Which, among the following is the right expression for converting from delta to star?a)R1=Ra*Rb/(Ra+Rb+Rc), R2=Rb*Rc/(Ra+Rb+Rc), R3=Rc*Ra/(Ra+Rb+Rc)b)R1=Ra/(Ra+Rb+Rc), R2=Rb/(Ra+Rb+Rc), Rc=/(Ra+Rb+Rc)c)R1=Ra*Rb*Rc/(Ra+Rb+Rc), R2=Ra*Rb/(Ra+Rb+Rc), R3=Ra/(Ra+Rb+Rc)d)R1=Ra*Rb*Rc/(Ra+Rb+Rc), R2=Ra*Rb*Rc/(Ra+Rb+Rc), R3=Ra*Rb*Rc/(Ra+Rb+Rc)Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Converting from delta to star (also known as wye) is a common operation in electrical circuits. This conversion is used when we need to simplify a complex circuit or when we want to analyze a circuit using different methods. The correct expression for converting from delta to star is given by option 'A'. Let's break down the individual steps involved in this conversion:

1. Understanding Delta and Star Connections:
- Delta Connection: In a delta connection, three resistors (Ra, Rb, Rc) are connected in a triangular shape, forming a closed loop. The three nodes of the delta are labeled A, B, and C.
- Star Connection: In a star connection, the three resistors (R1, R2, R3) are connected in a Y-shape, with one end of each resistor connected to a common point called the neutral or star point.

2. Conversion Equations:
To convert from delta to star, we use the following equations:

- R1 = Ra * Rb / (Ra + Rb + Rc)
- R2 = Rb * Rc / (Ra + Rb + Rc)
- R3 = Rc * Ra / (Ra + Rb + Rc)

These equations allow us to calculate the equivalent resistances in the star connection based on the given resistances in the delta connection.

3. Understanding the Expression in Option 'A':
Option 'A' correctly represents the conversion from delta to star. The expression for each resistor in the star connection is given by:

- R1 = Ra * Rb / (Ra + Rb + Rc)
- R2 = Rb * Rc / (Ra + Rb + Rc)
- R3 = Rc * Ra / (Ra + Rb + Rc)

This expression follows the conversion equations mentioned earlier, where the equivalent resistance in the star connection is calculated based on the resistances in the delta connection.

4. Importance of the Conversion:
Converting from delta to star allows us to simplify complex circuits, making analysis easier. It also helps in applying different circuit analysis techniques, such as Kirchhoff's laws or network theorems, to solve the circuit. Additionally, the conversion is useful when we need to find the equivalent resistance for a given set of resistors.

In conclusion, option 'A' represents the correct expression for converting from delta to star. This conversion is important in simplifying circuits and enabling the application of different analysis techniques.

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