# Wye‐Delta Transformation Study Notes for GATE and ECE Exams

By BYJU'S Exam Prep

Updated on: September 25th, 2023

• Wye-Delta transformation is also called as star-delta transformation.
• Wye-Delta Transformation is a technique to reduce common resistor connections that are neither series nor parallel

Here, we are providing a list of important topics of the Wye‐Delta Transformation asked in GATE, Electronics and Communication engineering exams.

In many circuit applications, we encounter components connected together in one of two ways to form a three-terminal network:

• Delta, or Δ (also known as the Pi, or π) configuration, and
• Star connected network which has the symbol of the letter “Y” (also known as the “T”) configuration.

• Conversion from Delta (Δ) to Wye (Y)

•  Conversion from Wye (Y) to Delta (Δ)

Transformations

• Star-Delta TransformationCase-1: If ZA = ZB = ZC = R (Ω)Case-2: If If ZA = ZB = ZC = jωL (Ω)

Case-3: If ZA = ZB = ZC = 1/jωC (Ω)

• Delta-Star Transformation

Note: Both Star to Delta Transformation and Delta to Star Transformation allows us to convert one type of circuit connection into another type in order to easily analyse the circuit. These transformation techniques can be used  for either star or delta circuits containing resistances or impedances.

Example-1: Calculate the Thevenin’s equivalent resistance Rab (in ohms) for the circuit shown in figure below:

Solution:

Given circuit is

Applying delta-to-star transformation,

After rearranging the circuit looks like as shown below

Applying star to delta transformation,

After rearranging the circuit looks like as shown below

Therefore Thevenin’s equivalent resistance Rab for the given circuit is 1.6 Ω.

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