# Star To Delta Conversion: Transformation, Diagram & Formula

## Star To Delta Conversion: Transformation, Diagram & Formula

Star to delta conversion is a method of simplifying a circuit of resistances that are connected in a star or delta configuration. It allows us to find the equivalent resistance of the circuit without solving a system of equations. In this article, we will learn how to perform star to delta conversion and vice versa, and how to apply them to solve some problems.

## What are star and delta configurations?

A star configuration, also known as a Y configuration, is a three-phase circuit or network of resistances where each resistance is connected between a common point (called the neutral point) and one of the three terminals. A delta configuration, also known as a Î configuration, is a three-phase circuit or network of resistances where each resistance is connected between two terminals. The following diagrams show the star and delta configurations:

## Star To Delta Conversion Solved Problems Pdf 40

## How to convert star to delta?

To convert a star configuration to a delta configuration, we need to find the equivalent resistance of each side of the delta using the formula:

where RA, RB, and RC are the resistances of the sides of the delta, and ra, rb, and rc are the resistances of the arms of the star. The formula can be derived by applying Kirchhoff's voltage law and Kirchhoff's current law to the circuit.

## How to convert delta to star?

To convert a delta configuration to a star configuration, we need to find the equivalent resistance of each arm of the star using the formula:

where ra, rb, and rc are the resistances of the arms of the star, and RA, RB, and RC are the resistances of the sides of the delta. The formula can be derived by applying Kirchhoff's voltage law and Kirchhoff's current law to the circuit.

## Example problems

Here are some examples of how to use star to delta conversion and delta to star conversion to solve problems involving circuits with resistances.

### Example 1

Find the equivalent resistance between terminals A and B in the following circuit:

Solution: We can simplify the circuit by converting the star configuration on the left to a delta configuration using the formula:

RA = (rarb + rbrc + rcra) / ra = (10Ã20 + 20Ã30 + 30Ã10) / 10 = 140 Î

RB = (rarb + rbrc + rcra) / rb = (10Ã20 + 20Ã30 + 30Ã10) / 20 = 70 Î

RC = (rarb + rbrc + rcra) / rc = (10Ã20 + 20Ã30 + 30Ã10) / 30 = 46.67 Î

The simplified circuit is shown below:

The equivalent resistance between terminals A and B is then given by:

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