This document contains information about several circuit analysis theorems:
- Thévenin's theorem states that a linear electrical network can be reduced to an equivalent circuit with a voltage source in series with a resistor.
- Norton's theorem states that a linear electrical network can be reduced to an equivalent circuit with a current source in parallel with a resistor.
- The superposition theorem allows analyzing circuits by considering each independent source separately and then summing the results.
- The maximum power transfer theorem establishes that maximum power is transferred from a source to a load when their resistances are equal.
- Examples are provided to demonstrate applying these theorems to calculate equivalent circuits and voltages in given circuits.
1. The circuit contains an inductor L and resistor R. A switch connecting the inductor to a voltage source Vs opens at t=0.
2. The initial current through the inductor is i(0)=I0. The final current is i(∞)=0 as there is no longer a voltage applied.
3. The time constant is τ=L/R. The current through the inductor will decay exponentially according to the equation i(t)=I0e-t/τ.
This document discusses circuit analysis techniques including:
1. Linearity and superposition principles, which allow analyzing circuits with multiple independent sources by considering each source individually.
2. Source transformations, which allow converting between current and voltage sources to simplify circuit analysis.
3. Thevenin's and Norton's theorems, which allow replacing complex linear circuits with simplified equivalent circuits containing a single voltage or current source with internal resistance.
4. The maximum power transfer theorem, which states that maximum power is delivered to a load when its resistance equals the internal resistance of the equivalent Thevenin source.
Aplicación de la serie Fourier en un circuito electrónico de potencia)JOe Torres Palomino
The document discusses the application of Fourier series in electronic power circuits. It begins with an introduction to Fourier series and how they can be used to represent periodic functions as an infinite sum of sines and cosines. It then provides an example of determining the Fourier series for a piecewise function. Next, it explains how harmonics are produced in electronic circuits due to nonlinear elements and discusses how the Fourier series can be used to determine parameters like current, voltage, impedance, and power absorption. It concludes by applying the Fourier series analysis to a square wave inverter circuit.
This document discusses the SEPIC (Single-ended primary-inductor converter) DC-DC converter. It provides theoretical calculations of various circuit parameters like voltage ratios, current values, and ripple quantities. It also determines the critical condition for the converter to operate in continuous or discontinuous mode. Corrections are made to account for non-ideal components in continuous mode analysis.
This document contains solutions to tutorial exercises on electronics circuits involving capacitors and other circuit elements. The first exercise involves determining currents and equivalent capacitance in a circuit with two capacitors. The second involves calculating capacitor voltage over time when a switch changes positions. The third determines capacitor voltage over time for virtually parallel capacitors driven by a voltage source. Subsequent exercises involve determining voltages, currents, and impedances in various RC, RL, and RLC circuits.
1) The document discusses electromagnetic oscillations in LC circuits. It describes how the electric and magnetic energy oscillate between the inductor and capacitor over time, with the total energy remaining constant.
2) Damped oscillations in an LC circuit with resistance R are also examined. The type of damping (underdamped, critically damped, or overdamped) depends on the ratio of R to other circuit parameters.
3) Forced oscillations occur when an external periodic force supplies energy to compensate for losses, maintaining a steady oscillation amplitude. Resonance effects occur near the natural frequency of the system.
The document discusses transient analysis of first order differential equations that model circuits containing energy storage elements like capacitors and inductors. It explains that when the circuit conditions change, there will be a transient response before reaching the steady-state. The complete solution consists of the natural/homogeneous response and the particular/forced response. The natural response dies out over time, while the forced response depends on the external excitation. Circuits are solved using the time constant, which relates to how long it takes for the transient response to decay to the steady-state.
1. The circuit contains an inductor L and resistor R. A switch connecting the inductor to a voltage source Vs opens at t=0.
2. The initial current through the inductor is i(0)=I0. The final current is i(∞)=0 as there is no longer a voltage applied.
3. The time constant is τ=L/R. The current through the inductor will decay exponentially according to the equation i(t)=I0e-t/τ.
This document discusses circuit analysis techniques including:
1. Linearity and superposition principles, which allow analyzing circuits with multiple independent sources by considering each source individually.
2. Source transformations, which allow converting between current and voltage sources to simplify circuit analysis.
3. Thevenin's and Norton's theorems, which allow replacing complex linear circuits with simplified equivalent circuits containing a single voltage or current source with internal resistance.
4. The maximum power transfer theorem, which states that maximum power is delivered to a load when its resistance equals the internal resistance of the equivalent Thevenin source.
Aplicación de la serie Fourier en un circuito electrónico de potencia)JOe Torres Palomino
The document discusses the application of Fourier series in electronic power circuits. It begins with an introduction to Fourier series and how they can be used to represent periodic functions as an infinite sum of sines and cosines. It then provides an example of determining the Fourier series for a piecewise function. Next, it explains how harmonics are produced in electronic circuits due to nonlinear elements and discusses how the Fourier series can be used to determine parameters like current, voltage, impedance, and power absorption. It concludes by applying the Fourier series analysis to a square wave inverter circuit.
This document discusses the SEPIC (Single-ended primary-inductor converter) DC-DC converter. It provides theoretical calculations of various circuit parameters like voltage ratios, current values, and ripple quantities. It also determines the critical condition for the converter to operate in continuous or discontinuous mode. Corrections are made to account for non-ideal components in continuous mode analysis.
This document contains solutions to tutorial exercises on electronics circuits involving capacitors and other circuit elements. The first exercise involves determining currents and equivalent capacitance in a circuit with two capacitors. The second involves calculating capacitor voltage over time when a switch changes positions. The third determines capacitor voltage over time for virtually parallel capacitors driven by a voltage source. Subsequent exercises involve determining voltages, currents, and impedances in various RC, RL, and RLC circuits.
1) The document discusses electromagnetic oscillations in LC circuits. It describes how the electric and magnetic energy oscillate between the inductor and capacitor over time, with the total energy remaining constant.
2) Damped oscillations in an LC circuit with resistance R are also examined. The type of damping (underdamped, critically damped, or overdamped) depends on the ratio of R to other circuit parameters.
3) Forced oscillations occur when an external periodic force supplies energy to compensate for losses, maintaining a steady oscillation amplitude. Resonance effects occur near the natural frequency of the system.
The document discusses transient analysis of first order differential equations that model circuits containing energy storage elements like capacitors and inductors. It explains that when the circuit conditions change, there will be a transient response before reaching the steady-state. The complete solution consists of the natural/homogeneous response and the particular/forced response. The natural response dies out over time, while the forced response depends on the external excitation. Circuits are solved using the time constant, which relates to how long it takes for the transient response to decay to the steady-state.
This document discusses RC circuits and their exponential response over time. It defines the time constant τ as the time it takes for the dependent variable (current or voltage) to decrease to 37% of its initial value. For an RC circuit, the voltage v(t) decreases exponentially over time according to the equation v(t)=V0e-t/RC. The document provides examples of calculating v(t) at different times for given RC circuits, as well as a homework problem involving finding v(t) values.
This document provides an overview of alternating current (AC) circuits. It begins by introducing AC voltage sources and defining key concepts like frequency, period, and angular frequency. It then analyzes simple circuits with a single circuit element - resistor, inductor, or capacitor - connected to an AC source. The behavior of current and voltage in each case is examined. Finally, the document considers the driven RLC series circuit, deriving the differential equation that governs it. Key circuit concepts like impedance and resonance are also introduced.
This document describes an experiment to study the discharge process of an RC circuit. The objectives are to measure the current and charge of a capacitor during discharge and determine the time constant of the RC circuit. The experiment involves charging a capacitor using a power supply, then discharging it through a resistor while measuring the voltage over time. Data is plotted and the slope is used to calculate the experimental time constant, which is compared to the theoretical value calculated from the circuit components.
This document section describes alternating current (AC) circuits containing a single circuit element: resistor, inductor, or capacitor, connected to an AC voltage source. For a resistive circuit, the current and voltage are in phase. For an inductive circuit, the current lags the voltage by 90 degrees. For a capacitive circuit, the current leads the voltage by 90 degrees. The document defines important concepts such as reactance, impedance, and phasor diagrams for analyzing AC circuits.
This document provides an overview of equivalent circuits and circuit analysis techniques including node-voltage analysis, mesh analysis, and dealing with dependent and independent sources. It defines equivalent circuits as circuits that can replace one another without changing the external behavior of the overall circuit. It also describes node-voltage and mesh analysis, specifying how to write equations for each method by applying Kirchhoff's laws. Techniques for handling dependent sources and circuits with no path to ground are discussed. Examples demonstrate transforming between delta-wye configurations and using the different analysis methods to solve for voltages and currents.
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.
1. Alternating current is an electric current whose magnitude and direction periodically revers. It can be expressed by the equation I = I0 sinωt, where I0 is the peak value and ω is the angular frequency.
2. When alternating current flows through a pure resistor, the current is in phase with the applied voltage. There is no phase difference. However, when it flows through a pure inductor, the current lags the applied voltage by 90 degrees.
3. Root mean square (RMS) value is a useful parameter for alternating current and voltage. It is defined as the square root of mean of the squares of instantaneous values over one complete cycle. The RMS value of a sinusoidal current
1. Light interference occurs when two light waves overlap and their amplitudes combine according to the principle of superposition.
2. Constructive interference occurs when the light waves are in phase, resulting in enhanced intensity. Destructive interference occurs when light waves are out of phase, cancelling each other out.
3. Interference patterns from thin films can be observed by overlapping the light waves that are reflected or transmitted through the film. The optical path difference between the waves determines whether constructive or destructive interference occurs.
- The document discusses first-order RC and RL circuits.
- Key aspects include: RC and RL circuits can be modeled with first-order differential equations; the natural response of source-free circuits decays exponentially with a time constant τ equal to RC or L/R.
- The energy initially stored in the capacitor or inductor is dissipated in the resistor over time according to an exponential function with the same time constant.
This document discusses alternating current and root mean square (RMS) values. It defines RMS as taking the square of a waveform, calculating the mean, and taking the square root. For a sinusoidal waveform, the RMS value is equal to the peak value divided by the square root of two. It also discusses how current and voltage are related for resistors, inductors, and capacitors in an AC circuit. Current lags voltage by 90 degrees for an inductor, and leads voltage by 90 degrees for a capacitor. The document provides examples of calculating peak current and voltage values given information about resistance, inductance, capacitance, and frequency in an RLC circuit. It notes that power is equal to RMS voltage times RMS current times
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 contains a collection of multiple choice questions related to earthquake engineering and vibration analysis. Some key topics covered include:
1. Types of vibrations such as free vibration, forced vibration, and damped vibration.
2. Parameters used to describe vibrations like logarithmic decrement, damping factor, and natural frequency.
3. Analysis of single degree of freedom vibrating systems including equations of motion.
4. Concepts like critical damping, resonance, and stiffness calculations for different structural configurations like springs in series and parallel.
- 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 discusses translational and rotational mechanical systems. It begins by defining variables for translational systems like displacement, velocity, acceleration, force, work, and power. It then discusses element laws for translational systems including viscous friction and stiffness elements. The document also introduces rotational systems and defines variables like angular displacement, velocity, acceleration, and torque. It discusses element laws for rotational systems including moment of inertia, viscous friction, and rotational stiffness. Finally, it covers interconnection laws for both translational and rotational systems and provides an example of obtaining the system model for a rotational system.
Real-time plasma impedance matching using an impedance mapping strategyImpedans Ltd
Mike Hopkins gave a talk on real-time plasma impedance matching using impedance mapping. Typically, impedance matching networks use tune and load capacitors to match the plasma impedance, but the network range may not include the plasma impedance. Impedance mapping measures the impedance looking into the matching network for different tune and load settings to map out the available range. The matching network is then set to provide a complex conjugate match to the measured plasma impedance in real-time. Impedance mapping provides fast, accurate matching without a search algorithm. Models show it can match with over 90% efficiency even with 1% error in impedance measurement.
1) The document discusses growth of current in an R-L series circuit and growth of charge in an R-C series circuit.
2) It explains that in an R-L series circuit, the current does not reach its maximum value instantly due to the inductor's property of opposing changes in current. It defines the inductive time constant as the time required for the current to reach 63% of its maximum value.
3) Similarly, in an R-C series circuit, the charge on the capacitor increases gradually and not instantly. It defines the capacitive time constant as the time required for the charge to increase to 63% of its maximum value.
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.
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.
This document contains the solutions to 4 problems presented as part of an Electrical Engineering course. It includes circuit diagrams and calculations to verify theorems related to Norton's theorem, maximum power transfer theorem, phase difference between voltage and current in an AC circuit with an inductor, and calculating the active power consumption of a home based on its electrical layout and appliances. Calculations are shown in detail and also validated using circuit simulation software.
This document contains the solutions to 4 problems presented as part of an Electrical Engineering course. It includes circuit diagrams and calculations to verify theorems related to Norton's theorem, maximum power transfer theorem, phase difference between voltage and current in an AC circuit with an inductor, and calculating the active power consumption of a home based on its electrical layout and appliances. Calculations are shown in detail and also validated using circuit simulation software.
This document introduces a presentation on the superposition theorem and Norton's theorem given by six students: Mahmudul Hassan, Mahmudul Alam, Sabbir Ahmed, Asikur Rahman, Omma Habiba, and Israt Jahan. The superposition theorem allows analysts to determine voltages and currents in circuits with multiple sources by considering each source independently and then summing their effects. Norton's theorem represents a linear two-terminal circuit as an equivalent circuit with a current source in parallel with a resistor. The document provides examples of applying both theorems to solve circuit problems.
This document discusses several network theorems for circuit analysis:
- Superposition theorem allows analysis of circuits with multiple sources by solving for each source individually and summing the results.
- Thevenin's and Norton's theorems allow complex circuits to be reduced to equivalent circuits with a single voltage/current source and resistance to simplify analysis.
- Maximum power transfer occurs when the load resistance equals the Thevenin equivalent resistance of the source circuit.
- Delta-Wye and Wye-Delta transformations allow easy conversion between equivalent star and delta circuit configurations.
This document discusses RC circuits and their exponential response over time. It defines the time constant τ as the time it takes for the dependent variable (current or voltage) to decrease to 37% of its initial value. For an RC circuit, the voltage v(t) decreases exponentially over time according to the equation v(t)=V0e-t/RC. The document provides examples of calculating v(t) at different times for given RC circuits, as well as a homework problem involving finding v(t) values.
This document provides an overview of alternating current (AC) circuits. It begins by introducing AC voltage sources and defining key concepts like frequency, period, and angular frequency. It then analyzes simple circuits with a single circuit element - resistor, inductor, or capacitor - connected to an AC source. The behavior of current and voltage in each case is examined. Finally, the document considers the driven RLC series circuit, deriving the differential equation that governs it. Key circuit concepts like impedance and resonance are also introduced.
This document describes an experiment to study the discharge process of an RC circuit. The objectives are to measure the current and charge of a capacitor during discharge and determine the time constant of the RC circuit. The experiment involves charging a capacitor using a power supply, then discharging it through a resistor while measuring the voltage over time. Data is plotted and the slope is used to calculate the experimental time constant, which is compared to the theoretical value calculated from the circuit components.
This document section describes alternating current (AC) circuits containing a single circuit element: resistor, inductor, or capacitor, connected to an AC voltage source. For a resistive circuit, the current and voltage are in phase. For an inductive circuit, the current lags the voltage by 90 degrees. For a capacitive circuit, the current leads the voltage by 90 degrees. The document defines important concepts such as reactance, impedance, and phasor diagrams for analyzing AC circuits.
This document provides an overview of equivalent circuits and circuit analysis techniques including node-voltage analysis, mesh analysis, and dealing with dependent and independent sources. It defines equivalent circuits as circuits that can replace one another without changing the external behavior of the overall circuit. It also describes node-voltage and mesh analysis, specifying how to write equations for each method by applying Kirchhoff's laws. Techniques for handling dependent sources and circuits with no path to ground are discussed. Examples demonstrate transforming between delta-wye configurations and using the different analysis methods to solve for voltages and currents.
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.
1. Alternating current is an electric current whose magnitude and direction periodically revers. It can be expressed by the equation I = I0 sinωt, where I0 is the peak value and ω is the angular frequency.
2. When alternating current flows through a pure resistor, the current is in phase with the applied voltage. There is no phase difference. However, when it flows through a pure inductor, the current lags the applied voltage by 90 degrees.
3. Root mean square (RMS) value is a useful parameter for alternating current and voltage. It is defined as the square root of mean of the squares of instantaneous values over one complete cycle. The RMS value of a sinusoidal current
1. Light interference occurs when two light waves overlap and their amplitudes combine according to the principle of superposition.
2. Constructive interference occurs when the light waves are in phase, resulting in enhanced intensity. Destructive interference occurs when light waves are out of phase, cancelling each other out.
3. Interference patterns from thin films can be observed by overlapping the light waves that are reflected or transmitted through the film. The optical path difference between the waves determines whether constructive or destructive interference occurs.
- The document discusses first-order RC and RL circuits.
- Key aspects include: RC and RL circuits can be modeled with first-order differential equations; the natural response of source-free circuits decays exponentially with a time constant τ equal to RC or L/R.
- The energy initially stored in the capacitor or inductor is dissipated in the resistor over time according to an exponential function with the same time constant.
This document discusses alternating current and root mean square (RMS) values. It defines RMS as taking the square of a waveform, calculating the mean, and taking the square root. For a sinusoidal waveform, the RMS value is equal to the peak value divided by the square root of two. It also discusses how current and voltage are related for resistors, inductors, and capacitors in an AC circuit. Current lags voltage by 90 degrees for an inductor, and leads voltage by 90 degrees for a capacitor. The document provides examples of calculating peak current and voltage values given information about resistance, inductance, capacitance, and frequency in an RLC circuit. It notes that power is equal to RMS voltage times RMS current times
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 contains a collection of multiple choice questions related to earthquake engineering and vibration analysis. Some key topics covered include:
1. Types of vibrations such as free vibration, forced vibration, and damped vibration.
2. Parameters used to describe vibrations like logarithmic decrement, damping factor, and natural frequency.
3. Analysis of single degree of freedom vibrating systems including equations of motion.
4. Concepts like critical damping, resonance, and stiffness calculations for different structural configurations like springs in series and parallel.
- 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 discusses translational and rotational mechanical systems. It begins by defining variables for translational systems like displacement, velocity, acceleration, force, work, and power. It then discusses element laws for translational systems including viscous friction and stiffness elements. The document also introduces rotational systems and defines variables like angular displacement, velocity, acceleration, and torque. It discusses element laws for rotational systems including moment of inertia, viscous friction, and rotational stiffness. Finally, it covers interconnection laws for both translational and rotational systems and provides an example of obtaining the system model for a rotational system.
Real-time plasma impedance matching using an impedance mapping strategyImpedans Ltd
Mike Hopkins gave a talk on real-time plasma impedance matching using impedance mapping. Typically, impedance matching networks use tune and load capacitors to match the plasma impedance, but the network range may not include the plasma impedance. Impedance mapping measures the impedance looking into the matching network for different tune and load settings to map out the available range. The matching network is then set to provide a complex conjugate match to the measured plasma impedance in real-time. Impedance mapping provides fast, accurate matching without a search algorithm. Models show it can match with over 90% efficiency even with 1% error in impedance measurement.
1) The document discusses growth of current in an R-L series circuit and growth of charge in an R-C series circuit.
2) It explains that in an R-L series circuit, the current does not reach its maximum value instantly due to the inductor's property of opposing changes in current. It defines the inductive time constant as the time required for the current to reach 63% of its maximum value.
3) Similarly, in an R-C series circuit, the charge on the capacitor increases gradually and not instantly. It defines the capacitive time constant as the time required for the charge to increase to 63% of its maximum value.
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.
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.
This document contains the solutions to 4 problems presented as part of an Electrical Engineering course. It includes circuit diagrams and calculations to verify theorems related to Norton's theorem, maximum power transfer theorem, phase difference between voltage and current in an AC circuit with an inductor, and calculating the active power consumption of a home based on its electrical layout and appliances. Calculations are shown in detail and also validated using circuit simulation software.
This document contains the solutions to 4 problems presented as part of an Electrical Engineering course. It includes circuit diagrams and calculations to verify theorems related to Norton's theorem, maximum power transfer theorem, phase difference between voltage and current in an AC circuit with an inductor, and calculating the active power consumption of a home based on its electrical layout and appliances. Calculations are shown in detail and also validated using circuit simulation software.
This document introduces a presentation on the superposition theorem and Norton's theorem given by six students: Mahmudul Hassan, Mahmudul Alam, Sabbir Ahmed, Asikur Rahman, Omma Habiba, and Israt Jahan. The superposition theorem allows analysts to determine voltages and currents in circuits with multiple sources by considering each source independently and then summing their effects. Norton's theorem represents a linear two-terminal circuit as an equivalent circuit with a current source in parallel with a resistor. The document provides examples of applying both theorems to solve circuit problems.
This document discusses several network theorems for circuit analysis:
- Superposition theorem allows analysis of circuits with multiple sources by solving for each source individually and summing the results.
- Thevenin's and Norton's theorems allow complex circuits to be reduced to equivalent circuits with a single voltage/current source and resistance to simplify analysis.
- Maximum power transfer occurs when the load resistance equals the Thevenin equivalent resistance of the source circuit.
- Delta-Wye and Wye-Delta transformations allow easy conversion between equivalent star and delta circuit configurations.
The document discusses several network theorems including superposition, Thevenin's, and Norton's theorems. Superposition theorem states that the total response of a network with multiple sources is the sum of the responses of each source acting alone. Thevenin's theorem shows that any linear network can be reduced to an equivalent circuit with a voltage source and single output resistance. Norton's theorem represents a network as a current source and parallel output resistance. Both theorems simplify analysis of complex networks. Maximum power transfer occurs when the load and source resistances are equal.
ELECTRICAL POWER SYSTEM - II. symmetrical three phase faults. PREPARED BY : J...Jobin Abraham
This document discusses symmetrical three-phase faults in electrical power systems. It defines a symmetrical fault as one where equal fault currents are produced in each line with 120 degree phase displacement. This is the most severe type of fault. The document covers transient currents on transmission lines during a fault, selection of circuit breakers based on maximum fault currents, fault currents and induced emfs for synchronous machines under no-load and loaded conditions, and provides an algorithm for short circuit studies.
Thevenin norton and max power theorem by ahsanul hoqueAhsanul Talha
The document discusses Thevenin's theorem, Norton's theorem, and the maximum power transfer theorem. It provides:
1) Definitions and steps to derive the Thevenin and Norton equivalent circuits for a given linear two-terminal circuit by calculating the open-circuit voltage, short-circuit current, and input resistances.
2) Examples showing how to use source transformations to simplify circuits using these theorems.
3) An explanation of the maximum power transfer theorem - that maximum power is delivered to a load when its resistance equals the Thevenin resistance of the circuit.
Thevenin's theorem states that a linear circuit containing sources and elements can be represented by a voltage source and resistance. It allows a complex circuit to be reduced to a simple series circuit. The four steps are: 1) remove the load, 2) determine voltage seen by load (Vth), 3) replace voltage source with short, 4) determine resistance seen by load (Rth). Using these steps, any linear circuit can be converted into a Thevenin equivalent circuit with a single voltage source and resistance.
The document discusses several theorems for analyzing DC networks:
1. Superposition theorem states that the current or voltage across an element is equal to the algebraic sum of currents/voltages from each independent source.
2. Thevenin's theorem states that any linear bilateral network can be reduced to a single voltage source in series with an equivalent resistance.
3. Norton's theorem states that any linear bilateral network can be reduced to a current source in parallel with an equivalent resistance.
4. Maximum power transfer theorem states that maximum power is delivered to a load when its resistance equals the Thevenin resistance of the network.
This document discusses Thévenin's and Norton's theorems, which state that a linear two-terminal circuit can be reduced to an equivalent circuit with either a voltage source and resistor or current source and resistor. It provides definitions and steps for determining the equivalent components. Examples are given to demonstrate simplifying circuits using source transformations between the Thévenin and Norton models.
The document discusses Thevenin's theorem, which states that any linear electric network can be reduced to an equivalent circuit with a single voltage source (VTH) and resistor (RTH) in series. It provides steps to use the theorem: 1) open the load, 2) measure open circuit voltage (VTH), 3) short sources, 4) measure open circuit resistance (RTH). An example applies the steps to calculate VTH, RTH, load current and voltage for a given circuit. Applications include simplifying complex circuits and determining power delivered to variable loads.
1. The document discusses several important network theorems including Kirchhoff's laws, Thevenin's theorem, maximum power transfer theorem, superposition theorem, and the growth and decay of charge and current in RC and LR circuits respectively.
2. Kirchhoff's laws include Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). KCL states the sum of currents at a node is zero, and KVL states the algebraic sum of voltages in a closed loop is zero.
3. Thevenin's theorem states any linear network can be reduced to a single voltage source in series with a resistance, with the Thevenin voltage and resistance values defined.
02 Basic Electrical Electronics and Instrumentation Engineering.pdfBasavaRajeshwari2
The document provides information about electrical circuits and instrumentation engineering including:
1. Questions and answers related to basic electrical concepts like Ohm's law, Kirchhoff's laws, series and parallel circuits, network analysis methods.
2. Definitions of terms used in AC circuits like impedance, resonance, real power, reactive power, apparent power.
3. Relationships and calculations related to 3-phase systems including line and phase quantities.
4. Brief descriptions of different types of wiring used for houses and industrial applications. Materials commonly used for wiring are also mentioned.
This document introduces several important network theorems: Superposition, Thevenin's, Norton's, Maximum Power Transfer, Millman's, Substitution, and Reciprocity. It provides details on each theorem, including definitions, procedures for applying them, and examples of their uses in analyzing and simplifying electrical networks.
- The reciprocity theorem states that the current in one branch of a linear network due to a voltage source in another branch is equal to the current that would flow in the second branch if the voltage source was placed there instead.
- To verify the theorem, the problem calculates the current in one branch with the voltage source in the other branch, and then vice versa, showing the currents are equal.
- The transfer resistance between the two branches can also be determined using the reciprocity theorem.
The document discusses Thévenin's theorem and how to derive the Thévenin equivalent circuit for a given network. It states that any two-terminal DC network can be replaced by an equivalent circuit of a voltage source and series resistor. It then provides the steps to calculate the Thévenin voltage (ETh) and resistance (RTh) by opening and shorting terminals. Three examples are worked through applying these steps to find the Thévenin equivalent circuits for various networks.
This document introduces several important network theorems: superposition, Thevenin's, Norton's, maximum power transfer, Millman's, substitution, and reciprocity. It provides definitions and procedures for applying each theorem, such as replacing network elements with voltage/current sources and determining equivalent resistances and voltages. The theorems allow analyzing complex networks, determining outputs when components change, and maximizing power transfer between networks.
1. The document discusses direct current (DC) and alternating current (AC). DC flows in one direction while AC periodically reverses direction.
2. Simple AC circuits containing a resistor, capacitor, or inductor are examined. A resistor allows both DC and AC. A capacitor blocks DC but allows AC, while an inductor opposes rapid changes in current.
3. Impedance, phase factor, and resonance effects are also covered. Impedance represents the total opposition to current flow. Resonance occurs at the frequency where capacitive and inductive reactances cancel out, producing a maximum current.
The maximum power transfer theorem states that maximum power is transferred from a source to a load when their resistances are equal. It results in maximum power transfer, not maximum efficiency. The theorem can be extended to AC circuits using impedance.
Ohm's law describes the direct proportional relationship between current and voltage in a circuit, where resistance is the constant of proportionality. R=V/I.
A Zener diode allows current to flow in the reverse direction above a certain breakdown voltage, known as the Zener or knee voltage. It is used to generate reference voltages or stabilize voltages in low current applications.
This document provides an introduction to concepts related to chemical equations and oxidation-reduction reactions. It defines key terms like oxidation number, oxidizing and reducing agents, and describes methods for balancing chemical equations including the ion-electron method and changing oxidation numbers. It also discusses concepts in electrochemistry and provides examples of balancing equations using different methods.
Integrales definidas y método de integración por partescrysmari mujica
The document discusses integrals and defined integrals. It defines integrals as the area under a curve and describes how integrals and derivatives are related. It also discusses integration by parts, giving the formula and examples of its application. Finally, it defines a definite integral as the area between a function's graph, the x-axis, and the boundaries x=a and x=b.
Integrales definidas y ecuaciones diferencialescrysmari mujica
The document contains worked solutions to 4 integral calculus problems. In the first problem, the integral of (4x - 6x^2) from -1 to 2 is evaluated to be -12 using theorems about integrals of sums and constants. The second problem evaluates the integral of (x^1/3 + x^4/3) from 1 to 8 to be 1839/28. The third problem evaluates the integral of 3sin(x) from 0 to π to be 6. The fourth problem evaluates the integral of [cos(2x) + sin(2x)] from 0 to π/4 to be 1.
Este documento define y clasifica diferentes tipos de peligros y riesgos en el lugar de trabajo. Define un peligro como una fuente o situación con potencial para causar daño y clasifica peligros en latentes, potenciales, activos y mitigados. Identifica peligros biológicos, biomecánicos, de seguridad, físicos, químicos y psicosociales en el trabajo y sus posibles consecuencias. Explica que un riesgo es la probabilidad de que ocurran consecuencias derivadas de un peligro y que existen
This document provides information on electrical generators and motors. It describes their main components, classifications, and types. For generators, it discusses alternators, dynamos, and different types such as hydroelectric, thermoelectric, wind, solar, and nuclear generators. For motors, it covers AC motors including induction, linear, and synchronous motors, as well as DC motors including series, shunt, and compound motors. It also explains the functioning of synchronous and induction motors.
The document is a report from the Industrial Technology Administration Institute Extension in Puerto La Cruz, Venezuela. It contains definitions and concepts regarding the derivative of a function, including the definition, formula, and examples of finding derivatives. It also lists theorems for finding derivatives of algebraic, trigonometric, and exponential functions, and provides examples of using each theorem.
Authoring a personal GPT for your research and practice: How we created the Q...Leonel Morgado
Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
The technology uses reclaimed CO₂ as the dyeing medium in a closed loop process. When pressurized, CO₂ becomes supercritical (SC-CO₂). In this state CO₂ has a very high solvent power, allowing the dye to dissolve easily.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skills
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...AbdullaAlAsif1
The pygmy halfbeak Dermogenys colletei, is known for its viviparous nature, this presents an intriguing case of relatively low fecundity, raising questions about potential compensatory reproductive strategies employed by this species. Our study delves into the examination of fecundity and the Gonadosomatic Index (GSI) in the Pygmy Halfbeak, D. colletei (Meisner, 2001), an intriguing viviparous fish indigenous to Sarawak, Borneo. We hypothesize that the Pygmy halfbeak, D. colletei, may exhibit unique reproductive adaptations to offset its low fecundity, thus enhancing its survival and fitness. To address this, we conducted a comprehensive study utilizing 28 mature female specimens of D. colletei, carefully measuring fecundity and GSI to shed light on the reproductive adaptations of this species. Our findings reveal that D. colletei indeed exhibits low fecundity, with a mean of 16.76 ± 2.01, and a mean GSI of 12.83 ± 1.27, providing crucial insights into the reproductive mechanisms at play in this species. These results underscore the existence of unique reproductive strategies in D. colletei, enabling its adaptation and persistence in Borneo's diverse aquatic ecosystems, and call for further ecological research to elucidate these mechanisms. This study lends to a better understanding of viviparous fish in Borneo and contributes to the broader field of aquatic ecology, enhancing our knowledge of species adaptations to unique ecological challenges.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
1. República Bolivariana De Venezuela.
Instituto Universitario De Tecnología
De Administración Industrial.
Extensión Puerto La Cruz.
Integrantes: Tutor:
Crysmari Mujica C.I: v-26.422.252 Ana Simons
Puerto La Cruz, 22 de Julio de 2020.
INSTITUTO UNIVERSITARIO DE
TECNOLOGÍA DE
ADMINISTRACIÓN INDUSTRIAL
EXTENSIÓN PUERTO LA CRUZ
2. Teorema de Thévenin:
Léon Charles Thévenin (1857 - 1926) fue un ingeniero en telegrafía francés, que
extendió el análisis de la Ley de Ohm a los circuitos eléctricos complejos. Su
aporte más importante fue el teorema que lleva su nombre y establece que si una
parte de un circuito eléctrico lineal está comprendida entre dos terminales, esta
parte en cuestión puede sustituirse por un circuito equivalente que esté constituido
únicamente por un generador de tensión en serie con una resistencia, de forma
que al conectar un elemento entre los dos terminales, la tensión que queda en él y
la intensidad que circula son las mismas tanto en el circuito real como en el
equivalente.
Figura 1: Circuito equivalente de Thévenin. Figura 2: Voltaje de Circuito Abierto.
El valor de la fuente independiente de voltaje 𝑽𝑻𝒉 es igual al voltaje entre los
nodos 𝑨 y 𝑩 , cuando se desconecta la carga arbitraria. Este voltaje 𝑽𝑻𝒉 es
causado por las fuentes independientes y las condiciones iniciales.
Para calcular la tensión de Thévenin (𝑽𝑻𝒉), se desconecta la carga (es decir, la
resistencia de la carga) y se calcula 𝑽𝑨𝑩. Al desconectar la carga, la intensidad
que atraviesa 𝑹𝑻𝒉 en el circuito equivalente es nula y por tanto la tensión de 𝑹𝑻𝒉
también es nula, por lo que ahora 𝑽𝑨𝑩 = 𝑽𝑻𝒉 por la segunda ley de Kirchhoff.
Para calcular la resistencia de Thévenin, se desconecta la resistencia de carga, se
cortocircuitan las fuentes de tensión y se abren las fuentes de corriente. Se calcula
la resistencia que se ve desde los terminales 𝑨 y 𝑩, y esa resistencia 𝑹𝑨𝑩 es la
resistencia de Thevenin buscada 𝑹𝑻𝒉 = 𝑹𝑨𝑩.
3. Teorema de Norton:
Edward Lawry Norton (18981 - 1983) fue un ingeniero y científico empleado de los
Laboratorios Bell. Es conocido principalmente por enunciar el Teorema de Norton,
que lleva su nombre y establece que cualquier circuito lineal se puede sustituir por
una fuente equivalente de corriente en paralelo con una impedancia equivalente.
El circuito equivalente de Norton consiste de una fuente independiente de
corriente 𝑰𝑵𝒐 en paralelo con una red eléctrica que se obtiene de la red original al
cancelar todas las fuentes independientes de corriente y de voltaje y con las
condiciones iniciales nulas ( 𝜼𝟎). Las fuentes dependientes no se modifican.
Figura 3: Circuito equivalente de Norton. Figura 4: Corriente de Corto Circuito.
El valor de la fuente independiente de corriente 𝑰𝑵𝒐 es igual a la corriente eléctrica
que circula entre los nodos 𝑨 y 𝑩, cuando se cortocircuita la carga arbitraria. Esta
corriente 𝑰𝑵𝒐 es causado por las fuentes independientes y las condiciones iniciales.
Es importante saber que sobre la carga arbitraria no se ha hecho ninguna
suposición, a excepción de que no hay ningún tipo de acoplamiento entre ella y la
red eléctrica lineal. Esto último implica que la carga arbitraria puede ser lineal o no
lineal, variante o invariante en el tiempo.
Para calcular la corriente de salida (𝑰𝑨𝑩), cuando se cortocircuita la salida, es decir,
cuando se pone una carga (tensión) nula entre 𝑨 y 𝑩. Al colocar un cortocircuito
entre 𝑨 y 𝑩 toda la intensidad 𝑰𝑵𝒐 circula por la rama 𝑨𝑩, por lo que ahora
𝑰𝑨𝑩 = 𝑰𝑵𝒐.
Para calcula la tensión de salida (𝑽𝑨𝑩 ), cuando no se conecta ninguna carga
externa, es decir, cuando se pone una resistencia infinita entre 𝑨 y 𝑩. La 𝑹𝑵𝒐 es
ahora igual a 𝑽𝑨𝑩 dividido entre 𝑰𝑵𝒐 porque toda la intensidad 𝑰𝑵𝒐 ahora circula a
través de 𝑹𝑵𝒐 y las tensiones de ambas ramas tienen que coincidir ( 𝑽𝑨𝑩 =
𝑰𝑵𝒐𝑹𝑵𝒐 ).
4. Equivalencia entre un circuito Thévenin y un circuito Norton:
Para analizar la equivalencia entre un circuito Thévenin y un circuito Norton se
pueden utilizar las siguientes ecuaciones:
𝑹𝑻𝒉 = 𝑹𝑵𝒐
𝑽𝑻𝒉 = 𝑰𝑵𝒐𝑹𝑵𝒐
Figura 5: equivalencia entre un circuito Thévenin y un circuito Norton
Teorema de Superposición:
El teorema de superposición establece que el efecto que dos o más fuentes tienen
sobre una impedancia es igual, a la suma de cada uno de los efectos de cada
fuente tomados por separado, sustituyendo todas las fuentes de tensión restantes
por un corto circuito, y todas las fuentes de corriente restantes por un circuito
abierto. Este teorema sólo se puede utilizar en el caso de circuitos eléctricos
lineales, es decir circuitos formados únicamente por componentes lineales (en los
cuales la corriente que los atraviesa es proporcional a la diferencia de tensión
entre sus terminales).
El teorema de superposición puede utilizarse para calcular circuitos haciendo
cálculos parciales, pero eso no presenta ningún interés práctico porque la
aplicación del teorema alarga los cálculos en lugar de simplificarlos. Otros
métodos de cálculo son mucho más útiles, en especial a la hora de tratar con
circuitos que poseen muchas fuentes y muchos elementos. El verdadero interés
del teorema de superposición es teórico, ya que este justifica métodos de trabajo
con circuitos que simplifican verdaderamente los cálculos. Por ejemplo, justifica
que se hagan separadamente los cálculos de corriente continua y los cálculos de
señales (corriente alterna) en circuitos con Componentes activos (transistores,
amplificadores operacionales, etc.).
5. Teorema de Máxima Transferencia de Potencia:
El teorema de máxima transferencia de potencia establece que, dada una fuente,
con una resistencia de fuente fijada de antemano, la resistencia de carga que
maximiza la transferencia de potencia es aquella con un valor óhmico igual a la
resistencia de fuente. Este ayuda a encontrar también los teoremas de Thévenin y
Norton.
Cuando una fuente o un circuito se conectan a una carga cualquiera es deseable
que tal fuente o circuito pueda transmitir la mayor cantidad de potencia a la carga
que la recibe. La Figura 6 muestra un equivalente de Thévenin de un circuito
cualquiera (a la izquierda de 𝑨𝑩) conectado a una carga cualquiera. Al conectar
esta carga aparece un voltaje 𝑽𝑪 y una corriente 𝑰𝑪 entre los nodos 𝑨 y 𝑩. Para
determinar las condiciones en las cuales se presenta máxima transferencia de
potencia de un circuito a otro vamos a considerar dos casos: el primero en el cual
solo hay una carga resistiva, y el segundo en el cual la carga puede tener
elementos pasivos y activos.
Figura 6: Equivalente de Thévenin de un circuito conectado a una carga.
6. Ejercicios:
Primer ejercicio: Teorema de Thévenin:
Calcular el equivalente Thevenin del circuito de la figura dónde:
𝑹𝟏 = 𝟕𝛀, 𝑹𝟐 = 𝟏𝟓𝛀, 𝑹𝟑 = 𝟒𝛀, 𝑽 = 𝟑𝟎 𝒗, 𝑰 = 𝟑 𝑨
El circuito equivalente debe de tener la forma:
Calcularemos la resistencia Thevenin. Para esto, ponemos a cero las fuentes
independientes y calculamos la resistencia de entrada:
𝑹𝒊𝒏 =
𝑹𝟏𝑹𝟐
𝑹𝟏 + 𝑹𝟐
+ 𝑹𝟑
𝑹𝒊𝒏 =
(𝟕𝛀)(𝟏𝟓𝛀)
(𝟕 + 𝟏𝟓)𝛀
+ 𝟒𝛀
Por tanto:
𝑹𝒊𝒏 = 𝟖, 𝟕𝟕𝛀
7. Calcularemos la tensión Thevenin, para esto calculamos la tensión de circuito
abierto en los terminales 𝑨𝑩:
Resolveremos usando el análisis de nodos:
Aplicando la Ley de Corriente de
Kirchhoff:
𝑰𝟏 + 𝑰𝟑 = 𝑰𝟐
Aplicando la Ley de Ohm:
𝑽 − 𝑽𝑻𝒉
𝑹𝟏
+ 𝑰 =
𝑽𝑻𝒉
𝑹𝟐
Despejando 𝑽𝑻𝒉, tenemos:
𝑽𝑻𝒉 =
𝑹𝟐[𝑽 + 𝑰𝑹𝟏]
𝑹𝟏 + 𝑹𝟐
=
𝟏𝟓𝛀[𝟑𝟎 𝒗 + (𝟑 𝑨)(𝟕𝛀)]
(𝟕 + 𝟏𝟓)𝛀
Por lo tanto:
𝑽𝑻𝒉 = 𝟑𝟒, 𝟕𝟖 𝒗
El circuito equivalente de Thévenin tendría la siguiente forma:
8. Segundo ejercicio: Teorema de Norton:
Calcular el equivalente Norton del
circuito de la figura:
𝑰𝒔 = 𝟒𝑨, 𝑽𝒔 = 𝟖𝒗, 𝑹𝟏 = 𝟗𝛀,
𝑹𝟐 = 𝑹𝟒 = 𝟑𝛀, 𝑹𝟑 = 𝟕𝛀
Calcularemos la Resistencia de Norton, para esto ponemos a cero las fuentes
independientes:
𝑹𝑵 =
𝑹𝟑(𝑹𝟏 + 𝑹𝟐 + 𝑹𝟒)
𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑 + 𝑹𝟒
𝑹𝑵 =
(𝟕𝛀)(𝟗 + 𝟑 + 𝟑)𝛀
(𝟗 + 𝟑 + 𝟕 + 𝟑)𝛀
Por lo tanto:
𝑹𝑵 = 𝟒, 𝟕𝟕 𝛀
Calcularemos la fuente de corriente de Norton, para esto calculamos primero la
corriente de cortocircuito:
Para la malla 1:
𝑰𝟏 = 𝑰𝑺
Aplicando la Ley de Voltaje de Kirchhoff en la malla 2:
−𝑽𝑺 − 𝑽𝟏 + 𝑽𝟐 + 𝑽𝟒 = 𝟎
10. Tercer ejercicio: Teorema de Superposición:
Calcular 𝑽 en el circuito en el
siguiente circuito aplicando el
principio de superposición.
𝑹𝒂 = 𝟏𝟐 𝛀 , 𝑹𝒃 = 𝟕 𝛀 , 𝑽𝒔 = 𝟏𝟎 𝒗 ,
𝑰 𝒔 = 𝟒 𝑨
Como hay dos fuentes:
𝑽 = 𝑽𝟏 + 𝑽𝟐
Dónde:
𝑽𝟏 es la tensión debida a 𝑽𝑺 con 𝑰𝒔 = 𝟎
Y 𝑽𝟐 es la tensión debida a 𝑰𝑺 con 𝑽𝑺 = 𝟎
Para calcular 𝑽𝟏, dejamos 𝑰𝑺 en circuito abierto:
Aplicando la Ley de Voltaje de
Kirchhoff:
𝑽𝑺 = 𝑹𝒂𝑰 + 𝑹𝒃𝑰
Despejando la intensidad de corriente
𝑰, tenemos:
𝑰 =
𝑹𝒂 + 𝑹𝒃
𝑽𝑺
Le damos valores:
𝑰 =
𝟏𝟐 𝛀 + 𝟕 𝛀
𝟏𝟎𝒗
= 𝟏, 𝟗 𝑨
Obtenida la intensidad de corriente, podemos calcular el valor de 𝑽𝟏:
𝑽𝟏 = 𝑹𝒃𝑰 = (𝟕 𝛀)(𝟏, 𝟗 𝑨)
Por tanto:
𝑽𝟏 = 𝟏𝟑, 𝟑 𝒗
11. Ahora calcularemos 𝑽𝟐, para esto cortocircuitamos 𝑽𝒔:
Aplicando la Ley de Corriente de
Kirchhoff:
𝑰𝑺 =
𝑽𝟐
𝑹𝒂
+
𝑽𝟐
𝑹𝒃
Despejando 𝑽𝟐, tenemos:
𝑽𝟐 =
𝑹𝒂𝑹𝒃
𝑹𝒂 + 𝑹𝒃
𝑰𝒔 =
(𝟏𝟐𝛀)(𝟕𝛀)
(𝟏𝟐 + 𝟕)𝛀
(𝟒𝑨)
Por tanto:
𝑽𝟐 = 𝟏𝟕, 𝟕 𝒗
Para concluir, debemos obtener el voltaje total del circuito:
𝑽 = 𝑽𝟏 + 𝑽𝟐
𝑽 = (𝟏𝟑, 𝟑 + 𝟏𝟕, 𝟕) 𝒗
Por lo tanto, el voltaje total del circuito es:
𝑽 = 𝟑𝟏 𝒗
12. Cuarto ejercicio: Teorema de la Máxima Potencia:
Determinar el valor de 𝑅𝐿 para que la transferencia de potencia en el circuito de la
figura sea máxima. Calcular la potencia máxima.
𝑹𝟏 = 𝟓𝛀, 𝑹𝟐 = 𝟕𝛀, 𝑹𝟑 = 𝟔𝛀, 𝑹𝟒 = 𝟑𝛀, 𝑰 = 𝟑𝑨, 𝑽 = 𝟏𝟎 𝒗:
Comenzaremos determinando el equivalente Thévenin del circuito fuente:
Calculamos la resistencia de Thévenin:
𝑹𝑻𝒉 =
𝑹𝟏𝑹𝟐
𝑹𝟏 + 𝑹𝟐
+ 𝑹𝟑 + 𝑹𝟒
𝑹𝑻𝒉 =
(𝟓𝛀)(𝟕𝛀)
(𝟓 + 𝟕)𝛀
+ (𝟔 + 𝟑)𝛀
Por lo tanto:
𝑹𝑻𝒉 = 𝟏𝟏, 𝟗𝟐𝛀
Calculamos la tensión de Thévenin:
En la malla 1, tenemos:
−𝑽 + 𝑹𝟏𝑰𝟏 + 𝑹𝟐(𝑰𝟏 + 𝑰) = 𝟎
Despejando 𝑰𝟏, tenemos:
𝑰𝟏 =
𝑽 − 𝑹𝟐𝑰
𝑹𝟏 + 𝑹𝟐
=
𝟏𝟎𝒗 − (𝟕𝛀)(𝟑𝑨)
(𝟓 + 𝟕)𝛀
𝑰𝟏 = −𝟎, 𝟗𝟐𝑨
En la malla 2, tenemos:
𝑰𝟐 = −𝑰 = −𝟑𝑨
13. Con esto ya podemos calcular la tensión:
𝑽𝑻𝒉 − 𝑽 + 𝑹𝟏𝑰𝟏 + 𝑹𝟑𝑰𝟐 = 𝟎
Despejando 𝑽𝑻𝒉, tenemos:
𝑽𝑻𝒉 = 𝑽 − 𝑹𝟏𝑰𝟏 − 𝑹𝟑𝑰𝟐
𝑽𝑻𝒉 = 𝟏𝟎𝒗 − (𝟓𝛀)(−𝟎, 𝟗𝟐𝑨) − (𝟔𝛀)(−𝟑𝑨)
𝑽𝑻𝒉 = 𝟑𝟐, 𝟔𝟎 𝒗
Por lo tanto el circuito equivalente de Thévenin en este caso es:
Ahora que conocemos esto, podemos calcular la potencia máxima:
𝑷𝒎á𝒙 =
𝑽𝑻𝒉
𝟐
𝟒𝑹𝑳
=
(𝟑𝟐, 𝟔𝟎 𝒗)𝟐
𝟒(𝟏𝟏, 𝟗𝟐𝛀)
Por lo tanto, la potencia máxima es:
𝑷𝒎á𝒙 = 𝟐𝟐, 𝟐𝟗 𝑾
14. Bibliografía:
Título: Léon Charles Thévenin. Sitio: Wikipedia. Fecha: 19/03/2020.
URL:https://es.wikipedia.org/wiki/L%C3%A9on_Charles_Th%C3%A9venin#:~:text=L%C3%A9on%
20Charles%20Th%C3%A9venin%20(Meaux%2C%2030,teorema%20que%20lleva%20su%20nombre.
Título: Teorema de Thévenin. Sitio: Wikipedia. Fecha: 20/09/2019.
URL: https://es.wikipedia.org/wiki/Teorema_de_Th%C3%A9venin
Título: Teoremas de redes eléctricas. Autor: V. Sánchez y A. Salvá.
URL: http://dctrl.fi-b.unam.mx/academias/aca_ace/txt/T_08.pdf
Título: Edward Lawry Norto. Sitio: Wikipedia. Fecha: 18/10/2019.
URL:https://es.wikipedia.org/wiki/Edward_Lawry_Norton#:~:text=Edward%20Lawry%20Norton
%20(Rockland%2C%20Maine,Marina%20entre%201917%20y%201919.
Título: Teorema de Norton. Sitio: Wikipedia. Fecha: 06/07/2020.
URL: https://es.wikipedia.org/wiki/Teorema_de_Norton
Título: Teorema de Superposición. Sitio: Wikipedia. Fecha: 19/03/2020.
URL:https://es.wikipedia.org/wiki/Teorema_de_superposici%C3%B3n#:~:text=Este%20teorema
%20establece%20que%20el,restantes%20por%20un%20circuito%20abierto.
Título: Thévenin, Norton Y Máxima Transferencia de Potencia. Autor: Antonio
Salazar. URL:http://wwwprof.uniandes.edu.co/~ant-
sala/cursos/FDC/Contenidos/06_Thevenin_Norton_Maxima_Transferencia_de_Potencia.pdf
Título: Teorema de máxima potencia. Sitio: Wikipedia. Fecha: 26/11/2019.
URL: https://es.wikipedia.org/wiki/Teorema_de_Norton
Título: Teoremas de las Teorías de Circuitos. Autor: José A. Pereda.
URL: https://personales.unican.es/peredaj/pdf_Apuntes_AC/Presentacion-Teoremas.pdf
Título: Fundamentos de circuitos eléctricos. Autor: C. K. Alexander, M. N. O.
Sadiku. Editorial: McGraw-Hill. 3ra Edición. Año: 2006.