☑️19 - Superposition Theorem: Circuits with Dependent Sources 1

Summary

This educational video script delves into the application of the superposition theorem for solving linear circuits involving dependent sources. The presenter guides through two examples, first calculating the voltage 'VX' using the theorem by deactivating one independent source at a time. The second example demonstrates finding 'V not' using a similar method, also introducing the principle of source transformation for circuit analysis. The script is a valuable resource for those learning to apply superposition in circuit problems.

Takeaways

• 🔌 The video script discusses the application of the Superposition Theorem in linear circuits involving dependent sources.
• 🔧 The Superposition Theorem is used when there are multiple independent sources in a circuit, and it involves considering each source one at a time while deactivating the others.
• 🔄 The first example given in the script illustrates how to find the voltage 'VX' by first considering the 20-volt source alone and then the 4-ampere current source alone.
• 🔍 In the first example, the dependent source is deactivated by treating it as an open circuit, and current distribution is used to set up equations.
• 📐 The script explains how to set up and solve equations involving voltage drops across resistors and the relationship between the currents in the circuit.
• 🔗 The concept of current division and the use of Ohm's law to find the value of unknown currents and voltages are demonstrated.
• 🔄 The second example in the script involves finding the voltage 'V naught' using the same principles of the Superposition Theorem.
• 🔄 The principle of source transformation is introduced, which allows for converting a voltage source in series with a resistor to a current source in parallel with the same resistor, and vice versa.
• 🔌 The script shows how to redraw circuits to simplify the analysis, such as combining resistors in parallel and transforming sources.
• 📘 The final values for 'VX' and 'V naught' are found by summing the effects of each independent source acting alone, as per the Superposition Theorem.
• 👋 The video concludes with a summary of the findings and a sign-off for the next video.

Q & A

What is the Superposition Theorem used for in the context of this script?

The Superposition Theorem is used to find the voltage across a particular point (VX in the script) in a linear circuit with multiple independent sources by considering the effect of each independent source one at a time while deactivating the others.

How is the dependent source in the circuit described in the script?

The dependent source in the circuit is described as a current source with a value of 0.1 VX, indicating that the current through this source is proportional to the voltage VX across it.

What is the first step in applying the Superposition Theorem to the circuit in the script?

The first step is to consider the 20-volt source acting alone and deactivate the 4-ampere current source, then find the value of the current I in the circuit.

How is the current distribution determined when the 20-volt source is acting alone?

The current distribution is determined by applying Ohm's Law to the circuit, considering the current I produced by the 20-volt source and the voltage drops across the resistors in the loop.

What is the equation derived from the loop with the 20-volt source acting alone?

The equation derived is 20 = 20I + 4I1, where I is the current through the 20-ohm resistor and I1 is the current in the branch with the dependent source.

What is the relationship between I1 and I in the circuit?

The relationship is given by the equation I1 = I + 0.1VX, indicating that the current I1 in the branch is the sum of the current I and 0.1 times the voltage VX.

How is the voltage VX across the 4-ohm resistor related to I1?

The voltage VX across the 4-ohm resistor is equal to I1 times the resistance value, which is 4 ohms, as per Ohm's Law.

What is the principle of source transformation mentioned in the script?

The principle of source transformation states that a voltage source in series with a resistor can be transformed into a current source in parallel with the same resistor, and vice versa, using Ohm's Law to find the equivalent source values.

How is the voltage source transformed into a current source in the script?

The voltage source is transformed into a current source by using Ohm's Law (V = I * R), where the current I is calculated as the voltage across the source divided by the resistance value.

What is the final value of VX calculated using the Superposition Theorem in the script?

The final value of VX is calculated to be 25 volts, obtained by summing the individual effects of the 20-volt source and the 4-ampere source acting alone.

What is the method used to find the value of V naught in the second example of the script?

The method used to find the value of V naught in the second example is also the Superposition Theorem, by considering the effects of the 10-volt source and the 2-ampere source acting alone and then summing their individual contributions.

How are the resistors treated when the 2-ampere source is acting alone in the second example?

When the 2-ampere source is acting alone, the 20-ohm and 4-ohm resistors are treated as being in parallel, and their combined resistance is calculated to simplify the circuit before finding the current and voltage values.

What is the final value of V naught calculated in the second example of the script?

The final value of V naught calculated in the second example is 11.2 volts, which is the sum of the individual effects of the 10-volt source and the 2-ampere source acting alone.