Y-Δ transform proof using superposition

In summary, the Y-Δ transform is proven by equalizing the equivalent resistance between any pair of terminals while disconnecting the other node. This is done by applying superposition, which is possible because the equations involved are linear. However, it may not be clear how to apply this principle in each situation. On the Wikipedia page, they provide conditions for the current in three different situations, but it may be unclear how these conditions are determined.
  • #1
Biker
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In the wikipedia page and on every book they proof the transformation by equaling the the equivalent resistance between any pair of terminals while disconnecting the other node.https://en.wikipedia.org/wiki/Y-Δ_transform

Why this should make the two circuits equal? How can we apply superposition here? I have searched everywhere for this answer, In no where anyone explained this. Please explain the principle or this way of proof
 
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  • #2
In general, when equations are linear you can apply superposition.
 
  • #3
anorlunda said:
In general, when equations are linear you can apply superposition.
Yes I know that but I am asking how you can do that? Like what codition do you put in each situation then sum it up?

In wikipedia they put some conditions on the current in 3 situation but I didnt understand how ?
 

1. What is the Y-Δ transform and why is it used in circuit analysis?

The Y-Δ transform is a method used to simplify a complex network of resistors into a simpler equivalent network. It is used in circuit analysis to make calculations easier and reduce the number of elements in a circuit, making it easier to analyze and design.

2. How does the Y-Δ transform work?

The Y-Δ transform uses the principle of superposition, which states that the total response of a linear circuit is equal to the sum of its individual responses. In this method, the resistors in a Y-shaped circuit are transformed into a Δ-shaped circuit by using a set of equivalent resistors. This simplifies the circuit and makes it easier to analyze.

3. What is the proof for the Y-Δ transform using superposition?

The proof for the Y-Δ transform using superposition involves breaking down the circuit into smaller parts and analyzing each part separately. The Y-Δ transform is applied to each individual part, and the results are combined to get the final equivalent circuit. This process is repeated for each of the three branches in a Y-shaped circuit.

4. What are the assumptions made in the Y-Δ transform proof using superposition?

The Y-Δ transform proof using superposition assumes that the circuit is linear, meaning that the components in the circuit follow Ohm's law and have a linear relationship between voltage and current. It also assumes that the circuit is in a steady state, meaning that the values of the components do not change over time.

5. Are there any limitations to the Y-Δ transform using superposition?

Yes, there are limitations to the Y-Δ transform using superposition. This method can only be applied to circuits that have a Y-shaped topology and contain only resistors. It also cannot be used for circuits that have dependent sources or non-linear elements. Additionally, the Y-Δ transform is only valid for steady-state analysis and cannot be used for transient analysis.

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