RCA=RC+RA+RC⋅RARBcap R sub cap C cap A end-sub equals cap R sub cap C plus cap R sub cap A plus the fraction with numerator cap R sub cap C center dot cap R sub cap A and denominator cap R sub cap B end-fraction : If all Star resistors are equal ( RYcap R sub cap Y
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
RBC=RB+RC+RB⋅RCRAcap R sub cap B cap C end-sub equals cap R sub cap B plus cap R sub cap C plus the fraction with numerator cap R sub cap B center dot cap R sub cap C and denominator cap R sub cap A end-fraction star delta transformation problems and solutions pdf
), then each Star resistor is exactly one-third of the Delta value ( Star to Delta Transformation ( Y→Δcap Y right arrow cap delta
The following formulas are essential for converting between the two types. Delta to Star Transformation ( Δ→Ycap delta right arrow cap Y RCA=RC+RA+RC⋅RARBcap R sub cap C cap A end-sub
RB=RAB⋅RBCRAB+RBC+RCAcap R sub cap B equals the fraction with numerator cap R sub cap A cap B end-sub center dot cap R sub cap B cap C 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
The Delta resistance between two terminals is the sum of the Star resistors connected to those terminals plus their product divided by the third resistor. Step-by-Step Problem Solving ) transformation is often the
RC=RBC⋅RCARAB+RBC+RCAcap R sub cap C equals the fraction with numerator cap R sub cap B cap C 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 : If all Delta resistors are equal ( RΔcap R sub cap delta
), then each Delta resistor is exactly three times the Star value ( 3. Step-by-Step Problem Solving
) transformation is often the only way to simplify it without reverting to complex Kirchhoff's Laws.