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:
<3