Question

How do you find the equivalent resistance of a star?

Answer 1

To find the equivalent resistance of a star (Y) configuration, you can convert it into a delta (Δ) configuration or calculate it directly based on the resistances. Here's how to approach it:

### Given:
Assume you have three resistors in a star configuration: \( R_1, R_2, \) and \( R_3 \).

### To find the equivalent resistance \( R_{eq} \) between any two terminals (e.g., A and B):

1. **Using the Star to Delta Transformation**:
   You can convert the star resistances into an equivalent delta configuration. The formulas for converting from star to delta are:

   \[
   R_{AB} = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_3}
   \]

   \[
   R_{BC} = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_1}
   \]

   \[
   R_{CA} = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_2}
   \]

   After calculating the delta resistances \( R_{AB}, R_{BC}, R_{CA} \), you can find the equivalent resistance using series or parallel combinations as appropriate.

2. **Direct Calculation**:
   If you want to find the equivalent resistance between two terminals (e.g., A and B) directly in the star configuration, you can use the following method:

   \[
   R_{AB} = R_1 + \frac{R_2 R_3}{R_2 + R_3}
   \]

   This method applies to find the resistance between any two terminals while considering the third resistor connected to the common point.

### Summary:
- Use star-to-delta conversion or apply the direct formula based on your needs.
- Remember to visualize or draw the circuit to ensure you're calculating the right paths.

Let me know if you need more details on a specific example!

Answer 2

Are you asking about finding the equivalent resistance of a star (or wye) network of resistors, or are you referring to a specific type of star network in electronics?