R_AB = R₁ + R₂ + (R₁·R₂)/R₃ = 10+20 + (10×20)/30 = 30 + 6.67 = 36.67Ω R_BC = R₂ + R₃ + (R₂·R₃)/R₁ = 20+30 + (20×30)/10 = 50 + 60 = 110Ω R_CA = R₃ + R₁ + (R₃·R₁)/R₂ = 30+10 + (30×10)/20 = 40 + 15 = 55Ω
RCA=5+10+5⋅1015=15+5015=15+3.33=18.33Ωcap R sub cap C cap A end-sub equals 5 plus 10 plus the fraction with numerator 5 center dot 10 and denominator 15 end-fraction equals 15 plus 50 over 15 end-fraction equals 15 plus 3.33 equals 18.33 space cap omega The Delta network resistors are Problem 3: Simplifying a Bridge Circuit
The principle of transformation is that the between these two networks is maintained if the resistance measured between any two terminals remains identical in both configurations. 2. Transformation Formulas
After conversion, from A: two (6\Omega) resistors to L and R. Each of L and R also have a (6\Omega) to the star’s neutral (which is not a terminal). But easier: Combine from B: B connects to L via (18\Omega), B connects to R via (18\Omega). And from L to R: now the star’s neutral is not B. star delta transformation problems and solutions pdf
In a Star network, three resistors connect to a single, shared central node (often called the neutral point). It resembles the letter "Y" or a star.
Example 1 — Δ → Y: Equivalent resistance between two terminals Problem: A delta of resistors R12 = 30 Ω, R23 = 60 Ω, R31 = 90 Ω is connected to a network; convert to star to find equivalent between nodes. Solution: Sum = 30 + 60 + 90 = 180 Ω Ra (at node 1) = (R12 R31)/Sum = (30 90)/180 = 15 Ω Rb (node 2) = (30 60)/180 = 10 Ω Rc (node 3) = (60 90)/180 = 30 Ω Replace delta by these star arms and proceed with series/parallel reductions as needed.
A specific format to test your memory of the formulas Share public link R_AB = R₁ + R₂ + (R₁·R₂)/R₃ =
The primary application of this transformation is in solving bridge networks or complex grids where resistors are neither purely in series nor purely in parallel. Problem 1: The Unbalanced Bridge
Balanced or unbalanced Wheatstone bridge. Convert one Delta (e.g., ABC) into Star to break the bridge.
A classic use case for star-delta conversion is solving an unbalanced circuit where traditional series-parallel reduction fails. Problem 3: Bridge Circuit Analysis Scenario: Find the equivalent resistance across terminals for a bridge circuit with the following values: Top loop delta mesh: Bottom remaining branches: 1. Identify the Delta Mesh Each of L and R also have a
RA=RAB⋅RCARAB+RBC+RCAcap R sub cap A equals the fraction with numerator cap R sub cap A cap B end-sub center dot cap R sub cap C cap A end-sub and denominator cap R sub cap A cap B end-sub plus cap R sub cap B cap C end-sub plus cap R sub cap C cap A end-sub end-fraction
Each star resistor is the product of the two adjacent delta resistors divided by the sum of all delta resistors. 2. Star to Delta (Y →Δright arrow cap delta ) Conversion To convert a Star network ( ) into a Delta network ( Solved Examples of Star-Delta Transformation Problems
Identify either the upper or lower half of the bridge as a delta network. Apply the Δ→cap delta right arrow