Question

How do you find the resistance of a star and Delta Connection?

Answer 1

To find the resistance in a **star** (Y) and **delta** (Δ) connection, you can use the following formulas. These connections are typically used for resistances or impedances in three-phase circuits, but the principles are the same for both resistances and impedances.

### 1. **Star (Y) Connection:**

In a star connection, three resistors are connected at a common point, forming a "Y" shape. Each resistor in the star connection is connected between the line and neutral.

- **If you know the resistance of each phase (Rs):**
    - Let’s say each resistor in the star connection is \( R_{Y} \).

- **To find the equivalent resistance of the delta connection (RΔ):**
    - The relation between the resistances in the **star** and **delta** connections is given by the formula:
    \[
    R_{\Delta} = 3 R_{Y}
    \]
    So, if you know the star resistance, you multiply by 3 to get the delta resistance.

### 2. **Delta (Δ) Connection:**

In a delta connection, the three resistors are connected in a triangle shape, and each resistor is connected between two phases.

- **If you know the resistance of each phase (Rd):**
    - Let’s say each resistor in the delta connection is \( R_{\Delta} \).

- **To find the equivalent resistance of the star connection (RY):**
    - The relation between the resistances in the **delta** and **star** connections is:
    \[
    R_{Y} = \frac{R_{\Delta}}{3}
    \]
    So, if you know the delta resistance, you divide it by 3 to get the star resistance.

### Summary:
- **Star to Delta:** Multiply by 3
    \[
    R_{\Delta} = 3 R_{Y}
    \]
- **Delta to Star:** Divide by 3
    \[
    R_{Y} = \frac{R_{\Delta}}{3}
    \]

These relationships help in converting resistances between the two types of connections.