Use superposition to solve for vs in the circuit

In summary, the conversation discusses the use of superposition to solve for vx in a circuit. The homework statement provides the equations for Vx and the attempt at a solution shows the steps taken to find the answer. However, the solution obtained is different from the solution manual and it is discovered that the reference point (ground) was moved between the solution for v1 and v2. It is clarified that the reference point should be kept consistent throughout v1 and v2 in order to obtain the correct answer.
  • #1
sugz
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Homework Statement



Use superposition to solve for vx in the circuit of attached document titled "Problem".

Homework Equations



Vx=V1+V2, where V1 is the voltage obtained using superposition by removing 6A source and V2 is the voltage obtained using superposition by removing 4A source.

The Attempt at a Solution



Solutions for the problem by me is shown in attached document titled "hand_solutions".

It seems as though my answer is incorrect as I obtained 5.33V whereas the solution manual (also attached as titled "solution_manual") shows the answer as -26.67. Can anyone tell me where I went wrong? It seems as though my steps are correct.
 

Attachments

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  • problem.jpg
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  • #2
You moved the reference point (ground) between your solution for v1 and v2. v2 is not the same as vx for that case.
 
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Likes sugz
  • #3
Hi gneill, thank you very much for your reply!
Does the reference point (ground) have to be kept consistent through v1 and v2? I made the assumption I could place them wherever since they v1 and v2 circuits were variations of the first circuit. I think I understand it now as I should choose my ground on the initial circuit given in the problem and then use superposition and remove the independent sources and keep the ground consistent. Is this right?
 
  • #4
sugz said:
Hi gneill, thank you very much for your reply!
Does the reference point (ground) have to be kept consistent through v1 and v2? I made the assumption I could place them wherever since they v1 and v2 circuits were variations of the first circuit. I think I understand it now as I should choose my ground on the initial circuit given in the problem and then use superposition and remove the independent sources and keep the ground consistent. Is this right?
You can move your reference point or even change analysis methods altogether as long as you actually determine the right quantity :smile: When you moved the reference point in your second part you placed the controlled voltage source between the 8 Ohm resistor and that reference . So it's now in the path from v2 through the 8 Ohm resistor to the reference. You'd have to take that into account to determine vx.
 

FAQ: Use superposition to solve for vs in the circuit

1. What is superposition and how is it used in circuit analysis?

Superposition is a principle in circuit analysis that states that the total current or voltage in a circuit is equal to the sum of the individual currents or voltages caused by each source. It is used to simplify complex circuits by breaking them down into smaller, more manageable parts.

2. How do I identify the individual currents or voltages caused by each source in a circuit?

You can identify the individual currents or voltages by considering each source separately and treating all other sources as if they were turned off. This means setting voltage sources to 0 and replacing current sources with an open circuit. Then, you can use Ohm's Law and Kirchhoff's Laws to solve for the individual currents or voltages.

3. Can superposition be used for both DC and AC circuits?

Yes, superposition can be used for both DC and AC circuits. However, it is important to note that for AC circuits, the individual currents or voltages must be expressed in complex form and then added using vector addition.

4. What are the benefits of using superposition in circuit analysis?

Superposition allows for the analysis of complex circuits by breaking them down into smaller, easier to solve parts. It also helps to identify the contribution of each source in the circuit and can be useful in troubleshooting and optimizing circuit designs.

5. Are there any limitations to using superposition in circuit analysis?

Yes, there are some limitations to using superposition in circuit analysis. It can only be applied to linear circuits, meaning that all components in the circuit must follow Ohm's Law. It also cannot be used to analyze circuits with dependent sources, such as transistors or operational amplifiers.

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