Home / Topics / Current Electricity & Circuits
Delta–star conversion
Advanced
Convert between triangle and star resistor networks.
A triangle (Δ) of three resistors can be replaced by a star (Y) with R_a = R₁R₂/(R₁ + R₂ + R₃) etc., simplifying bridge circuits.
Three 30 Ω Δ → three 10 Ω Y.
Both forms give the same terminal behaviour.
In more detail
A delta network of three resistors can be converted to an equivalent star network, and vice versa. This makes some complex networks solvable by series and parallel reduction.
Real-world uses
- Three-phase power networks are analysed using delta-star conversions.
- Bridge circuits are simplified this way.
- Engineers use delta–star transforms to simplify circuits that contain three resistors arranged in a triangle.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What are the formulas?
Each star resistor equals the product of the two adjacent delta resistors over their sum.
Is the conversion exact?
Yes, for the terminal behaviour, the networks are electrically equivalent.
Why transform a network?
It reduces the problem to a series and parallel combination that is easy to solve with the standard rules.
Related topics in Current Electricity & Circuits
Thevenin's theorem · Norton's theorem · Superposition theorem · RC circuit charging · RC circuit discharging · Time constant