This document discusses RL circuits and inductors. Some key points:
- Inductors oppose changes in current through a circuit by inducing a back EMF. This causes the current in an RL circuit to rise or fall exponentially towards its final value with a time constant of L/R.
- Initially after closing a switch, the current through an inductor is 0 A as it cannot instantly change. Over time it rises exponentially towards its final value. When opening a switch, the current cannot instantly drop to 0 A.
- Kirchhoff's loop rule and exponential equations can be used to analyze currents in RL circuits during switching events and as the current changes over time. The potential across an inductor depends
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.
An RC circuit contains a resistor and capacitor in series. When power is applied, maximum current (I0) flows which charges the capacitor. The charge on the capacitor (Q) is equal to the capacitance (C) multiplied by the voltage (Ɛ). The expressions for the charge (q(t)), voltage across the capacitor (VC), and current (I) during the charging phase are given. The time constant (RC) represents the time for the current to decrease to 37% of its initial value. For the discharging phase, the expression for the remaining charge is given.
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) An RC circuit contains a resistor and capacitor in series. The charge on the capacitor and current through the circuit can be expressed as exponential functions of time, with the time constant τ=RC.
2) For an RL circuit, the current through the inductor is expressed as 1-e^(-t/τ) where τ=L/R. This shows the current rising exponentially towards its maximum value.
3) In an RLC circuit, the charge on the capacitor undergoes damped harmonic oscillations expressed as e^(-Rt/2L)cos(ωdt), where ωd is the angular frequency of oscillations.
The document provides an overview of series R-L circuits, discussing the phase angle relationship between current and voltage, the initial and steady-state current conditions, how current grows over time according to the exponential function, and how the time constant is defined as L/R. It also examines the energy and power relationships for the resistor, inductor, and battery in the circuit.
Capacitors play an important role in AC circuits by storing and releasing charge as the voltage alternates. In an AC circuit, a capacitor charges and discharges continuously as the voltage oscillates, drawing current from the circuit during charging and supplying current during discharging. This causes the current through a capacitor to lag 90 degrees behind the voltage. Impedance describes the total opposition to current in an AC circuit and takes into account both resistance and reactance. Impedance can be calculated using Pythagoras' theorem by treating resistance and reactance as vectors.
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 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.
An RC circuit contains a resistor and capacitor in series. When power is applied, maximum current (I0) flows which charges the capacitor. The charge on the capacitor (Q) is equal to the capacitance (C) multiplied by the voltage (Ɛ). The expressions for the charge (q(t)), voltage across the capacitor (VC), and current (I) during the charging phase are given. The time constant (RC) represents the time for the current to decrease to 37% of its initial value. For the discharging phase, the expression for the remaining charge is given.
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) An RC circuit contains a resistor and capacitor in series. The charge on the capacitor and current through the circuit can be expressed as exponential functions of time, with the time constant τ=RC.
2) For an RL circuit, the current through the inductor is expressed as 1-e^(-t/τ) where τ=L/R. This shows the current rising exponentially towards its maximum value.
3) In an RLC circuit, the charge on the capacitor undergoes damped harmonic oscillations expressed as e^(-Rt/2L)cos(ωdt), where ωd is the angular frequency of oscillations.
The document provides an overview of series R-L circuits, discussing the phase angle relationship between current and voltage, the initial and steady-state current conditions, how current grows over time according to the exponential function, and how the time constant is defined as L/R. It also examines the energy and power relationships for the resistor, inductor, and battery in the circuit.
Capacitors play an important role in AC circuits by storing and releasing charge as the voltage alternates. In an AC circuit, a capacitor charges and discharges continuously as the voltage oscillates, drawing current from the circuit during charging and supplying current during discharging. This causes the current through a capacitor to lag 90 degrees behind the voltage. Impedance describes the total opposition to current in an AC circuit and takes into account both resistance and reactance. Impedance can be calculated using Pythagoras' theorem by treating resistance and reactance as vectors.
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.
1) The document discusses RC and RL circuits, also known as first-order natural response circuits.
2) It provides the general equations that describe the natural response of an inductor current (iL) in an RL circuit and the natural response of a capacitor voltage (vC) in an RC circuit.
3) The key aspects of the natural response are that the inductor current cannot change instantaneously in an RL circuit, and the capacitor voltage cannot change instantaneously in an RC circuit.
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.
The document discusses AC circuits using phasors to represent voltages and currents. It introduces the concepts of resistive reactance (R), capacitive reactance (XC), and inductive reactance (XL). R causes voltage to be in phase with current, while XC causes voltage to lag current by 90° and XL causes voltage to lead current by 90°. Together, R, XC and XL determine the impedance (Z) and phase angle (φ) of the circuit. The document uses an example of an L-C circuit to show how to calculate the frequency where XC and XL are equal.
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.
The document discusses Kirchhoff's rules for circuit analysis and RC circuits. Kirchhoff's rules state that the sum of currents entering a junction must be 0, and the sum of potential differences in any closed loop must be 0. RC circuits have time-dependent behavior when charging and discharging based on the time constant, which is the resistance times the capacitance. The document provides examples of applying Kirchhoff's rules to solve for currents in circuits and calculating the time it takes a capacitor to charge to half its final value in an RC circuit.
This document discusses single-phase AC circuits and alternating quantities. It defines key terms like cycle, time period, frequency, phase, and phase difference. It also describes how an alternating electromotive force (EMF) is generated by rotating a coil within a magnetic field, producing a sinusoidal waveform. The maximum and instantaneous values of the generated EMF are defined in terms of the magnetic field strength, coil dimensions, number of turns, rotational speed, and angular position of the coil. An example calculation is provided to illustrate these relationships.
Time domain response in rc & rl circuitsDharit Unadkat
The document summarizes time domain responses in RC and RL circuits. It describes that transients are the time-varying currents and voltages resulting from sudden changes in sources. RC circuits with a single energy storage element are first-order circuits that can be used for filtering. The time constant for an RC circuit is RC and for an RL circuit is L/R. It represents the time required for an exponential to decay to 36.7% of its initial value. The document also discusses determining the initial conditions for transient analysis based on inductor current and capacitor voltage remaining constant during circuit changes.
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.
This document outlines the experiments for the Electrical Circuit Laboratory course handled by Mr. Karthikeyan.R. The 10 listed experiments include verifying Ohm's and Kirchoff's laws, Thevenin's and Norton's theorems, superposition theorem, maximum power transfer theorem, reciprocity theorem, measuring self-inductance of a coil, mesh and nodal analysis, transient response of RL and RC circuits, frequency response of series and parallel resonance circuits, and frequency response of single tuned coupled circuits. The course is 3 credits and totals 45 periods.
This document summarizes key concepts about transformers:
1) Transformers transfer electrical energy from one voltage level to another through magnetic coupling between primary and secondary coils. They do not directly convert electrical to mechanical energy.
2) An ideal transformer transfers power without losses, but real transformers have resistive losses in their coils and core that reduce efficiency.
3) The voltage and current ratios between primary and secondary coils are determined by their relative turn ratios; this relationship allows impedances to be transferred between sides.
- 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 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.
1) The document discusses DC and AC circuits, defining key concepts like voltage, current, resistance, inductance, and capacitance.
2) It describes different types of circuit elements and how they are connected in series, parallel and series-parallel configurations.
3) Kirchhoff's laws and theorems like superposition, phasor representation, and analysis of RL, RC, and RLC circuits under alternating current are explained.
1) DC circuits can be linear or non-linear depending on whether their parameters such as resistance, inductance, and capacitance remain constant or change with voltage and current.
2) Kirchhoff's laws, including Kirchhoff's current law and Kirchhoff's voltage law, are important laws for analyzing electrical circuits and networks.
3) Circuit analysis methods such as mesh analysis, nodal analysis, and Thevenin's theorem allow circuits to be simplified to aid in calculation of voltage and current.
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.
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
- The natural response of a circuit refers to the behavior of the circuit when external sources are removed. This allows the stored energy in inductors and capacitors to dissipate.
- The general solution for the natural response of RL and RC circuits is an exponential decay from an initial value to a final value, with the decay rate determined by the circuit time constant.
- For an RL circuit, the inductor current decays exponentially with time constant L/R. For an RC circuit, the capacitor voltage decays exponentially with time constant RC.
This document summarizes the characteristics of purely resistive, inductive, and capacitive AC circuits. It also describes R-L and R-C series circuits, explaining how the current and voltage are phase shifted. Finally, it covers R-L-C series circuits in detail, showing how the phase relationship depends on whether the inductive or capacitive reactance is larger. Power calculations and definitions of impedance and power factor are provided throughout.
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.
Capacitors and inductors are passive circuit elements that can store energy.
- Capacitors store energy in an electric field between conducting plates separated by an insulator. The capacitance is affected by the area of the plates, distance between plates, and the material between the plates.
- Inductors store energy in a magnetic field created by current through a coil of wire. The inductance depends on the number of wire turns, length of the coil, and material inside the coil.
- Capacitors and inductors have characteristic equations relating voltage, current, charge, and energy that make them useful for circuit analysis. Their properties allow them to be combined in series and parallel configurations.
B tech ee ii_ eee_ u-2_ ac circuit analysis_dipen patelRai University
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.
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) The document discusses RC and RL circuits, also known as first-order natural response circuits.
2) It provides the general equations that describe the natural response of an inductor current (iL) in an RL circuit and the natural response of a capacitor voltage (vC) in an RC circuit.
3) The key aspects of the natural response are that the inductor current cannot change instantaneously in an RL circuit, and the capacitor voltage cannot change instantaneously in an RC circuit.
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.
The document discusses AC circuits using phasors to represent voltages and currents. It introduces the concepts of resistive reactance (R), capacitive reactance (XC), and inductive reactance (XL). R causes voltage to be in phase with current, while XC causes voltage to lag current by 90° and XL causes voltage to lead current by 90°. Together, R, XC and XL determine the impedance (Z) and phase angle (φ) of the circuit. The document uses an example of an L-C circuit to show how to calculate the frequency where XC and XL are equal.
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.
The document discusses Kirchhoff's rules for circuit analysis and RC circuits. Kirchhoff's rules state that the sum of currents entering a junction must be 0, and the sum of potential differences in any closed loop must be 0. RC circuits have time-dependent behavior when charging and discharging based on the time constant, which is the resistance times the capacitance. The document provides examples of applying Kirchhoff's rules to solve for currents in circuits and calculating the time it takes a capacitor to charge to half its final value in an RC circuit.
This document discusses single-phase AC circuits and alternating quantities. It defines key terms like cycle, time period, frequency, phase, and phase difference. It also describes how an alternating electromotive force (EMF) is generated by rotating a coil within a magnetic field, producing a sinusoidal waveform. The maximum and instantaneous values of the generated EMF are defined in terms of the magnetic field strength, coil dimensions, number of turns, rotational speed, and angular position of the coil. An example calculation is provided to illustrate these relationships.
Time domain response in rc & rl circuitsDharit Unadkat
The document summarizes time domain responses in RC and RL circuits. It describes that transients are the time-varying currents and voltages resulting from sudden changes in sources. RC circuits with a single energy storage element are first-order circuits that can be used for filtering. The time constant for an RC circuit is RC and for an RL circuit is L/R. It represents the time required for an exponential to decay to 36.7% of its initial value. The document also discusses determining the initial conditions for transient analysis based on inductor current and capacitor voltage remaining constant during circuit changes.
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.
This document outlines the experiments for the Electrical Circuit Laboratory course handled by Mr. Karthikeyan.R. The 10 listed experiments include verifying Ohm's and Kirchoff's laws, Thevenin's and Norton's theorems, superposition theorem, maximum power transfer theorem, reciprocity theorem, measuring self-inductance of a coil, mesh and nodal analysis, transient response of RL and RC circuits, frequency response of series and parallel resonance circuits, and frequency response of single tuned coupled circuits. The course is 3 credits and totals 45 periods.
This document summarizes key concepts about transformers:
1) Transformers transfer electrical energy from one voltage level to another through magnetic coupling between primary and secondary coils. They do not directly convert electrical to mechanical energy.
2) An ideal transformer transfers power without losses, but real transformers have resistive losses in their coils and core that reduce efficiency.
3) The voltage and current ratios between primary and secondary coils are determined by their relative turn ratios; this relationship allows impedances to be transferred between sides.
- 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 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.
1) The document discusses DC and AC circuits, defining key concepts like voltage, current, resistance, inductance, and capacitance.
2) It describes different types of circuit elements and how they are connected in series, parallel and series-parallel configurations.
3) Kirchhoff's laws and theorems like superposition, phasor representation, and analysis of RL, RC, and RLC circuits under alternating current are explained.
1) DC circuits can be linear or non-linear depending on whether their parameters such as resistance, inductance, and capacitance remain constant or change with voltage and current.
2) Kirchhoff's laws, including Kirchhoff's current law and Kirchhoff's voltage law, are important laws for analyzing electrical circuits and networks.
3) Circuit analysis methods such as mesh analysis, nodal analysis, and Thevenin's theorem allow circuits to be simplified to aid in calculation of voltage and current.
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.
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
- The natural response of a circuit refers to the behavior of the circuit when external sources are removed. This allows the stored energy in inductors and capacitors to dissipate.
- The general solution for the natural response of RL and RC circuits is an exponential decay from an initial value to a final value, with the decay rate determined by the circuit time constant.
- For an RL circuit, the inductor current decays exponentially with time constant L/R. For an RC circuit, the capacitor voltage decays exponentially with time constant RC.
This document summarizes the characteristics of purely resistive, inductive, and capacitive AC circuits. It also describes R-L and R-C series circuits, explaining how the current and voltage are phase shifted. Finally, it covers R-L-C series circuits in detail, showing how the phase relationship depends on whether the inductive or capacitive reactance is larger. Power calculations and definitions of impedance and power factor are provided throughout.
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.
Capacitors and inductors are passive circuit elements that can store energy.
- Capacitors store energy in an electric field between conducting plates separated by an insulator. The capacitance is affected by the area of the plates, distance between plates, and the material between the plates.
- Inductors store energy in a magnetic field created by current through a coil of wire. The inductance depends on the number of wire turns, length of the coil, and material inside the coil.
- Capacitors and inductors have characteristic equations relating voltage, current, charge, and energy that make them useful for circuit analysis. Their properties allow them to be combined in series and parallel configurations.
B tech ee ii_ eee_ u-2_ ac circuit analysis_dipen patelRai University
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.
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. The document discusses electricity and various electrical concepts like charge, current, voltage, resistance, and circuits. It defines these terms and explains properties and relationships between concepts.
2. Key points covered include that electricity is the flow of electrons in a circuit, current is the rate of flow of charge, and Ohm's Law defines the relationship between current, voltage, and resistance.
3. The document also compares series and parallel circuits, explaining that series circuits have higher total resistance while parallel circuits have lower total resistance.
- Electricity involves the movement of electric charge. There are two types of charge: positive and negative. Like charges repel and unlike charges attract.
- Potential difference is the difference in electric potential or voltage between two points in a circuit. It is measured in volts. A voltmeter is used to measure potential difference.
- Current is the flow of electric charge. It is represented by I and measured in amperes. An ammeter is used to measure current. Ohm's law defines the relationship between voltage, current and resistance in a circuit.
1) The document discusses concepts related to current electricity including electric charge, potential difference, flow of current, Ohm's law, resistance, and electrical circuits.
2) Key points covered include that rubbing glass with silk creates a positive charge on the glass and negative charge on the silk due to electron transfer, and that potential difference is required for electric current to flow.
3) The document also discusses measuring instruments like ammeters, voltmeters, and potentiometers; the heating effect of current; electric power; fuses; and Wheatstone bridges.
This document discusses electricity and related concepts. It begins by defining electric charge and its properties. It then discusses methods of charging objects and defines electricity as the flow of electrons in a circuit. It explains electric current, electric field, electric potential and potential difference. It introduces Ohm's law and discusses resistance, resistivity, and factors that affect resistance. It describes electric circuits and components for measuring current and voltage. It explains how resistances can be combined in series or parallel and compares the key differences between series and parallel circuits.
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 cathode ray oscilloscope (CRO) uses an electron gun and deflection plates to control the movement of an electron beam across a fluorescent screen, allowing the visualization of electrical waveforms and phenomena. It consists of three main parts: the electron gun, deflection system, and fluorescent screen. The CRO is used to analyze waveforms, transients, and other time-varying quantities across a wide frequency range from low to radio frequencies.
This document discusses different types of generators and their components. It begins by defining a generator as a device that converts mechanical energy to electricity. It then discusses common electricity terms like current, voltage, and EMF. The document outlines different types of generators including X-ray generators. It explains the workings of 3-phase, 6-pulse, and 12-pulse generators. Advantages are provided such as reduced ripple factor and increased X-rays. Overall, the document provides an overview of generators, their components, different pulse types, and their applications.
The document describes the key characteristics and equations of an ideal transformer and how they differ from a practical transformer.
1) An ideal transformer has no winding resistance, no leakage flux, and no core losses. It transfers power efficiently between its primary and secondary windings according to turns ratio.
2) A practical transformer has winding resistance, leakage flux, and core losses that reduce its efficiency compared to an ideal model. It draws a small magnetizing current to produce flux and a power loss component to account for iron losses.
3) Faraday's law of induction and Lenz's law explain how an alternating voltage is induced in transformer windings via a changing magnetic flux. In practice, some flux leaks and does not
There are three types of electrical charges: positive charges consist of protons, negative charges consist of electrons, and the SI unit of charge is the coulomb. Conductors contain free or loosely bound electrons that allow them to conduct electricity, while insulators do not have free electrons and obstruct electricity flow. Potential difference is defined as the work required to move a unit positive charge between two points in an electric field. Common measuring instruments include the voltmeter, which measures potential difference, and the ammeter, which measures electric current in amperes. Resistors can be connected in series, where the total resistance is the sum of individual resistances, or parallel, where the total resistance is lower than the lowest individual resistance.
There are two types of charges: positive charges consist of protons, and negative charges consist of electrons. The standard unit of charge is the coulomb. Conductors contain free or loosely bound electrons that allow them to conduct electricity, while insulators do not have free electrons and obstruct electricity flow. Ohm's law defines the relationship between voltage, current, and resistance in a circuit. Joule's law states that the heat produced is directly proportional to the square of the current, the resistance, and the time of current flow. Electric power is defined as voltage multiplied by current and measured in watts.
based on class 10 chapter electricity.
consists of topic such as-
electric potential,electric current, resistors ,series and parallel connection, heating effect of electric current, electric power,etc.
based on class 10 chapter electricity.
consists of topic such as-
electric potential,electric current, resistors ,series and parallel connection, heating effect of electric current, electric power,etc.
There are two types of charges: positive charges consist of protons, and negative charges consist of electrons. The standard unit of charge is the coulomb. Conductors contain free or loosely bound electrons that allow them to conduct electricity, while insulators do not have free electrons and obstruct electricity flow. Resistance is a measure of the difficulty electrons have in moving through a material. Ohm's law states that current is directly proportional to voltage and inversely proportional to resistance. Joule's law describes how electrical energy is converted to heat energy when a current passes through a resistor.
* I1 = 2.5 A (given)
* I2 = 4 A (given)
* Using Kirchhoff's junction rule: I1 = I2 + I3
* So: 2.5 A = 4 A + I3
* Solving for I3: I3 = 2.5 A - 4 A = -1.5 A
The value of I3 is -1.5 A. The answer is 3.
Cyclic voltammetry is an electroanalytical technique that measures current during redox reactions at an electrode. It involves scanning the potential of a working electrode versus a reference electrode and measuring the current. The potential is ramped from an initial value to a set switching potential and back to the initial value. This process is repeated in cycles. A cyclic voltammogram plots the current response of the working electrode versus the applied potential and provides information about redox potentials and reaction reversibility. Reversible reactions produce symmetrical peaks while irreversible reactions have wider separation between peaks. Cyclic voltammetry is useful for studying electrode reaction mechanisms and kinetics.
This document provides an overview of transformer principles and operation. It discusses how transformers work by using mutual induction between two coils to change voltage levels. Key points covered include transformer components, turns ratio, step-up and step-down functions, efficiency losses, tap changing, and three-phase configurations. Transformer types like power, distribution, instrument and phase shifting transformers are also summarized.
O.C & S.C Test, Sumpner or back to back Test, Condition for maximum efficienc...Abhishek Choksi
Sub: DC Machines and Transformer (2130904)
Active Learning Assignment
Topic: O.C & S.C Test, Sumpner or back to back Test, Condition for maximum efficiency, All day Efficiency
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.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
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Answers about how you can do more with Walmart!"
The chapter Lifelines of National Economy in Class 10 Geography focuses on the various modes of transportation and communication that play a vital role in the economic development of a country. These lifelines are crucial for the movement of goods, services, and people, thereby connecting different regions and promoting economic activities.
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How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
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This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
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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2. • A circuit that contains a coil, such as a solenoid,
has a self-inductance that prevents the current
from increasing or decreasing instantaneously.
• A circuit element that has a large inductance is
called an inductor.
• The circuit symbol for an inductor is
• We will always assume that the self-inductance
of the remainder of the circuit is negligible
compared to that of the inductance.
• Keep in mind that even a circuit without a coil
has some self-inductance that can affect the
behavior of the circuit.
3. • Because the inductance of the inductor esults in a
back EMF, an inductor in a circuit opposes
changes in the current in that circuit.
– The inductor attempts to keep the current the same as
it was before the change occurred.
– If the battery voltage in the circuit is increased so that
the current rises, the inductor opposes this change
and the rise is not instantaneous.
– If the battery voltage is decreased, the presence of the
inductor results in a slow drop in the current rather
than an immediate drop.
– The inductor causes the circuit to be “sluggish” as it
reacts to changes in the voltage.
4. • Consider a circuit consisting of a resistor, an
inductor, and a battery.
– The internal resistance of the battery will be neglected.
• The switch is closed at t = 0 and the current
begins to increase.
• Due to the increasing current, the inductor will
produce an EMF
(the back EMF)
that opposes the
increasing current.
5. • The inductor acts like a battery whose polarity is
opposite that of the battery in the circuit.
• The back EMF produced by the inductor is:
• Since the current is
increasing, dI/dt is
positive; therefore,
EMFL is negative.
L
dI
EMF L
dt
= − ×
6. • This corresponds to the fact that there is a
potential drop in going from a to b across the
inductor.
• Point a is at a higher potential than point b.
• Apply Kirchhoff’s loop rule to the circuit:
0
dI
EMF I R L
dt
− × − × =
7. • Divide through by R:
• Let ; EMF and R are constant;
I is variable
• Take the derivative of x:
0
dI dI
EMF I R L EMF I R L
dt dt
EMF I R L dI EMF L dI
I
R R R dt R R dt
− × − × = − × = ×
×
− = × − = ×
EMF
x I
R
= −
0
EMF EMF
dx d I d dI dI
R R
dx dI dI dx
= − = − = − ÷
= − = −
8. • Replace the variables in the equation:
• Combine like terms and differentiate the differential
equation:
EMF L dI L dx L dx
I x
R R dt R dt R dt
− −
− = × = × = ×
1
1 1
ln ln ln
ln
o
x
ox
o
L dx L dx R
x dt dx
R dt R dt L x
R R
dt dx dt dx
L x L x
R R
t x t x x
L L
R x
t
L x
− − −
= × = × × = ×
− −
× = × × = ×
− −
× = × = −
−
× =
∫ ∫ ∫ ∫
9. • Exponentiate both sides of the equation:
• At t = 0 s, I = 0 A, so:
ln
ln o
xR R
t t
xL L
o o
R
t
L
o
R x x
t e e e
L x x
x x e
− −
× ×
−
×
−
× = = =
= ×
0o
o
EMF EMF
x I
R R
EMF
x
R
= − = −
=
10. • Replacing the substituted variables:
• The current I as a function of time:
1
R
t
L
o o
R R
t t
L L
R
t
L
EMF EMF
x x e x I x
R R
EMF EMF EMF EMF
I e I e
R R R R
EMF
I e
R
−
×
− −
× ×
−
×
= × = − =
− = × = − ×
÷= × −
÷
( ) 1
R
t
L
EMF
I t e
R
−
×
÷= × −
÷
11. • The equation shows how the inductor effects the current.
• The current does not increase instantly to its final
equilibrium value when the switch is closed but instead
increases according to an exponential function.
• If the inductance approaches zero, the exponential term
becomes zero and there is no time dependence for the
current – the current increases instantaneously to its
final equilibrium value in the absence of the inductance.
• Time constant for an RL circuit:
1L R
so
R L
τ
τ
= =
12. • The current I as a function of time:
• The time constant τ is the time it takes for the current to
reach (1 – e-1
) = 0.63 of the final value, EMF/R.
• The graph of current versus time, where I = 0 A at t = 0
s; the final equilibrium value of the current occurs at
t = ∞ and is equal to EMF/R.
• The current rises very fast initially
and then gradually approaches the
equilibrium value EMF/R as
t → ∞.
( ) 1 1
tR
t
L
EMF EMF
I t e e
R R
τ
−−
×
÷ ÷= × − = × −
÷ ÷
13. • The rate of increase of current dI/dt is a maximum
(equal to EMF/L) at t = 0 s and decreases exponentially
to zero as t → ∞.
• Consider the RL circuit shown
in the figure below:
14. • The curved lines on the switch S represent a switch that
is connected either to a or b at all times. If the switch is
connected to neither a nor b, the current in the circuit
suddenly stops.
• Suppose that the switch has been set at position a long
enough to allow the current to reach its equilibrium
value EMF/R. The circuit is described by the outer loop
only.
• If the switch is thrown from
a to b, the circuit is described
by just the right hand loop
and we have a circuit with
no battery (EMF = 0 V).
15. • Applying Kirchhoff’s loop rule to the right-hand loop at
the instant the switch is thrown from a to b:
• Divide through by R:
0
dI
I R L
dt
− × − × =
0
dI dI
I R L I R L
dt dt
I R L dI L dI
I
R R dt R dt
− × − × = × = − ×
× − −
= × = ×
16. • Combine the current I terms and differentiate the
differential equation:
1
1
ln ln ln
ln
o
I
oI
o
L dI R
I dI dt
R dt I L
R
dI dt
I L
R R
I dt I I t
L L
I R
t
I L
− −
= × × = ×
−
× = ×
− −
= × − = ×
−
= ×
∫ ∫
∫
17. • Exponentiate both sides of the equation:
• The current I as a function of time for an RL circuit in
which the current is decaying over time:
ln
ln o
I R
t
I L
o
R R
t t
L L
o
o
I R
t e e
I L
I
e I I e
I
−
×
− −
× ×
−
= × =
= = ×
( )
R
t
L
oI t I e
−
×
= ×
18. • When t = 0 s, Io = EMF/R and τ = L/R:
• The current is continually decreasing with time.
– The slope, dI/dt, is always negative and has its maximum
value at t = 0 s.
– The negative slope indicates that the
is now positive; that is, point a is at a lower
potential than point b.
( )
t t
o
EMF
I t I e e
R
τ τ
− −
= × = ×
L
dI
EMF L
dt
= − ×
19. Time Constant of an RL Circuit
• The circuit shown in the figure consists of a 30 mH
inductor, a 6 Ω resistor, and a 12 V battery. The switch
is closed at t = 0 s.
• Find the time constant of the circuit.
• Determine the current in the circuit at t = 0.002 s.
0.03
0.005
6
L H
s
R
τ = = =
Ω
0.002
0.00512
( ) 0.659
6
st t
s
o
EMF V
I t I e e e A
R
τ τ
−− −
= × = × = × =
Ω
20. Kirchhoff’s Rule and Inductors
• For the circuit shown in the figure:
A.find the currents I1, I2, and I3 immediately after switch S is
closed.
21. • Answer: The current in an inductor cannot change
instantaneously from 0 A to the steady state current,
therefore, the current in the inductor must be zero after
the switch is closed because it is 0 A before the switch is
closed.
• I3 = 0 A
22. • The current in the left loop equals the EMF divided by
the equivalent resistance of the two resistors in series.
• Req = 10 Ω + 20 Ω = 30 Ω
1 2
e
150
5
R 30q
EMF V
I I A= = = =
Ω
23. B. find the currents I1, I2, and I3 a long time after switch S
has been closed.
• Answer: when the current reaches its steady-state
value, dI/dt = 0, so there is no potential drop across the
inductor. The inductor acts like a short circuit (a wire
with zero resistance).
24. Parallel resistances:
Total resistance = 10 Ω + 10 Ω = 20 Ω
Total current:
( ) ( )
1
1 1
20 20 10pR
−
− − = Ω + Ω = Ω
1
150
7.5
20
T
EMF V
I I A
RT
= = = =
Ω
25. The 7.5 A current will split in half to travel through the
two equal 20 Ω resistors; I2 = I3 = 3.75 A
C.find the currents I1, I2, and I3 immediately after switch
S has been opened.
26. • Answer: The current in an inductor cannot change
instantaneously from the steady state current to 0 A,
therefore, the current in the inductor must be the same
after the switch is opened as it was just before the switch
is opened.
• I3 = 3.75 A
27. • When the switch is opened, I1 drops to 0 A.
• To oppose the change in the direction of the magnetic
flux through the inductor, the direction of the induced
current in the loop changes direction;
I2 = −I3 = −3.75 A.
28. D. find the currents I1, I2, and I3 a long time after switch
S has been opened.
Answer: all currents must be 0 A a long time after the
switch is opened.
I1 = I2 = I3 = 0 A
29. RL Circuits Summary
• The inductor acts like a wire when t is large:
• The inductor acts like an open circuit when t = 0 s;
i = 0 A
• The current starts from 0 A and increases up to a
maximum of with a time constant given by
• As the current increases from 0 A
to its steady-state value:
– Current:
EMF
I
R
=
EMF
I
R
=
L
L
R
τ =
1 L
t
EMF
i e
R
τ
−
= × − ÷
÷
30. – Voltage across the resistor:
– Voltage across the inductor:
1 L
t
RV i R EMF eτ
−
= × = × − ÷
÷
1 L
L
L R
t
L
t
L
V EMF V
V EMF EMF e
V EMF e
τ
τ
−
−
= −
= − × − ÷
÷
= ×
31. • The potential difference across a resistor depends on the
current.
• The potential difference across an inductor depends on
the rate of change of the current.
32. • The potential difference across an inductor depends on
the rate of change of the current.
33. • When the EMF source is removed from the circuit and
the current begins to decay from the steady-state current
to 0 A:
– Current decay:
– Voltage across resistor:
– Voltage across inductor:
VR(V)
L
t
EMF
i e
R
τ
−
= ×
L
t
RV i R EMF eτ
−
= × = ×
t R
t RL
L
L
di EMF de
V L L EMF e
dt R dt
− ×
− ×
= × = × × = − ×
34. What is Happening During Current Decay?
• When the battery is removed and the RL series circuit is
shorted, the current keeps flowing in the same direction
it was for awhile. How can this be?
• What is happening is that the current tries to drop
suddenly, but this induces an EMF to oppose the
change, causing the current to keep flowing for awhile.
• Another way of thinking about it is that the magnetic
field that was stored in the inductor is “collapsing.”
• There is energy stored in the magnetic field, and when
the source of current is removed, the energy flows from
the magnetic field back into the circuit.
35. November 7, 2007
Make Before Break Switches
• The switch in a circuit like the one at right has to be a special
kind, called a “make before break” switch.
• The switch has to make the connection to b before breaking
the connection with a.
• If the circuit is allowed to be in the state like this…even
momentarily, midway between a and b, then a big problem
results.
• Recall that for a capacitor, when we disconnect the circuit the
charge will merrily stay on the capacitor indefinitely.
• Not so on an inductor. The inductor needs current, i.e.
flowing charge. It CANNOT go immediately to zero.
• The collapsing magnetic field in the inductor will force the
current to flow, even when it has no where to go.
• The current will flow in this case by jumping the air gap.
Link to video
You have probably
seen this when
unplugging something
with a motor—a spark
that jumps from the
plug to the socket.
36. Start Your Engines: The
Ignition Coil
• The gap between the spark plug in
a combustion engine needs an
electric field of ~107
V/m in order to
ignite the air-fuel mixture. For a
typical spark plug gap, one needs
to generate a potential difference >
104
V.
• But, the typical EMF of a car
battery is 12 V. So, how does a
spark plug work?
spark
12V
The “ignition coil” is a double layer solenoid:
• Primary: small number of turns , connected to
12 V battery
• Secondary: MANY turns -- connected to spark
plug
•Breaking the circuit changes the current
through the “primary coil”
• Result: LARGE change in flux thru
secondary -- large induced EMF