Equivalent Resistance

Practical applications, such as three-phase electrical transmission and motors, use interconvertible three-terminal Y or T, and delta or pi networks.

Consider a delta network composed of three resistors. Its transformation into a Y network involves overlaying the corresponding Y network onto the delta network by adding a central node.

Since the resistance between each pair of nodes in the delta network is equivalent to the resistance between the same pair in the Y network, a set of three equations is established. Solving these equations yields the resistances for the Y network.

In the Y network, each resistor's value is the product of the resistances in the two adjacent delta branches, divided by the sum of the three delta resistors.

Similarly, a Y network can be transformed into an equivalent delta network. In the delta network, each resistor's value is determined by summing all possible products of Y resistors taken two at a time and then dividing by the opposite Y resistor.

For a balanced network with equal resistances in both Y and delta configurations, the conversion formula simplifies.