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Prove the equation of resistors value when converting from delta to star circuit

User Runsis
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Answer:

When converting from a delta circuit to a star circuit, the equation to determine the value of resistors can be derived using the concept of equivalent resistance. In a delta circuit, each resistor is connected between two neighboring nodes, forming a triangle. In a star circuit, three resistors are connected to a common node, forming a star shape.

To prove the equation for converting resistors from delta to star circuit, we can start with the following diagram:

```

A ________ R1 ________ B

| |

R2 R4 R3

| |

C ________ R6 ________ D

```

In a delta circuit, the resistors R1, R2, and R3 are connected between nodes A, B, and C respectively. In a star circuit, these resistors are connected to a common node D.

To find the equivalent resistance in terms of the resistors in a star circuit, we can use the following equation:

1/R_AB = 1/R1 + 1/R2 + 1/R3

Where R_AB represents the equivalent resistance between nodes A and B.

Next, we can consider the equivalent resistance between nodes B and C:

1/R_BC = 1/R3 + 1/R4 + 1/R6

Finally, let's calculate the equivalent resistance between nodes C and A:

1/R_CA = 1/R2 + 1/R4 + 1/R5

Now, we can equate the equivalent resistances in the delta circuit to the resistances in the star circuit:

R_AB = 1/(1/R1 + 1/R2 + 1/R3)

R_BC = 1/(1/R3 + 1/R4 + 1/R6)

R_CA = 1/(1/R2 + 1/R4 + 1/R5)

Simplifying these equations will give us the conversion equation for resistors when converting from a delta to star circuit.

Step-by-step explanation:

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User Wes Doyle
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