What is a Delta-to-Wye transformation and when is it used?

• A. Converts a star network into a triangle to simplify current multiplication.
• B. Converts a line of resistors into a single equivalent resistor.
• C. Converts a triangle of resistors into a star network to simplify network analysis; typically used when three resistors form a triangle around a node.
• D. Used to compute capacitor impedance at high frequency.

Answer: (C)

The Delta-to-Wye transformation replaces a triangle (delta) arrangement of three resistors with an equivalent star (Wye) network, preserving the same behavior at the outer terminals. This is useful when the three resistors form a closed loop around a node and you want to simplify the network so you can more easily combine resistors with others connected to the triangle’s corners or solve for voltages and currents.

If the delta has resistors on the sides between nodes, the equivalent star has a resistor from each outer node to a new central node. The values are chosen so the external connections see the same resistance, meaning:

R_from_node1_to_center = (R12 * R31) / (R12 + R23 + R31)

R_from_node2_to_center = (R12 * R23) / (R12 + R23 + R31)

R_from_node3_to_center = (R23 * R31) / (R12 + R23 + R31)

Using these, the triangle becomes a star, and many circuits become easier to analyze with series/parallel reductions. This transformation isn’t about just collapsing a line of resistors or about capacitor impedance at high frequency; it’s specifically about converting a delta into an equivalent star to simplify network analysis while preserving external behavior.