ejemplo superposición c a

roxana garcia

13 Dec 202010:12

Summary

TLDRThe video script discusses the method of superposition in electrical circuits, focusing on calculating the voltage across a specific point labeled 'v2'. It explains the process of analyzing the circuit with a single source at a time, calculating the current through various impedances using Ohm's law and the current divider rule. The script involves converting impedances to polar form, applying the method to alternating current, and obtaining the resultant voltage by superposing the effects of different sources. The explanation includes mathematical calculations and the use of complex numbers to find the final voltage in rectangular form.

Takeaways

🔌 The method of superposition is used to solve for voltages and currents in a circuit with multiple sources.
🔍 The script focuses on finding the voltage V2 at specific points in a circuit with complex impedances.
🔧 The first step involves analyzing the circuit with respect to the first voltage source, treating it as an open circuit for the other sources.
📡 The script describes a scenario with a current source and impedances in parallel, requiring the use of current division theorems.
🔢 The current I2 is calculated using the total current from the source and the impedances involved, applying Ohm's law for AC circuits.
📚 Impedance values are converted to polar form for calculation, which includes magnitude and phase angle.
🔗 The voltage V2 across an impedance is found by multiplying the current through that impedance by its impedance value.
🔄 The process is repeated for a second source, considering the circuit with respect to this new source and calculating the resultant voltage.
📉 The equivalent impedance of the circuit is recalculated when considering different sources, which affects the current and voltage calculations.
📌 The final voltage V2 is obtained by superposing the voltages calculated with respect to each individual source.
📝 The script emphasizes the importance of checking calculations, especially when converting between rectangular and polar forms of complex numbers.

Q & A

What is the method being discussed in the script?
-The method being discussed is the method of superposition.
What is the first step in applying the method of superposition according to the script?
-The first step is to work with one source at a time, starting with the first source.
What is the main objective of the exercise in the script?
-The main objective is to find the voltage V2 at certain points in the circuit.
What is the significance of the term 'circuito abierto' in the script?
-'Circuito abierto' refers to an open circuit, which is a condition where the circuit is broken and no current flows.
What does the script mention about the impedance in the circuit?
-The script discusses the impedance in the circuit, including the calculation of impedance in parallel and the use of impedance in the method of superposition.
How is the current I2 calculated in the script?
-I2 is calculated using the current divider rule, which involves dividing the total current by the sum of the impedances.
What is the significance of converting impedance to polar form in the script?
-Converting impedance to polar form helps in performing complex arithmetic and finding the magnitude and phase angle of the impedance.
What is the role of the current source in the second part of the exercise?
-In the second part of the exercise, the current source is used to find the voltage V2 across the impedance when the direction of the current source is downward.
How is the voltage V2 related to the current I2 in the script?
-V2 is calculated as the product of I2 and the impedance Zc, according to Ohm's law.
What is the final step described in the script for finding the voltage V2?
-The final step is to sum the voltages obtained from both sources, considering their rectangular forms, to get the total voltage V2.

Outlines

00:00

🔌 Introduction to Superposition Method

The script begins with an introduction to the superposition method, a technique used to solve electrical circuits. The speaker explains that the method involves analyzing the circuit with one source at a time. The focus is on finding the voltage 'v2' across certain points in the circuit. The speaker then describes the setup of the circuit with a current source and impedances in parallel, outlining the steps to calculate the current 'i2' using the current divider rule. The current is then used to find the voltage 'v2' across the impedance 'c' by multiplying the current by the impedance in polar form, resulting in a complex number representing the voltage magnitude and phase angle.

05:00

🔍 Calculating Voltage 'v2' with Different Sources

In this paragraph, the speaker continues the exercise by considering a different source configuration. The circuit now includes a current source with a negative imaginary component, indicating a phase shift. The speaker calculates the equivalent impedance for the circuit and uses it to find the voltage 'v2' across the same points as before. The calculation involves converting the impedance and current source into polar form, multiplying them to get the voltage in polar form, and then converting it back to rectangular form. The speaker emphasizes the importance of checking the calculations and provides the resulting voltage 'v2' in both polar and rectangular forms.

10:01

📚 Conclusion of the Electrical Circuit Exercise

The final paragraph wraps up the exercise with a summary of the results obtained. The speaker combines the voltage values calculated for 'v2' from the different source configurations, emphasizing the process of adding complex numbers in rectangular form. The conclusion highlights the final result for 'v2' and expresses hope that the exercise was of interest to the audience. The speaker thanks the viewers for their attention and concludes the video script.

Mindmap

Keywords

💡Superposition Method

The superposition method is a fundamental principle in electrical engineering used to analyze linear circuits. It involves breaking down a complex circuit into simpler ones by considering each independent source separately and then combining the results. In the video's context, the superposition method is used to find the voltage across a specific point, with the speaker initially focusing on one source at a time and then moving on to the next.

💡Voltage (V2)

Voltage, denoted as V2 in the script, is the electric potential difference between two points in a circuit. It is a key parameter in understanding the behavior of the circuit. In the video, the speaker is trying to calculate the voltage across a certain point, which is a central goal of the exercise and is used to demonstrate the application of the superposition method.

💡Impedance

Impedance is a measure of the opposition that a circuit presents to the flow of alternating current (AC). It is a complex quantity that may include resistance, inductive reactance, and capacitive reactance. In the script, the speaker discusses calculating the impedance in parallel and series configurations, which is crucial for determining the current and voltage in AC circuits.

💡Current Divider

The current divider is a principle used in circuit analysis to determine the distribution of current through parallel paths. It states that the current through a branch is inversely proportional to its impedance. In the video, the speaker uses the current divider rule to find the current flowing through specific impedances when the circuit is open.

💡Polar Form

Polar form is a way of representing complex numbers, which include both magnitude and phase angle. In the context of the video, the speaker converts impedance values to polar form to perform calculations more easily, especially when dealing with AC circuits where phase angles are significant.

💡Phase Angle

The phase angle is the angle by which a sinusoidal waveform is shifted in time, and it is a critical aspect of AC circuits. In the script, the speaker calculates and uses phase angles to determine the behavior of the circuit under analysis, particularly when converting impedances to polar form.

💡Rectangular Form

Rectangular form, also known as Cartesian coordinates, is another way to represent complex numbers, using real and imaginary parts. The speaker in the video switches between polar and rectangular forms to perform different calculations related to the circuit's voltage and impedance.

💡Source of Voltage

A source of voltage is an element in a circuit that provides energy, typically in the form of an electromotive force (EMF). In the script, the speaker refers to different sources of voltage, which are essential for applying the superposition method and for understanding how the circuit will respond to different conditions.

💡Circuit Open

A circuit being 'open' refers to a break in the circuit that prevents current from flowing. In the context of the video, the speaker mentions having a circuit open to simplify the analysis by focusing on one source at a time, which is a standard approach in the superposition method.

💡AC (Alternating Current)

Alternating current is a type of electrical current that periodically reverses direction. The speaker in the video is analyzing an AC circuit, which is why concepts like impedance, phase angle, and the use of both polar and rectangular forms are essential for understanding the circuit's behavior.

💡Equivalent Impedance

Equivalent impedance is the total opposition to the flow of current in a circuit when components are combined. The speaker calculates the equivalent impedance by considering the series and parallel connections of various impedances, which is necessary for determining the overall behavior of the circuit under the superposition method.

Highlights

Introduction to the method of superposition for solving electrical circuits.

Explanation of working with a single voltage source first in the superposition method.

Description of the circuit setup with an open circuit for the first source.

Identification of the voltage V2 and its location in the circuit.

Discussion on the use of impedance in parallel in the circuit analysis.

Application of current divider theorem for AC circuits to find current I2.

Calculation of I2 using the total current and impedance values.

Conversion of impedance values to polar form for complex calculations.

Determination of the equivalent impedance for current I2.

Calculation of the voltage V2 across impedance C using current I2.

Introduction of the second part of the exercise with a different voltage source.

Setup of the circuit for the second source with an open circuit condition.

Explanation of the current flow through impedances in the second scenario.

Calculation of the equivalent impedance for the second voltage source.

Determination of the voltage V2 with respect to the second source.

Combination of results from both sources to find the final voltage V2.

Conversion of the final result into rectangular form for clarity.

Conclusion of the exercise with a summary of the findings.