created at June 5, 2021

Triangle and star connections of resistors

The triangle resistor connection scheme is a connection of three branches, which form a closed loop:

Sometimes it's easier to compute the circuit when resistors form a star connection (this reduces a number of closed loops in circuit):

We can replace three resistors connected in triangle with equivalent scheme of three resistors connected in star. This would be equivalent connection, meaning that the electric currents in other circuit branches will remain the same. The new resistances for resistors RA, RB, RC are calculated as:

RA=RABRCARAB+RBC+RCAR_{A} = \frac{R_{AB}\cdot R_{CA}}{R_{AB} + R_{BC} + R_{CA}}
RB=RBCRABRAB+RBC+RCAR_{B} = \frac{R_{BC}\cdot R_{AB}}{R_{AB} + R_{BC} + R_{CA}}
RC=RCARBCRAB+RBC+RCAR_{C} = \frac{R_{CA}\cdot R_{BC}}{R_{AB} + R_{BC} + R_{CA}}

We can also transform the star connection back to triangle connection:

RAB=RA+RB+RARBRCR_{AB} = R_{A} + R_{B} + \frac{R_{A}\cdot R_{B}}{R_{C}}
RBC=RB+RC+RBRCRAR_{BC} = R_{B} + R_{C} + \frac{R_{B}\cdot R_{C}}{R_{A}}
RCA=RC+RA+RCRARBR_{CA} = R_{C} + R_{A} + \frac{R_{C}\cdot R_{A}}{R_{B}}