbalanced loads &...vishalgohel12195
This document presents information on calculations for AC distribution methods, three-phase unbalanced loads, four-wire star-connected unbalanced loads, and ground detectors. It discusses two methods for calculating AC distribution based on load power factors referred to the receiving end voltage or respective load voltages. It also describes different types of unbalanced three-phase loads including four-wire star-connected and delta-connected loads. Ground detectors are defined as devices used to detect ground faults on ungrounded AC systems.
The document summarizes an advanced grid connection workshop that took place on July 16th, 2013. The workshop covered various topics related to connecting renewable energy projects to the grid, including variation in grid voltage, rural grid infrastructure, larger grid connection projects, and the application process. It included exercises for participants to complete site surveys and applications. The workshop aimed to provide interactive learning and support for connecting wind and other renewable technology projects to the grid.
Glenda Cox on Open Educational Resources in Higher EducationDaniela Gachago
This document discusses open education resources (OER) and their potential benefits. OER refer to educational materials that are openly licensed and freely available online. They can be shared, reused, remixed and redistributed. The document outlines several challenges in higher education globally and in South Africa that OER could help address, such as increasing demand, costs, and quality issues. It also discusses factors that impact OER adoption like philosophy, technology, finances, legal issues, pedagogy and quality. Potential benefits of OER include increasing access to education, reducing costs, improving teaching quality and visibility for institutions.
This document discusses phasor diagrams and their use in analyzing AC circuits. It begins by defining phasors and explaining that phasor diagrams represent the magnitude and phase of sinusoidal voltages and currents. The document then examines phasor diagrams for pure resistive, inductive, and capacitive circuits. In a pure resistive circuit, the current and voltage are in phase. In a pure inductive circuit, the current lags the voltage by 90 degrees. In a pure capacitive circuit, the current leads the voltage by 90 degrees. Characteristics of each type of circuit are provided along with examples of phasor diagrams.
This document discusses phasor analysis of RC, RL, and RLC circuits.
For an RC circuit, the voltage across the capacitor lags behind the current by 90 degrees. For an RL circuit, the voltage across the inductor leads the current by 90 degrees.
For an RLC circuit, the behavior depends on whether the reactance of the inductor or capacitor is higher. If the inductor reactance is higher, it behaves like an RL circuit. If the capacitor reactance is higher, it behaves like an RC circuit. If the reactances are equal, it behaves like a resistive circuit.
1. Nodal analysis can be used to analyze the circuit. There are 3 non-reference nodes so 3 node voltage equations are required. (2) The node voltage equations relate the node voltages (v1, v2, v3) to the independent current sources (I1, I2) through the conductance matrix. (3) Writing the equations in matrix form produces: Gv=i where G is the 3x3 conductance matrix, v is the 3x1 node voltage vector, and i is the 3x1 independent current source vector.
Alternating Current Machines-Synchronous MachinesTalia Carbis
This document provides an overview of synchronous machines including:
- Synchronous machines operate at synchronous speed and lock into the rotating magnetic field produced by the stator.
- The rotor is a magnet that is dragged along for the ride as the rotating magnetic field rotates.
- Torque is produced as the magnetic fields of the rotor and stator interact. The torque allows the motor to operate at a constant synchronous speed under varying load.
The Parallel RLC Circuit is the exact opposite to the series circuit we looked at in the previous tutorial although some of the previous concepts and equations still apply.
This document discusses two methods for circuit analysis: mesh analysis and supermesh analysis. Mesh analysis involves identifying each loop or "mesh" in the circuit and assigning a mesh current to each one. Kirchhoff's voltage law is applied to write an equation for each mesh. Supermesh analysis combines meshes that share a current source into a single "supermesh". This reduces the number of mesh equations but introduces additional equations for the current sources. The document provides examples of setting up and solving systems of equations using both mesh and supermesh analysis.
This document discusses marketing channels and channel management. It defines marketing channels as sets of interdependent organizations that make a product available for use. Channels perform important functions like information gathering, stimulating purchases, negotiating prices, ordering, financing inventory, storage, and payment. Channel design considers customer expectations, objectives, constraints, alternatives that are evaluated. Channel management includes selecting, training, motivating, and evaluating channel members. Channels are dynamic and can involve vertical, horizontal, and multi-channel systems. Conflicts between channels must be managed to balance cooperation and competition.
The document introduces the mesh-current method for solving electric circuits. It defines key terms like mesh and essential branch. The steps of the mesh-current method are: 1) identify meshes, 2) assign a current to each mesh, 3) write Kirchhoff's voltage law equations for each mesh in terms of the mesh currents, and 4) solve the resulting system of equations. Examples are provided to demonstrate how to apply the method to circuits with different elements like dependent sources.
Mesh analysis is a technique for analyzing electrical circuits using loops or meshes. It involves assigning a mesh current to each loop and writing Kirchhoff's voltage law equations for each mesh. The mesh equations take the form of a matrix equation that can be solved for the unknown mesh currents. Key aspects of mesh analysis include defining mesh currents, writing KVL equations clockwise around each mesh, identifying common resistance terms between meshes, and handling circuits with current sources by removing the source and including it as a constraint.
The document discusses three-phase circuits and their analysis. It covers balanced and unbalanced three-phase configurations, power in balanced systems, and analyzing unbalanced systems using PSpice. The objectives are to understand different three-phase connections, distinguish balanced and unbalanced circuits, calculate power in balanced systems, analyze unbalanced systems, and apply the concepts to measurement and residential wiring. Key points covered include wye-wye, wye-delta, delta-delta, and delta-wye connections for both sources and loads.
The document discusses mesh analysis, which is a technique for solving circuits. It begins by defining some key concepts of mesh analysis, such as assigning a mesh current to each closed loop in the circuit. It then provides the general procedure for performing mesh analysis, which involves counting meshes, defining currents, writing Kirchhoff's voltage law equations for each mesh, and solving the equations. Finally, it provides an example circuit and walks through setting up and solving the mesh equations for that circuit.
The document discusses a three phase diode rectifier presentation. It describes several three phase rectifier circuits including a half wave rectifier using three diodes, a six pulse midpoint rectifier, and a full wave bridge rectifier using six diodes. Equations are provided for the output voltage and current calculations for each circuit. Key specifications of automotive-grade rectifier diodes are also listed.
This document discusses node and mesh analysis techniques for solving circuit problems. Node analysis involves applying Kirchhoff's Current Law (KCL) at nodes and solving the resulting equations. Mesh analysis involves labeling mesh currents, applying Kirchhoff's Voltage Law (KVL) in each mesh, and solving for the unknown currents. Examples are provided for both node and mesh analysis. Common methods for solving the linear equations generated include substitution, determinants, calculators, and numerical methods.
Electric Circuit - Introduction + Lecture#1Hassaan Rahman
This document outlines the course details for EEE 121: Electric Circuit Analysis - I. It includes information on:
1. The course credits (3 credits for theory, 1 credit for lab), marks distribution (assignments, quizzes, exams), and textbooks.
2. An overview of the high-level lecture topics which will be covered, including circuit variables, resistive circuits, analysis techniques, inductance, capacitance, and first/second order circuits.
3. A list of 15 experiments to be performed in the lab component of the course covering topics like Ohm's law, resistor combinations, Kirchhoff's laws, voltage and current dividers, and more.
The document summarizes a seminar presentation on AC-DC converters given by Ankur Mahajan. The presentation covered single phase half wave and full wave converters. It discussed various rectifier types including uncontrolled, half controlled, and fully controlled bridges. It provided calculations for average and RMS voltage values for different converter configurations under resistive and inductive loads. The presentation also covered single phase half controlled and fully controlled bridge converters in both continuous and discontinuous conduction modes.
The document summarizes key concepts about electromagnetic induction, including:
- Electromagnetic induction occurs when a magnet moves in and out of a solenoid, cutting the magnetic flux and inducing a current in the wire coil.
- Faraday's law and Lenz's law govern the direction and magnitude of induced currents.
- An AC generator uses the principle of electromagnetic induction to generate an alternating current through the rotation of a coil within a magnetic field.
- Transformers are used to change the voltage of an AC supply through electromagnetic induction between a primary and secondary coil.
The document summarizes the working principles of an AC generator. It describes how an AC generator converts mechanical energy into alternating electrical energy using electromagnetic induction. As a coil rotates in a magnetic field, the changing magnetic flux induces an alternating current in the coil. Slip rings and carbon brushes allow the alternating current to flow to an external load. The induced electromotive force and current follow a sinusoidal waveform as the coil rotates, with the current reversing direction each half cycle to produce an alternating current. Modern power plants use large AC generators powered by turbines to produce electricity on a massive scale.
1) AC voltage periodically reverses direction, switching polarity back and forth 50-60 times per second, whereas DC voltage flows in one direction only.
2) Any change in a coil's magnetic environment, such as moving it within a magnetic field, induces an electromotive force (EMF) in the coil based on Faraday's law of induction.
3) In a basic single coil AC generator, the coil's rotation within a magnetic field produces a sinusoidal alternating current, with the instantaneous voltage determined by the coil's position and the maximum induced voltage.
1) The document discusses the generation of alternating current using a single-turn alternator with a rotating coil within a magnetic field.
2) As the coil rotates, an alternating voltage is induced based on Faraday's law of electromagnetic induction. The magnitude of the induced voltage depends on the angle of rotation and reaches its maximum when the coil is perpendicular to the magnetic field lines.
3) The instantaneous induced voltage can be expressed as a sinusoidal function of the angle of rotation, with the maximum voltage achieved at 90° of rotation. This generates an alternating current through a load that also follows a sinusoidal pattern.
unit-1-Three phase circuits and power systems.pdfdeepaMS4
This document outlines the objectives and topics covered in a course on basics of electrical and instrumentation engineering. The objectives are to analyze operation of three phase electrical circuits, deal with principles of electrical machines, and understand various measuring instruments. Key topics covered include three phase power supply, balanced and unbalanced loads, power equations, star delta conversions, and electrical measurements. Outcomes include understanding concepts of three phase power circuits and measurement, electrical generators/motors/transformers, and choosing appropriate measuring instruments for applications.
Incomplete PPT on first topic.pptx [Autosaved] [Autosaved].pptShubhobrataRudr
The document provides information on rotating electrical machines. It discusses the basic concepts of electromechanical energy conversion that occurs due to changes in flux linkages resulting from mechanical motion. It describes different types of machine windings including armature, field, AC, and distributed windings. The document also covers the generation of a rotating magnetic field in a three-phase system using three coils with currents that are equal in magnitude and phase-displaced by 120 degrees, resulting in a constant magnitude rotating magnetic field. It derives expressions for the induced voltages in coils and discusses factors that affect the induced voltages.
lec 8 and 9 single phase transformer.pptxssuser76a9bc
The document discusses single phase transformers, including their construction, operation principle, ideal and non-ideal models, and methods to determine component values. A transformer transfers energy between circuits through electromagnetic induction. It has a core made of laminated silicon steel and windings wrapped around the core. Varying the primary current induces a voltage in the secondary according to Faraday's law of induction and the turns ratio. Real transformers have losses accounted for in their equivalent circuit model, which is used to analyze power flow and regulation. Component values are found through short-circuit, open-circuit, and DC tests.
This document discusses key concepts related to three-phase electrical circuits and power measurement. It begins by outlining the objectives and outcomes of the course, which are to analyze three-phase circuits, understand electrical machines, and choose appropriate measuring instruments. The document then covers topics such as the advantages of three-phase power systems, generation of three-phase voltages, phase sequences, balanced and unbalanced loads, power equations for star and delta connections, and star-delta conversions. Diagrams are provided to illustrate three-phase waveforms, voltage and current relationships in star and delta configurations, and power calculations.
This document discusses electricity and defines key concepts related to electric current. It defines current as the rate of flow of electric charge and gives its SI unit as the ampere. It describes conventional current as the flow of positive charges and electric current as the flow of negative charges. It also discusses different types of current sources and the effects of electric current, including heating, chemical, and magnetic effects.
This document defines electricity and electric current. It explains that electric current is the flow of electric charge and is measured in Amperes. It also discusses different types of current sources like cells, generators, thermo-couples and solar cells. The document then covers several effects of electric current including heating, chemical, and magnetic effects. It explains electromagnetism and how electric currents produce magnetic fields based on experiments by Hans Oersted.
DC generators convert mechanical energy to electrical energy using electromagnetic induction. They have a stationary part that produces a magnetic field and a rotating part called the armature. As the armature rotates in the magnetic field, a current is induced based on Faraday's law of induction. The commutator ensures the current flows in one direction to the load. The main parts are the magnetic frame, field coils, armature core and windings, commutator and brushes. The types of DC generators are separately excited, shunt, series and compound wound which differ in how the field and armature windings are connected. They have various applications including battery charging, motor operation, and power distribution.
1. Electromagnetic induction occurs when a changing magnetic field induces a current in a conductor. This can be generated by moving a magnet near a coil or changing the current in a neighboring circuit.
2. Faraday's law states that an electromotive force (EMF) is induced in a conductor whenever the magnetic flux through the conductor changes. The magnitude of the induced EMF is proportional to the rate of change of flux.
3. Transformers use electromagnetic induction to change the voltage of alternating current. A step-up transformer increases voltage by having fewer turns in the primary coil, while a step-down transformer decreases voltage with more turns in the primary coil.
The document summarizes the key components and working principle of an AC generator. The AC generator converts mechanical energy to electrical energy through electromagnetic induction. It has a field magnet that produces a magnetic field, an armature coil that rotates in this field, slip rings to carry the alternating current produced, and brushes to transfer the current to an external circuit. As the coil rotates, the changing magnetic flux induces an alternating current whose frequency depends on the rotation speed.
A transformer is a device that changes alternating current (ac) electric power at one voltage level to ac power at another voltage level through magnetic induction. It consists of two or more coils wound around a core and linked by a magnetic field. An ideal transformer has no losses and the power input equals the power output. Real transformers have losses due to winding resistance, core losses, and leakage fluxes. The performance of real transformers can be modeled using an equivalent circuit with parameters determined from open-circuit and short-circuit tests. Transformer voltage regulation and efficiency are important performance metrics.
- Electromagnetic induction is the process of generating current through a wire in a changing magnetic field. When a wire moves perpendicular to a magnetic field, charges in the wire move and create an induced electromotive force (EMF).
- Transformers use electromagnetic induction to increase or decrease alternating current voltages. They have primary and secondary coils wound around an iron core. The ratio of turns determines the ratio of voltages.
- Lenz's law states that the direction of the induced current is such that the magnetic field it creates opposes the original change in magnetic flux that caused it. This induced magnetic field allows transformers, motors, and generators to function.
The document discusses alternating current (AC) and provides details about its key characteristics:
1) AC electricity alternates direction periodically in a back-and-forth motion, unlike direct current which flows in one direction.
2) The instantaneous value of AC varies sinusoidally over time between a maximum and minimum value.
3) Common applications of AC include power transmission and use in homes/businesses due to advantages like easy voltage transformation.
The document discusses alternating current (AC) and provides details about its key characteristics:
1) AC electricity alternates direction periodically in a back-and-forth motion, unlike direct current which flows in one direction.
2) The instantaneous value of AC varies sinusoidally over time between a maximum and minimum value.
3) Common applications of AC include transmission of electricity over long distances using transformers and conversion to DC using rectifiers.
1. Michael Faraday discovered the principles of electromagnetic induction in the early 19th century through experiments showing that a changing magnetic field can induce an electromotive force (emf) in a nearby conductor.
2. Faraday's law of induction states that the magnitude of the induced emf is proportional to the rate of change of the magnetic flux through a circuit.
3. Generators and motors operate based on Faraday's law - a rotating coil of wire inside a magnetic field will experience a changing magnetic flux, inducing an emf to generate electricity in a generator, or experience a torque to cause rotation as a motor.
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B tech ee ii_ eee_ u-2_ ac circuit analysis_dipen patel
1. Unit 2
AC Circuit Analysis
Course : B.Tech
Branch : EE
Semester : II
Subject : Elements of Electrical Engineering
2. AC circuit
• In alternating current (AC, also ac), the flow of electric
charge periodically reverses direction. In direct
current (DC, alsodc), the flow of electric charge is only
in one direction. The abbreviations AC and DC are often
used to mean simply alternating and direct, as when
they modify current or voltage.
• AC is the form in which electric power is delivered to
businesses and residences. The usual waveform of
an AC power circuit is a sine wave. In certain
applications, different waveforms are used, such
as triangular or square waves. Audio and radio signals
carried on electrical wires are also examples of
alternating current. In these applications, an important
goal is often the recovery of information encoded
(or modulated) onto the AC signal.
4. Cont..
• However, if the conductor moves in parallel with the
magnetic field in the case of points A and B, no lines of
flux are cut and no EMF is induced into the conductor,
but if the conductor moves at right angles to the
magnetic field as in the case of points C and D, the
maximum amount of magnetic flux is cut producing the
maximum amount of induced EMF.
• Also, as the conductor cuts the magnetic field at
different angles between points A and C, 0 and 90o the
amount of induced EMF will lie somewhere between
this zero and maximum value. Then the amount of emf
induced within a conductor depends on the angle
between the conductor and the magnetic flux as well
as the strength of the magnetic field.
5. Cont..
• to convert a mechanical energy such as
rotation, into electrical energy, a Sinusoidal
Waveform. A simple generator consists of a pair of
permanent magnets producing a fixed magnetic
field between a north and a south pole. Inside this
magnetic field is a single rectangular loop of wire
that can be rotated around a fixed axis allowing it to
cut the magnetic flux at various angles as shown
below.
7. Cont..
• As the coil rotates anticlockwise around the central axis which
is perpendicular to the magnetic field, the wire loop cuts the
lines of magnetic force set up between the north and south
poles at different angles as the loop rotates. The amount of
induced EMF in the loop at any instant of time is proportional
to the angle of rotation of the wire loop.
• As this wire loop rotates, electrons in the wire flow in one
direction around the loop. Now when the wire loop has
rotated past the 180o point and moves across the magnetic
lines of force in the opposite direction, the electrons in the
wire loop change and flow in the opposite direction. Then the
direction of the electron movement determines the polarity
of the induced voltage.
8. Cont..
• So we can see that when the loop or coil physically rotates
one complete revolution, or 360o, one full sinusoidal
waveform is produced with one cycle of the waveform
being produced for each revolution of the coil. As the coil
rotates within the magnetic field, the electrical connections
are made to the coil by means of carbon brushes and slip-
rings which are used to transfer the electrical current
induced in the coil.
• The amount of EMF induced into a coil cutting the magnetic
lines of force is determined by the following three factors.
• • Speed – the speed at which the coil rotates inside the
magnetic field.
• • Strength – the strength of the magnetic field.
• • Length – the length of the coil or conductor passing
through the magnetic field.
9. Cont..
• We know that the frequency of a supply is the
number of times a cycle appears in one second
and that frequency is measured in Hertz. As one
cycle of induced emf is produced each full
revolution of the coil through a magnetic field
comprising of a north and south pole as shown
above, if the coil rotates at a constant speed a
constant number of cycles will be produced per
second giving a constant frequency. So by
increasing the speed of rotation of the coil the
frequency will also be increased. Therefore,
frequency is proportional to the speed of
rotation, ( ƒ ∝ Ν ) where Ν = r.p.m.
10. Cont..
• Also, our simple single coil generator above only
has two poles, one north and one south pole,
giving just one pair of poles. If we add more
magnetic poles to the generator above so that it
now has four poles in total, two north and two
south, then for each revolution of the coil two
cycles will be produced for the same rotational
speed. Therefore, frequency is proportional to
the number of pairs of magnetic poles, ( ƒ ∝ P ) of
the generator where P = is the number of “pairs
of poles”.
• Then from these two facts we can say that the
frequency output from an AC generator is:
12. Instataneous voltage.
• The EMF induced in the coil at any instant of time
depends upon the rate or speed at which the coil
cuts the lines of magnetic flux between the poles
and this is dependant upon the angle of rotation,
Theta ( θ ) of the generating device. Because an AC
waveform is constantly changing its value or
amplitude, the waveform at any instant in time will
have a different value from its next instant in time.
• For example, the value at 1ms will be different to the
value at 1.2ms and so on. These values are known
generally as the Instantaneous Values, or Vi Then
the instantaneous value of the waveform and also its
direction will vary according to the position of the
coil within the magnetic field as shown below.
13. Cont..
• The instantaneous values of a sinusoidal waveform is
given as the “Instantaneous value = Maximum value
x sin θ ” and this is generalized by the formula.
• Where, Vmax is the maximum voltage induced in the coil
and θ = ωt, is the angle of coil rotation.
• If we know the maximum or peak value of the waveform,
by using the formula above the instantaneous values at
various points along the waveform can be calculated. By
plotting these values out onto graph paper, a sinusoidal
waveform shape can be constructed. In order to keep
things simple we will plot the instantaneous values for the
sinusoidal waveform at every 45o and assume a maximum
value of 100V.
14. AC circuits -- Impedance
• Impedance and Ohm’s Law for AC:
– Impedance is Z = R + jX,
where j = -1, and X is the reactance in [].
– Ohm’s AC Law in s domain: v = i Z
• Resistance R dissipates power as heat.
• Reactance X stores and returns power.
– Inductors have positive reactance Xl=L
– Capacitors have negative reactance Xc=-1/C
15. 15
1.2: Three-Phase System
In a three phase system the source consists of three
sinusoidal voltages. For a balanced source, the three
sources have equal magnitudes and are phase
displaced from one another by 120 electrical degrees.
A three-phase system is superior economically and
advantage, and for an operating of view, to a single-
phase system. In a balanced three phase system the
power delivered to the load is constant at all times,
whereas in a single-phase system the power pulsates
with time.
17. 17
1.3: Generation of Three-Phase
Three separate windings or coils with terminals R-R’,
Y-Y’ and B-B’ are physically placed 120o apart
around the stator.
Y’
BY
B’
Stator
Rotor
Y
R
B
R
R’
N
S
19. The instantaneous e.m.f. generated in phase R, Y and B:
eR = EmR sin ωt
eY = EmY sin (ωt -120o)
eB = EmB sin (ωt -240o) = EmBsin (ωt +120o)
In phasor domain:
ER = ERrms 0o
EY = EYrms -120o
EB = EBrms 120o
Phase voltage
120o
-120o
0o
ERrms = EYrms = EBrms = Ep
Magnitude of phase voltage
19
25. 25
25
Line voltage
EBR = EB - ER
120o
-120o
0o
-ER
EBR
= Ep 120o - Ep 0o
= 1.732Ep
EBR
150o
150o= √3 Ep
= EL 150o
For star connected supply, EL= √3 Ep
26. 26
120o
-120o
0o
Phase voltages
ER = Ep 0o
EY = Ep -120o
EB = Ep 120o
Line voltages
ERY = EL 30o
EYB = EL -90o
EBR = EL 150o
It can be seen that the phase voltage ER
is reference.
27. 27
27
Phase voltages
ER = Ep -30o
EY = Ep -150o
EB = Ep 90o
Line voltages
ERY = EL 0o
EYB = EL -120o
EBR = EL 120o
Or we can take the line voltage ERY as
reference.
30. 30
Connection in Three Phase System
4-wire system (neutral line with impedance)
3-wire system (no neutral line )
4-wire system (neutral line without impedance)
Star-Connected Balanced Loads
a) 4-wire system b) 3-wire system
3-wire system (no neutral line ), delta connected load
Delta-Connected Balanced Loads
a) 3-wire system
38. 38
4-wire system (neutral line with impedance)
IR + IY + IB= IN
Substitute Eq. 1.2, Eq.1.3, Eq. 1.4 and Eq. 1.5 into Eq. 1.1:
=
EB – VN
ZB
+
EY – VN
ZY
ER – VN
ZR
+
VN
ZN
ER – VN EY – VN
+ + EB – VN =
VN
ZNZR ZR ZY ZY ZB ZB
ER
ZR
+
EY
ZY
+
EB
ZB
=
1
ZN
+
1
ZR
+
1
ZY
VN +
1
ZB
39. 39
4-wire system (neutral line with impedance)
ER
ZR
+
EY
ZY
+
EB
ZB
=
1
ZN
+
1
ZR
+
1
ZY
VN +
1
ZB
VN =
ER
ZR
+
EY
ZY
+
EB
ZB
1
ZN
+
1
ZR
+
1
ZY
+
1
ZB
1.6
40. 4-wire system (neutral line with impedance)
VN =
ER
ZR
+
EY
ZY
+
EB
ZB
1
ZN
+
1
ZR
+
1
ZY
+
1
ZB
1.6
VN is the voltage drop across neutral line impedance or the potential
different between load star point and supply star point of three-phase
system.
We have to determine the value of VN in order to find the values of currents and
voltages of star connected loads of three-phase system.
40
45. 3-wire system (no neutral line ),delta connected load
ER
Three-phase
Load
Three-phase
AC generator
VY
IR
VR
EY
EB
ZR
IY
IB
ZB ZY
VB
46. 3-wire system (no neutral line ),delta connected load
ER
Three-phase
Load
Three-phase
AC generator
IR
EY
EB
IY
IB
VRY
ZRYZBR
ZYB
VYB
VBR
Ir
Ib
Iy
47. 3-wire system (no neutral line ),delta connected load
ER
Three-phase
Load
Three-phase
AC generator
IR
EY
EB
IY
IB
VRY
ZRYZBR
ZYB
VYB
VBR
Ir
Ib
Iy
ERY =VRY
EYB =VYB
EBR =VBR
48. 48
3-wire system (no neutral line ),delta connected load
Phase currents
30o
Ir =
VRY
ZRY
=
ERY
ZRY
=
EL
ZRY
-90o
Iy =
VYB
ZYB
=
EYB
ZYB
=
EL
ZYB
150o
Ib =
VBR
ZBR
=
EBR
ZBR
=
EL
ZBR
49. 3-wire system (no neutral line ),delta connected load
ER
Three-phase
Load
Three-phase
AC generator
IR
EY
EB
IY
IB
VRY
ZRYZBR
ZYB
VYB
VBR
Ir
Ib
Iy
ERY =VRY
EYB =VYB
EBR =VBR
Line currents
IR = Ir Ib-
=
EL
ZRY
30o
-
150oEL
ZBR
IY = Iy Ir-
=
EL
ZYB
-90o
-
30oEL
ZRY
50. 3-wire system (no neutral line ),delta connected load
ER
Three-phase
Load
Three-phase
AC generator
IR
EY
EB
IY
IB
VRY
ZRYZBR
ZYB
VYB
VBR
Ir
Ib
Iy
ERY =VRY
EYB =VYB
EBR =VBR
Line currents
IB = Ib Iy-
=
EL
ZBR
150o
-
-90oEL
ZYB
54. 54
4-wire system (neutral line without impedance)
For 4-wire three-phase system, VN is equal to 0, therefore Eq.
1.3, Eq. 1.4, and Eq. 1.5 become,
IB =
EB
ZB
1.5
EB – VN
IY =
EY
ZY
1.4
EY – VN
IR =
ER
ZR
1.3
ER – VN
57. 57
1.4: Phase sequences
RYB and RBY
120o
-120o
120o
VR
VY
VB
o
)rms(RR 0VV
o
)rms(YY 120VV
o
)rms(B
o
)rms(BB
120V
240VV
VR leads VY, which in turn leads VB.
This sequence is produced when the rotor rotates
in
the counterclockwise direction.
(a) RYB or positive sequence
58. 58
(b) RBY or negative sequence
120o
-120o
120o
VR
VB
VY
o
)rms(RR 0VV
o
)rms(BB 120VV
o
rmsY
o
rmsYY
V
V
120
240
)(
)(
V
VR leads VB, which in turn leads VY.
This sequence is produced when the rotor rotates
in
the clockwise direction.
59. 59
1.5: Connection in Three Phase System
R
Y
B
ZR
Z Y Z
B
1.5.1: Star Connection
a) Three wire system
65. 65
Example
ER
Three-phase
Load
ZY= 20 Ω
IR
VR
EY
EB
ZR = 20 Ω
IY
IB
ZB = 20 Ω
VB
VN
EL = 415 volt
Find the line currents IR ,IY and IB . Also find the voltages VR,
VY and VB.
Wye-Connected Balanced Loads
b) Three wire system
67. 67
Example
ER
Three-phase
Load
ZY= 20 Ω
IR
VR
EY
EB
ZR = 20 Ω
IY
IB
ZB = 20 Ω
VB
IN
VN
Find the line currents IR ,IY and IB . Also find the neutral
current IN.
EL = 415 volt
1.6.1: Wye-Connected Balanced Loads
a) Four wire system
68. 68
VRN
VBN
Z1
Z 2
Z
3
R
B
N
Y
VYN
IR
IY
IB
IN
BYRN IIII
For balanced load system,
IN = 0 and Z1 = Z2 = Z3
3
o
BN
B
2
o
YN
Y
1
o
RN
R
Z
120V
I
Z
120V
I
Z
0V
I
BNYNRNphasa
phasaBN
phasaYN
phasaRN
VVVVwhere
120VV
120VV
0VV
1.6.1: Wye-Connected Balanced Loads
a) Four wire system
69. 69
Wye-Connected Balanced Loads
b) Three wire system
R
Y
B
Z1
Z 2 Z
3
IR
IY
IB
VRY
VYB
VBR S
0III BYR
3
o
BS
B
2
o
YS
Y
1
o
RS
R
Z
120V
I
Z
120V
I
Z
0V
I
BSYSRSphasa
phasaBS
phasaYS
phasaRS
VVVVwhere
240VV
120VV
0VV
70. 70
1.6.2: Delta-Connected Balanced Loads
Z
Z
Z
R
Y
B
VRY
VYB
VBR
IR
IRY
IBR
IYB
IB
IY
Phase currents:
3
o
BR
BR
2
o
YB
YB
1
o
RY
RY
Z
120V
I
Z
120V
I
Z
0V
I
Line currents:
YBBRB
RYYBY
BRRYR
III
III
III
lineBYR
phasaBRYBRY
IIIIand
IIIIwhere
72. 72
1.7.1: Wye-Connected Unbalanced Loads
Four wire system
VRN
VBN
Z1
Z 2
Z
3
R
B
N
Y
VYN
IR
IY
IB
IN
BYRN IIII
For unbalanced load system,
IN 0 and Z1 Z2 Z3
3
o
BN
B
2
o
YN
Y
1
o
RN
R
Z
120V
I
Z
120V
I
Z
0V
I
120VV
120VV
0VV
phasaBN
phasaYN
phasaRN
73. 73
1.7.2: Delta-Connected Unbalanced Loads
Z
Z
Z
R
Y
B
VRY
VYB
VBR
IR
IRY
IBR
IYB
IB
IY
Phase currents:
3
o
BR
BR
2
o
YB
YB
1
o
RY
RY
Z
120V
I
Z
120V
I
Z
0V
I
Line currents:
YBBRB
RYYBY
BRRYR
III
III
III
120VV
120VV
0VV
phasaBN
phasaYN
phasaRN
75. 75
Power Calculation
The three phase power is equal the sum of
the phase powers
P = PR + PY + PB
If the load is balanced:
P = 3 Pphase = 3 Vphase Iphase cos θ
76. 76
1.8.1: Wye connection system:
I phase = I L and
Real Power, P = 3 Vphase Iphase cos θ
Reactive power,
Q = 3 Vphase Iphase sin θ
Apparent power,
S = 3 Vphase Iphase
or S = P + jQ
phaseLL VV 3
WattIV LLL cos3
VARIV3 LLL sin
VAIV3 LLL