The document discusses resonance in AC circuits. It defines resonance as occurring in an RLC circuit when the capacitive and inductive reactances are equal, resulting in a purely resistive impedance. Key points include:
- Resonance occurs at the resonant frequency where the impedance is purely real. Maximum current flows through the circuit at this point.
- The quality factor Q measures the sharpness of resonance and is defined as the ratio of peak stored energy to energy lost per cycle.
- The bandwidth is the frequency range where power is at least half the maximum power at resonance. Half-power points occur when the current magnitude is 1/√2 times the maximum.
- In a series R
A brief session including the introduction about the RLC resonance circuit placed in series. Also discussed about the mathematical calculations and verification of formula. Circuit diagrams are included as well as the graphs to enhance the better view for the viewer. This is a wholesome package for the engineers at the first stage of their aim.
This document discusses resonance circuits and their applications. Resonance occurs when the capacitive and inductive reactances are equal, resulting in a purely resistive impedance. Key parameters of resonance circuits include the resonance frequency, half-power frequencies, bandwidth, and quality factor. Resonance circuits are useful for constructing filters and are used in applications like bandpass and bandstop filters, which allow only certain frequency ranges to pass.
The document discusses resonance in R-L-C series and parallel circuits. In series circuits, resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC), resulting in maximum current. The resonant frequency is 1/2π√LC. In parallel circuits, resonance occurs when the current through the inductor equals the current through the capacitor, resulting in minimum current. The resonant frequency is 1/2π√(L/C - R2/L). Key differences between series and parallel resonance are also summarized.
This document discusses electrical circuit resonance in series and parallel RLC circuits. It explains that resonance occurs when the inductive and capacitive reactances are equal in magnitude. For series resonance, the input impedance and current response are described, and formulas are provided for the resonant frequency, bandwidth, quality factor Q, and half-power points. For parallel resonance, the input impedance is derived and the condition for zero phase angle and resonant frequency is shown. Examples of calculating component values and bandwidth from known parameters are also presented.
- AC circuits use alternating current that constantly changes in amplitude and direction. This allows the magnitude to be easily changed using transformers.
- The sine wave is the most common AC waveform, defined by amplitude, frequency, phase, and time. Peak, RMS, and average amplitudes are important measurements.
- Impedance combines resistance with reactance from inductors and capacitors. Reactance depends on frequency and causes current to lead or lag voltage in circuits.
This document discusses resonance in series and parallel RLC circuits. It defines key parameters for both circuit types including resonance frequency, half-power frequencies, bandwidth, and quality factor. The series resonance circuit is analyzed showing that impedance is purely resistive at resonance, with maximum current and unity power factor. Parallel resonance is also examined, with admittance being purely conductance at resonance. Formulas for calculating important resonant characteristics are provided.
The document discusses series and parallel resonance circuits. Some key points:
- In a series RLC circuit, the impedance is purely resistive at resonance when the inductive and capacitive reactances are equal. Maximum current flows at this resonant frequency.
- Parallel RLC circuits also exhibit resonance when the reactances cancel out. Minimum current flows at resonance for a parallel circuit.
- For both circuits, the quality factor Q and bandwidth depend on the resistance, with lower resistance leading to higher Q and narrower bandwidth.
A brief session including the introduction about the RLC resonance circuit placed in series. Also discussed about the mathematical calculations and verification of formula. Circuit diagrams are included as well as the graphs to enhance the better view for the viewer. This is a wholesome package for the engineers at the first stage of their aim.
This document discusses resonance circuits and their applications. Resonance occurs when the capacitive and inductive reactances are equal, resulting in a purely resistive impedance. Key parameters of resonance circuits include the resonance frequency, half-power frequencies, bandwidth, and quality factor. Resonance circuits are useful for constructing filters and are used in applications like bandpass and bandstop filters, which allow only certain frequency ranges to pass.
The document discusses resonance in R-L-C series and parallel circuits. In series circuits, resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC), resulting in maximum current. The resonant frequency is 1/2π√LC. In parallel circuits, resonance occurs when the current through the inductor equals the current through the capacitor, resulting in minimum current. The resonant frequency is 1/2π√(L/C - R2/L). Key differences between series and parallel resonance are also summarized.
This document discusses electrical circuit resonance in series and parallel RLC circuits. It explains that resonance occurs when the inductive and capacitive reactances are equal in magnitude. For series resonance, the input impedance and current response are described, and formulas are provided for the resonant frequency, bandwidth, quality factor Q, and half-power points. For parallel resonance, the input impedance is derived and the condition for zero phase angle and resonant frequency is shown. Examples of calculating component values and bandwidth from known parameters are also presented.
- AC circuits use alternating current that constantly changes in amplitude and direction. This allows the magnitude to be easily changed using transformers.
- The sine wave is the most common AC waveform, defined by amplitude, frequency, phase, and time. Peak, RMS, and average amplitudes are important measurements.
- Impedance combines resistance with reactance from inductors and capacitors. Reactance depends on frequency and causes current to lead or lag voltage in circuits.
This document discusses resonance in series and parallel RLC circuits. It defines key parameters for both circuit types including resonance frequency, half-power frequencies, bandwidth, and quality factor. The series resonance circuit is analyzed showing that impedance is purely resistive at resonance, with maximum current and unity power factor. Parallel resonance is also examined, with admittance being purely conductance at resonance. Formulas for calculating important resonant characteristics are provided.
The document discusses series and parallel resonance circuits. Some key points:
- In a series RLC circuit, the impedance is purely resistive at resonance when the inductive and capacitive reactances are equal. Maximum current flows at this resonant frequency.
- Parallel RLC circuits also exhibit resonance when the reactances cancel out. Minimum current flows at resonance for a parallel circuit.
- For both circuits, the quality factor Q and bandwidth depend on the resistance, with lower resistance leading to higher Q and narrower bandwidth.
A tuned amplifier uses a tuned circuit in the load to selectively amplify signals of a desired frequency. It employs the phenomenon of resonance to pass a narrow band of frequencies centered around the resonant frequency of the tuned circuit. Tuned amplifiers are commonly used in radio transmitters and receivers to select and amplify the carrier frequency from a mixture of frequencies. They can be classified as small signal or large signal amplifiers depending on the power level and class of operation. Common circuit configurations include single tuned, double tuned, and stagger tuned amplifiers.
This document provides a summary of a seminar presentation on analyzing single phase AC circuits. The presentation covered various circuit elements in AC circuits including resistors, inductors, and capacitors in both series and parallel configurations. It discussed the concepts of impedance, phase relationships between voltage and current, and resonance. Resonance occurs when the inductive and capacitive reactances are equal, resulting in maximum current flow. The key topics were analyzing purely resistive, inductive, and capacitive circuits, and combinations using circuit laws and phasor diagrams.
Q-Factor In Series and Parallel AC CircuitsSurbhi Yadav
The document defines Q factor as a measure of the quality of a resonant circuit, with a higher Q factor indicating a more narrow bandwidth. It gives the formula for Q factor as the ratio of power stored to power dissipated in a circuit. For series resonant circuits, Q equals the reactance divided by the resistance. For parallel resonant circuits with resistance in series with the inductor, Q is also defined as reactance over resistance. The document discusses how series and parallel resonant circuits behave at, below, and above resonance, and how Q factor relates to bandwidth and peak impedance/voltage in each type of circuit.
This unit covers series and parallel resonance, quality factor, bandwidth, self and mutual inductance, and coefficient of coupling. It discusses resonance occurring when the applied voltage and source current are in phase, making the circuit purely resistive. At resonance, the power factor is unity. Series resonance occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other out. This happens at the resonant frequency. Applications of series resonance circuits include AC mains filters and radio/TV tuning circuits. The bandwidth, selectivity, and quality factor of series resonance circuits are also defined in relation to the resonant frequency, current, and cutoff frequencies.
This document discusses electrical resonance in series RLC circuits. It explains that series resonance occurs when the inductive and capacitive reactances cancel each other out, resulting in a minimum impedance at the resonant frequency. The bandwidth of a series resonant circuit is defined as the frequency range over which the current is at least half of its maximum value. The quality factor Q is a measure of how sharp the resonance peak is, and is equal to the ratio of the resonant frequency to the bandwidth.
Resonance in electrical circuits – series resonancemrunalinithanaraj
This document discusses electrical resonance in series RLC circuits. It explains that series resonance occurs when the inductive and capacitive reactances cancel each other out, resulting in a minimum impedance. This is useful for applications that require a stable oscillating frequency, like radio transmission. The document defines key terms like resonant frequency, bandwidth, and quality factor (Q factor). It describes how the Q factor relates the peak stored energy to energy lost, and how a higher Q factor results in a narrower bandwidth.
Introduction
Band Pass Amplifiers
Series & Parallel Resonant Circuits & their Bandwidth
Analysis of Single Tuned Amplifiers
Analysis of Double Tuned Amplifiers
Primary & Secondary Tuned Amplifiers with BJT & FET
Merits and de-merits of Tuned Amplifiers
This document discusses differential equations and linear algebra topics including RLC circuits and pendulums. It provides details on RLC circuits such as their components, applications as filters and oscillators, and an example using values in a circuit calculation. It also briefly describes pendulum oscillation between potential and kinetic energy. The conclusion recaps that an RLC circuit connects the resistor, inductor and capacitor in parallel to an AC source, and discusses voltage and impedance across the components.
Resonance in an RLC circuit occurs when the capacitive and inductive reactances cancel each other out. This happens at a specific frequency called the resonance frequency. In a series RLC circuit, resonance occurs when the inductive and capacitive reactances are equal, resulting in maximum current and minimum impedance. In a parallel RLC circuit, resonance occurs when the impedance is at its maximum. Resonant circuits have applications in devices like Tesla coils and radio tuners due to their ability to selectively respond to specific frequencies.
This is the experiment for undergraduate science and engineering students in the subjects of Physics, Applied Physics, Basic electronics etc. The experiment is explained in detail so that the students and faculty member can get the better knowledge of the experiment.
This document discusses frequency response and resonance in AC circuits. It begins by introducing the concept of a transfer function, which is the ratio of an output to an input of a circuit and describes its frequency response. Bode plots are then presented as a way to plot the magnitude and phase of a transfer function over frequency on logarithmic scales. The document covers series and parallel resonance, where the impedances of inductive and capacitive elements cancel out. Key concepts are introduced, such as resonant frequency, quality factor Q, and bandwidth, and how these relate to the selectivity of a resonant circuit.
This chapter describes RC circuits and their behavior when a sinusoidal voltage is applied. Key points include: the current in an RC circuit leads the source voltage; resistor voltage is in phase with current while capacitor voltage lags current by 90 degrees; impedance of a series RC circuit decreases with increasing frequency while the phase angle decreases; and RC circuits can be used as phase shifters or filters.
1) The document discusses power in RC circuits and how power is dissipated by resistance as heat or stored by capacitors. It provides formulas to calculate active power, reactive power, and apparent power.
2) A RC circuit can function as an oscillator if the resistance value is chosen such that the output voltage leads the input by 60 degrees. The amplifier must have a gain of at least 29 for oscillations to be maintained.
3) RC circuits can also function as filters, either passing low frequencies while blocking high (low-pass) or passing high while blocking low (high-pass), depending on whether the output is taken across the resistor or capacitor. Cutoff frequency determines which frequencies are passed or stopped.
1) An inductor resists changes in current and has an impedance of iωL.
2) In an RLC circuit, the behavior is determined by the time constant L/R. If L/R is small, the circuit is overdamped; if L/R is large, it is underdamped and will ring.
3) An RLC circuit can act as a bandpass filter, with peak gain occurring at the resonant frequency of 1/√LC. The quality factor Q relates to the bandwidth around the peak gain.
This document discusses RL circuits and their properties. It describes how inductors cause a phase shift between voltage and current in RL circuits. The impedance and phase angle of series and parallel RL circuits are determined. Power in RL circuits is analyzed, including reactive power. Power factor correction is also discussed. RL circuits can function as low-pass or high-pass filters depending on how output is measured.
1) A series RLC circuit can be either capacitive or inductive depending on the frequency. At the resonant frequency where the capacitive and inductive reactances cancel each other out, the circuit is purely resistive.
2) RLC circuits can be used as filters. A series resonant circuit creates a band-pass filter that allows a range of frequencies to pass, while a parallel resonant circuit creates a band-stop filter that rejects frequencies near the resonant frequency.
3) Important concepts for both series and parallel resonance include the capacitive and inductive reactances cancelling each other out, total impedance being minimized/maximized, and current being maximized/minimized. The resonant frequency is given
1) A series RLC circuit can be either capacitive or inductive depending on the frequency. At the resonant frequency where the capacitive and inductive reactances cancel each other out, the circuit is purely resistive.
2) RLC circuits can be used as band-pass or band-stop filters by taking advantage of their behavior at resonant frequencies. A band-pass filter passes signals near the resonant frequency while attenuating others, while a band-stop filter does the opposite.
3) Important concepts for both series and parallel resonance include the capacitive and inductive reactances cancelling each other out, total impedance being minimized/maximized, and current being maximized/minimized. The
1) A series RLC circuit can be either capacitive or inductive depending on the frequency. At the resonant frequency where the capacitive and inductive reactances cancel each other out, the circuit is purely resistive.
2) RLC circuits can be used as band-pass or band-stop filters by taking advantage of their behavior at resonant frequencies. A band-pass filter passes signals near the resonant frequency while attenuating others, while a band-stop filter does the opposite.
3) Important concepts for both series and parallel resonance include the capacitive and inductive reactances cancelling each other out, total impedance being minimized/maximized, and current being maximized/minimized. The
The document discusses various resistance measurement techniques including the Wheatstone bridge, Kelvin bridge, and AC bridges. The Wheatstone bridge is based on balancing two voltage ratios and can measure resistances from 1 ohm to 10 megohms. The Kelvin bridge is a more precise version that eliminates errors from lead resistance and can measure down to 0.00001 ohms. AC bridges can measure impedances that include resistance, inductance, and capacitance components.
Tuned amplifiers are used to amplify narrowband signals at a specific frequency. They use a tuned or resonant circuit, such as a parallel LC circuit, as the collector load. This tuned circuit provides high impedance and maximum gain at the resonant frequency. Tuned amplifiers include single tuned, double tuned, and staggered tuned configurations depending on the number of tuned circuits used. The Q factor and bandwidth of the tuned circuit determine the selectivity of the amplifier. Tuned amplifiers are used in radio transmitters and receivers due to their ability to selectively amplify signals within a narrow bandwidth.
The document discusses grounding systems from an engineering perspective. It addresses grounding as both an art and a science, requiring both data and design flexibility. Key points covered include the importance of soil resistivity testing to inform grounding designs, different grounding system types, factors that influence resistivity readings, and the need for acceptance testing and maintenance over time. The overall message is that grounding deserves careful consideration upfront given its role in safety and system coordination and the high costs of problems later on.
This document provides information about static electricity and circuits. It discusses how static electricity is built up and the three ways an object can become electrically charged: friction, conduction, and induction. It defines static electricity as the build up of electrical charges on an object when it is not moving. The document also covers the basics of circuits, including the components of a simple circuit and different types of circuits. It defines a circuit as a complete path for current to flow and discusses series and parallel circuits.
A tuned amplifier uses a tuned circuit in the load to selectively amplify signals of a desired frequency. It employs the phenomenon of resonance to pass a narrow band of frequencies centered around the resonant frequency of the tuned circuit. Tuned amplifiers are commonly used in radio transmitters and receivers to select and amplify the carrier frequency from a mixture of frequencies. They can be classified as small signal or large signal amplifiers depending on the power level and class of operation. Common circuit configurations include single tuned, double tuned, and stagger tuned amplifiers.
This document provides a summary of a seminar presentation on analyzing single phase AC circuits. The presentation covered various circuit elements in AC circuits including resistors, inductors, and capacitors in both series and parallel configurations. It discussed the concepts of impedance, phase relationships between voltage and current, and resonance. Resonance occurs when the inductive and capacitive reactances are equal, resulting in maximum current flow. The key topics were analyzing purely resistive, inductive, and capacitive circuits, and combinations using circuit laws and phasor diagrams.
Q-Factor In Series and Parallel AC CircuitsSurbhi Yadav
The document defines Q factor as a measure of the quality of a resonant circuit, with a higher Q factor indicating a more narrow bandwidth. It gives the formula for Q factor as the ratio of power stored to power dissipated in a circuit. For series resonant circuits, Q equals the reactance divided by the resistance. For parallel resonant circuits with resistance in series with the inductor, Q is also defined as reactance over resistance. The document discusses how series and parallel resonant circuits behave at, below, and above resonance, and how Q factor relates to bandwidth and peak impedance/voltage in each type of circuit.
This unit covers series and parallel resonance, quality factor, bandwidth, self and mutual inductance, and coefficient of coupling. It discusses resonance occurring when the applied voltage and source current are in phase, making the circuit purely resistive. At resonance, the power factor is unity. Series resonance occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other out. This happens at the resonant frequency. Applications of series resonance circuits include AC mains filters and radio/TV tuning circuits. The bandwidth, selectivity, and quality factor of series resonance circuits are also defined in relation to the resonant frequency, current, and cutoff frequencies.
This document discusses electrical resonance in series RLC circuits. It explains that series resonance occurs when the inductive and capacitive reactances cancel each other out, resulting in a minimum impedance at the resonant frequency. The bandwidth of a series resonant circuit is defined as the frequency range over which the current is at least half of its maximum value. The quality factor Q is a measure of how sharp the resonance peak is, and is equal to the ratio of the resonant frequency to the bandwidth.
Resonance in electrical circuits – series resonancemrunalinithanaraj
This document discusses electrical resonance in series RLC circuits. It explains that series resonance occurs when the inductive and capacitive reactances cancel each other out, resulting in a minimum impedance. This is useful for applications that require a stable oscillating frequency, like radio transmission. The document defines key terms like resonant frequency, bandwidth, and quality factor (Q factor). It describes how the Q factor relates the peak stored energy to energy lost, and how a higher Q factor results in a narrower bandwidth.
Introduction
Band Pass Amplifiers
Series & Parallel Resonant Circuits & their Bandwidth
Analysis of Single Tuned Amplifiers
Analysis of Double Tuned Amplifiers
Primary & Secondary Tuned Amplifiers with BJT & FET
Merits and de-merits of Tuned Amplifiers
This document discusses differential equations and linear algebra topics including RLC circuits and pendulums. It provides details on RLC circuits such as their components, applications as filters and oscillators, and an example using values in a circuit calculation. It also briefly describes pendulum oscillation between potential and kinetic energy. The conclusion recaps that an RLC circuit connects the resistor, inductor and capacitor in parallel to an AC source, and discusses voltage and impedance across the components.
Resonance in an RLC circuit occurs when the capacitive and inductive reactances cancel each other out. This happens at a specific frequency called the resonance frequency. In a series RLC circuit, resonance occurs when the inductive and capacitive reactances are equal, resulting in maximum current and minimum impedance. In a parallel RLC circuit, resonance occurs when the impedance is at its maximum. Resonant circuits have applications in devices like Tesla coils and radio tuners due to their ability to selectively respond to specific frequencies.
This is the experiment for undergraduate science and engineering students in the subjects of Physics, Applied Physics, Basic electronics etc. The experiment is explained in detail so that the students and faculty member can get the better knowledge of the experiment.
This document discusses frequency response and resonance in AC circuits. It begins by introducing the concept of a transfer function, which is the ratio of an output to an input of a circuit and describes its frequency response. Bode plots are then presented as a way to plot the magnitude and phase of a transfer function over frequency on logarithmic scales. The document covers series and parallel resonance, where the impedances of inductive and capacitive elements cancel out. Key concepts are introduced, such as resonant frequency, quality factor Q, and bandwidth, and how these relate to the selectivity of a resonant circuit.
This chapter describes RC circuits and their behavior when a sinusoidal voltage is applied. Key points include: the current in an RC circuit leads the source voltage; resistor voltage is in phase with current while capacitor voltage lags current by 90 degrees; impedance of a series RC circuit decreases with increasing frequency while the phase angle decreases; and RC circuits can be used as phase shifters or filters.
1) The document discusses power in RC circuits and how power is dissipated by resistance as heat or stored by capacitors. It provides formulas to calculate active power, reactive power, and apparent power.
2) A RC circuit can function as an oscillator if the resistance value is chosen such that the output voltage leads the input by 60 degrees. The amplifier must have a gain of at least 29 for oscillations to be maintained.
3) RC circuits can also function as filters, either passing low frequencies while blocking high (low-pass) or passing high while blocking low (high-pass), depending on whether the output is taken across the resistor or capacitor. Cutoff frequency determines which frequencies are passed or stopped.
1) An inductor resists changes in current and has an impedance of iωL.
2) In an RLC circuit, the behavior is determined by the time constant L/R. If L/R is small, the circuit is overdamped; if L/R is large, it is underdamped and will ring.
3) An RLC circuit can act as a bandpass filter, with peak gain occurring at the resonant frequency of 1/√LC. The quality factor Q relates to the bandwidth around the peak gain.
This document discusses RL circuits and their properties. It describes how inductors cause a phase shift between voltage and current in RL circuits. The impedance and phase angle of series and parallel RL circuits are determined. Power in RL circuits is analyzed, including reactive power. Power factor correction is also discussed. RL circuits can function as low-pass or high-pass filters depending on how output is measured.
1) A series RLC circuit can be either capacitive or inductive depending on the frequency. At the resonant frequency where the capacitive and inductive reactances cancel each other out, the circuit is purely resistive.
2) RLC circuits can be used as filters. A series resonant circuit creates a band-pass filter that allows a range of frequencies to pass, while a parallel resonant circuit creates a band-stop filter that rejects frequencies near the resonant frequency.
3) Important concepts for both series and parallel resonance include the capacitive and inductive reactances cancelling each other out, total impedance being minimized/maximized, and current being maximized/minimized. The resonant frequency is given
1) A series RLC circuit can be either capacitive or inductive depending on the frequency. At the resonant frequency where the capacitive and inductive reactances cancel each other out, the circuit is purely resistive.
2) RLC circuits can be used as band-pass or band-stop filters by taking advantage of their behavior at resonant frequencies. A band-pass filter passes signals near the resonant frequency while attenuating others, while a band-stop filter does the opposite.
3) Important concepts for both series and parallel resonance include the capacitive and inductive reactances cancelling each other out, total impedance being minimized/maximized, and current being maximized/minimized. The
1) A series RLC circuit can be either capacitive or inductive depending on the frequency. At the resonant frequency where the capacitive and inductive reactances cancel each other out, the circuit is purely resistive.
2) RLC circuits can be used as band-pass or band-stop filters by taking advantage of their behavior at resonant frequencies. A band-pass filter passes signals near the resonant frequency while attenuating others, while a band-stop filter does the opposite.
3) Important concepts for both series and parallel resonance include the capacitive and inductive reactances cancelling each other out, total impedance being minimized/maximized, and current being maximized/minimized. The
The document discusses various resistance measurement techniques including the Wheatstone bridge, Kelvin bridge, and AC bridges. The Wheatstone bridge is based on balancing two voltage ratios and can measure resistances from 1 ohm to 10 megohms. The Kelvin bridge is a more precise version that eliminates errors from lead resistance and can measure down to 0.00001 ohms. AC bridges can measure impedances that include resistance, inductance, and capacitance components.
Tuned amplifiers are used to amplify narrowband signals at a specific frequency. They use a tuned or resonant circuit, such as a parallel LC circuit, as the collector load. This tuned circuit provides high impedance and maximum gain at the resonant frequency. Tuned amplifiers include single tuned, double tuned, and staggered tuned configurations depending on the number of tuned circuits used. The Q factor and bandwidth of the tuned circuit determine the selectivity of the amplifier. Tuned amplifiers are used in radio transmitters and receivers due to their ability to selectively amplify signals within a narrow bandwidth.
The document discusses grounding systems from an engineering perspective. It addresses grounding as both an art and a science, requiring both data and design flexibility. Key points covered include the importance of soil resistivity testing to inform grounding designs, different grounding system types, factors that influence resistivity readings, and the need for acceptance testing and maintenance over time. The overall message is that grounding deserves careful consideration upfront given its role in safety and system coordination and the high costs of problems later on.
This document provides information about static electricity and circuits. It discusses how static electricity is built up and the three ways an object can become electrically charged: friction, conduction, and induction. It defines static electricity as the build up of electrical charges on an object when it is not moving. The document also covers the basics of circuits, including the components of a simple circuit and different types of circuits. It defines a circuit as a complete path for current to flow and discusses series and parallel circuits.
This document provides an overview of Microsoft Excel. It begins with an introduction to Excel, explaining that it is a program used to create electronic spreadsheets for organizing data, creating charts, and performing calculations. The document then covers various Excel topics like the office button, ribbons, working with cells, formatting text, conditional formatting, inserting rows and columns, editing with fill, sorting, cell referencing, functions, and shortcuts keys. Functions covered include SUM, IF, COUNT, LOWER, UPPER, and text functions like LEFT, RIGHT, and MID.
New Microsoft PowerPoint Presentation (5).pptxRajneesh501415
Rational numbers can be expressed as fractions where the numerator and denominator are integers and the denominator is not zero. They were studied by classical Greek and Indian mathematicians as part of number theory. Rational numbers are needed for measurement and describing quantities that cannot be adequately described by integers alone. Early fractions represented reciprocals of integers, and Egyptians used Egyptian fractions around 1000 BC to divide quantities. The modern notation for fractions using a horizontal bar was introduced by Arabs.
1. The document discusses fundamentals of electric circuits including circuit elements like resistors, capacitors, inductors, and sources. It defines voltage, current, charge, resistance, capacitance, and inductance.
2. Kirchhoff's laws and methods for analyzing simple series, parallel, and series-parallel circuits are presented including voltage and current divider rules.
3. Different types of sources are examined including ideal sources and practical sources with internal resistance. Source transformations are discussed.
This document provides an overview of alternating current (AC) fundamentals. It defines AC as current that periodically reverses direction, unlike direct current (DC) which flows in one direction. AC is used in power transmission because voltage can be transformed between levels using transformers. The document discusses sinusoidal AC quantities and their peak, average, and root mean square values. It describes purely resistive, inductive, and capacitive AC circuits. It also covers AC series circuits containing combinations of resistors, inductors, and capacitors. The concepts of impedance, phase angle, and power factor are introduced. The document concludes with sections on resonance, resonance frequency, and resonance curves.
- Thevenin's theorem states that any linear electrical network can be reduced to an equivalent circuit with a voltage source Voc in series with a resistance Rth for the purposes of analyzing external connections.
- Voc is the open circuit voltage measured across the terminals and Rth is the internal resistance measured between the terminals with all independent sources removed (made inactive).
- The document provides examples of applying Thevenin's theorem to calculate currents and voltages in external loads by replacing the original network with the equivalent Thevenin circuit.
The document discusses Thevenin's theorem, which states that any linear electrical network can be reduced to an equivalent circuit with a voltage source Voc in series with a resistance Rth. Voc is the open circuit voltage between the terminals and Rth is the resistance measured between the terminals with all independent sources removed. The document provides examples of applying the theorem to find voltages and currents in different circuits. It also notes that Thevenin's theorem was first proposed by French engineer M.L. Thevenin and is useful for analyzing networks by reducing them to a simplified form.
This document outlines the key concepts and learning outcomes for a circuit theory course, including:
1) Explaining DC circuits using concepts like EMF, internal resistance, and potential dividers.
2) Analyzing DC circuits using Kirchhoff's laws to solve problems involving resistors, capacitors, and energy stored.
3) Giving a microscopic description of resistance in wires using concepts like resistivity and conductivity.
4) Covering related practical work using equipment like voltmeters and capacitors.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
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7. WHY STUDY RESONANCE?
• Resonance is the frequency response of a circuit or network when it is
operating at its natural frequency called “ Resonance Frequency”.
• For many applications, the supply (defined by its voltage and frequency)
is constant. e.g. The supply to residential homes is 230 V, 50 Hz.
• However, many communication systems involve circuits in which the
supply voltage operates with a varying frequency.
• To understand communication systems, one requires a knowledge of how
circuits are affected by a variation of the frequency. Examples of such
communication systems are,
Radio, television, telephones, and machine control systems.
7
8. WHEN RESONANCE OCCURS? AND WHAT IT RESULTS?
• Resonance occurs in any circuit that has energy storage elements, at least
one inductor and one capacitor.
• Under resonance, the total supply voltage and supply current are in phase.
So, the power factor (PF) becomes unity.
• At resonance, L and C elements exchange energy freely as a function of
time, which results in sinusoidal oscillations either across L or C.
TYPES OF RESONANCE
• Series resonance.
• Parallel resonance. L
8
C
9. RESONANCE IN SERIES RLC CIRCUIT
Resonance is a condition in an RLC circuit in which the capacitive and
inductive reactances are equal in magnitude, thereby resulting in a purely
resistive impedance.
The input impedance is as follows,
At resonance, the net reactance becomes zero. Therefore,
Series resonant RLC
circuit
1 1
jC
Z R j
L R j
L
C
1
r r r
r
1
LC
C
L rad/s; f
1
Hz
2 LC
where r and fr represent resonant frequency in rad/s and in Hz, respectively
9
10. VARIATION OF REACTANCE AND IMPEDANCE WITH
FREQUENCY
• At resonant frequency fr, |Z| = R, the
power factor is unity (purely resistive).
• Below fr, |XL| < |XC |, so the circuit is more
capacitive and the power factor is leading.
• Above fr, |XL| > |XC |, so
the circuit is more
inductive and the power
factor is lagging. Variation of resistance, reactance and
impedance with frequency
XL + XC
10
11. VARIATION OF MAGNITUDE AND PHASE OF
CURRENT WITH FREQUENCY
• The current is maximum at resonant
frequency (fr).
Variation of magnitude |I|
and phaseof current with
frequency in a series RLC
circuit
11
12. QUALITY FACTOR (Q)
• The “sharpness” of the resonance in a resonant circuit is measured
quantitatively by the quality factor Q.
• The quality factor relates the maximum or peak energy stored to the
energy dissipated in the circuit per cycle of oscillation:
• It is also regarded as a measure of the energy storage property of a circuit
in relation to its energy dissipation property.
Peak energy stored in the circuit
Q 2Energy dissipated by the circuit in one period at resonance
12
13. QUALITY FACTOR (Q)
• In the series RLC circuit, the quality factor (Q) is,
2
1
r
1
LI2
R
I2
R(
fr
2f L
Q 2 1
)
2
Q
r L
1
1 L
R C
r R R C
13
14. QUALITY FACTOR (Q)
• The Q factor is also defined as the ratio of the reactive power, of either
the capacitor or the inductor to the average power of the resistor at
resonance:
• For capacitive reactance XL at resonance:
Q
Reactive power
Average power
• For inductive reactance XL at resonance:
Reactive power I2
X L
Q L
r
Average power I2
R R
Reactive power I2
X 1
Q C
Average power I2
R CR
r 14
15. VOLTAGES IN A SERIES RLC CIRCUIT
(a) f < f
15
r
Capacitive,
I leads V
(c) f > fr
Inductive,
I lags V
(b) f = fr
Resistive,
V and I in
phase
16. VOLTAGES ACROSS RLC ELEMENTS AT RESONANCE
26
The voltage across resistor at fr is,
The voltage across inductor at fr is,
R R m R
R
V I R I R
V
R V V
L L r m r
R R
VL X I L I L
V
r L
V QV
VL QV
The voltage across capacitor at fr is,
1
m C
r r r
C C R CR
1 1 V
VC XC IC I V QV V QV
17. VOLTAGES ACROSS RLC ELEMENTS AT RESONANCE
27
• Q is
magnification, because VC or VL
termed as Q factor or voltage
equals Q
multiplied by the source voltage V.
• In a series RLC circuit, values of VL and VC
can actually be very large at resonance and
can lead to component damage if not
recognized and subject to careful design.
r
R CR R
L
Q
r L
1
1
C
Voltage magnification
Q in series resonant circuit
18. VOLTAGES ACROSS RLC ELEMENTS
28
Effect of frequency variation on voltages across R, L and C
19. BANDWIDTH AND HALF POWER FREQUENCIES
• The bandwidth of a circuit is also defined as
the frequency range between the half-power
points when I = Imax/√2.
• In a series RLC circuit, at resonance, maximum power is drawn. i.e.,
P I 2
R; where I
V
at resonance
r max max
R
• Bandwidth represents the range of frequencies for which the power level
in the signal is at least half of the maximum power.
2 2
P I 2
R I
2
r
max
max
R
2
19
20. BANDWIDTH AND HALF POWER FREQUENCIES
• Thus, the condition for half-power is given when
• The vertical lines either side of |I | indicate
that only the magnitude of the current is
under consideration – but the phase angle
will not be neglected.
• The impedance corresponding to half
power-points including phase angle is
I
Imax V
2 R 2
Z(
1,2 ) R 2 45
The resonance peak, bandwidth
and half-power frequencies
20
21. BANDWIDTH AND HALF POWER FREQUENCIES
I
V
R1 j1
• The impedance in the complex form
Z(,12 ) R1 j1
• Thus for half power,
and Z R1 j1
• At the half-power points, the phase angle of the current is 45°. Below the
resonant frequency, at ω1, the circuit is capacitive and Z(ω1) = R(1 − j1).
• Above the resonant frequency, at ω2, the circuit is inductive and
Z(ω2) = R(1 + j1).
21
22. BANDWIDTH AND HALF POWER FREQUENCIES
• Now, the circuit impedance is given by,
• At half power points,
• By comparison of above two equations, resulting in
• As we know,
Z R1 j1
Z R j
L
1 R
1 j
L
C
R
CR
1
L 1 1
R CR
1
R
C
r R
Q
r L
22
23. BANDWIDTH AND HALF POWER FREQUENCIES
• Now, by multiplying and dividing with ωr :
• For ω2 :
• For ω1 :
L
r 1 r 1 Q r Q 1 Q
r
1
R r
CR
r r
r
r
Q
2
r
1
2
Q
1
r
1
r 1
23
24. BANDWIDTH AND HALF POWER FREQUENCIES
• The half-power frequencies ω2 and ω1 are obtained as,
• The bandwidth is obtained as:
i.e.
• Resonant frequency in terms of ω2 and ω1, is expressed as:
2 r
2Q
1
4Q2
r
1 1 r
2Q
1
4Q2
r
1
2 1
Q
BW
r
Q factor
Bandwidth
Resonant frequency
r
1
2
24
25. BANDWIDTH AND HALF POWER FREQUENCIES
The bandwidth is also expressed as:
For Q >> 1,
2 1 2 1
(or)
Hz
Q L
R
2L
r
R
rad/s
f2 f1
rad/s
r 1 1 r 1 r
2 2 2L
BW
BW
R
rad/s
2 r 2 r 2 r
2 2 2L
BW
BW
R
25
26. CONCLUSIONS
Resonance in series RLC circuit:
• The voltages which appear across the reactive
components can be many times greater than that of the
supply. The factor of magnification, the voltage
magnification in the series circuit, is called the Q factor.
• An RLC series circuit accepts maximum current from
the source at resonance and for that reason is called an
acceptor circuit.
26
27. RESONANCE IN PARALLEL RLC CIRCUIT
•
is the net impedance of the three
parallel branches.
• In parallel circuits, it is simpler to
consider the total admittance Y of the
three branches. Thus,
where
The supply voltage: V IZ where Z
V IZ
I
Y
1
jL
j
L
Y G j
C G jC G jC
1
L
27
28. RESONANCE IN PARALLEL RLC CIRCUIT
• At resonance (ω = ωr), the net susceptance is zero.
i.e.
• Therefore, the resonant frequency (ωr) :
• At the resonant frequency, Y = G = 1/R, the
conductance of the parallel resistance, and I = VG.
C
1 0
L
r
1
rad/s
LC
28
29. CURRENT THROUGH RESISTANCE
• The supply voltage magnitude:
• At resonance, ω = ωr,
The three-branch
parallel resonant circuit
V
I
1 1
2
R2
C
L
I
R2
V |V || I |R
1
02
r R R
• Current through the resistance at ω : I
VR
V
I R
I
R R R
I
29
30. CURRENT MAGNIFICATION
• Magnitude of current through inductor at ωr :
• Magnitude of current through capacitor at ωr :
where Q is the current magnification i.e.,
L
L r
X L
| I |
V
I R
R
I Q I
L
r
1
C r
C
X
rC
| I |
V
I R
CR I Q I
r
Q
R
CR
L
r The three-branch parallel resonant circuit
30
31. CURRENT MAGNIFICATION
Current magnification Q is also expressed in terms of inductive or capacitive
susceptance (B), inductive or capacitive reactance (X ) and conductance (G) :
By substituting ωr = 1/√(LC) in Q :
C
L
Q
1 C
R
G L
1 r B R
C
Q
G G X
LG
r
The three-branch parallel resonant circuit
31
32. BANDWIDTH AND HALF POWER FREQUENCIES
49
The parallel RLC circuit is the dual of the series RLC circuit. Therefore, by
replacing R, L, and C in the expressions for the series circuit with 1∕R, C, and
L respectively, we obtain for the parallel circuit, the Ymin/21/2 frequencies:
1 1
1
2RC
2RC
LC
1
RC
• Bandwidth: BW 21
1 1 1 1
2
2
2
2RC
2RC
LC
BW
r
r
R
L
• Relation between BW and Q: Q
r
RC
33. BANDWIDTH AND HALF POWER FREQUENCIES
The half-power frequencies in terms of quality factor:
For Q >> 1,
1
2
1
r 1 r
2Q 2Q
1
2
2
r 1 r
2Q 2Q
2
r 1
BW
2
2 r
BW
The three-branch parallel resonant circuit
33
34. PRACTICAL PARALLEL RESONANCE CIRCUIT
Computation of resonant frequency of a “tank circuit”:
• The Figure shown is the two branch parallel resonant circuit.
Also called tank circuit.
• The total admittance (YT) of the circuit shown is:
The two-branch
parallel resonant circuit
(or) tank circuit
1 1
Y Y Y
,
T 1 2 R
jX jX
S L C
2
L
j
,
jX
Y
RS
T X
R X 2
S L C
2 2 2
S C S
RS
R2
,
Y
j
1
T X
R X
XL
X
L L 34
35. PRACTICAL PARALLEL RESONANCE CIRCUIT
Computation of resonant frequency of a “tank circuit”:
At resonance (ω = ωr), the net susceptance is zero.
i.e.
•
The two-branch
parallel resonant circuit
(or) tank circuit
2 2 2
S C S
RS
R2
,
Y
j
1
T X
R X
XL
X
L L
1
S L r
C S L r
X R2
C
0 R2
X 2
L ,
XL 1
X 2
S L
L
R2
C
X 2
2 2 2
rad/s
S r
R2
L
C
1
LC
S
L2
R L r
35
36. PRACTICAL PARALLEL RESONANCE CIRCUIT
Computation of resonant frequency of a “tank circuit”:
• The resonant frequency in Hz is:
• The admittance at resonance is:
The two-branch parallel
resonant circuit (or) tank circuit
R2
S
L2
1 1
2 LC
fr Hz
2 2
L
Y ( f f )
RS
RSC
,
T r
R X
S L
36
37. IDEAL TANK CIRCUIT
Computation of resonant frequency of a “ ideal tank circuit”:
• In ideal tank circuit, the series resistance RS is made zero.
• The total admittance (YT) of the circuit shown (Rs = 0) is:
• At resonance (ω = ωr), the net susceptance is zero.
i.e. Ideal tank circuit
with RS = 0
1 1
,
YT YL YC
jX jX
L C
T
C X
Y j
1
1
.
X
L
Hz
r r
C L
X X LC 2 LC
1
1 1 1
0 rad/s; f
37
38. CONCLUSIONS
Resonance in parallel RLC circuit:
• The lowest current from the source occurs at the resonant frequency of
a parallel circuit hence it is called a rejector circuit.
• At resonance, the current in the branches of the parallel circuit can be
many times greater than the supply current.
• The factor of magnification, the current magnification in the parallel
circuit, is again called the Q factor.
• At the resonant frequency of a resonant parallel network, the impedance
is wholly resistive. The value of this impedance is known as the
dynamic resistance or dynamic impedance.
38
39. APPLICATIONS OF RESONANCE
• Resonant circuits (series or parallel) are used in many applications
such as selecting the desired stations in radio and TV receivers.
• Most common applications of resonance are based on the frequency
dependent response. (“tuning” into a particular frequency/channel)
• Aseries resonant circuit is used as voltage amplifier.
• Aparallel resonant circuit is used as current amplifier.
• Aresonant circuit is also used as a filter.
39
40. DYNAMIC IMPEDANCE (OR) DYNAMIC RESISTANCE
• The dynamic impedance (dynamic resistance) is the resistance offered by
the circuit to the input signal under resonance condition.
Q1. What is the dynamic impedance in a standard series RLC circuit?
Ans. In a standard series RLC circuit, at resonance the
net reactance becomes zero. Therefore, the input supply
see only resistance. Hence,
dynamic impedance Zdynamic = R.
40
41. DYNAMIC IMPEDANCE (OR) DYNAMIC RESISTANCE
Q2. What is the dynamic impedance in a general parallel RLC circuit?
Ans. In a general parallel RLC circuit, at
resonance, the net susceptance becomes zero.
Therefore, the input supply see only resistance.
Hence, dynamic impedance Zdynamic = R.
41
42. DYNAMIC IMPEDANCE (OR) DYNAMIC RESISTANCE
Ideal tank circuit with RS = 0
Q3. What is the dynamic impedance in a ideal tank circuit?
Ans. In ideal tank circuit, at resonance, the
circuit acts like a open circuit. Because, in ideal
tank circuit, the RS = 0. Therefore, the
dynamic impedance Zdynamic
42
43. DYNAMIC IMPEDANCE (OR) DYNAMIC RESISTANCE
Q4. Determine the dynamic impedance of a practical tank circuit?
Ans.
Practical tank circuit
dynamic
S
L
Z
R C
43