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
R12=R1+R2+R1×R2R3cap R sub 12 equals cap R sub 1 plus cap R sub 2 plus the fraction with numerator cap R sub 1 cross cap R sub 2 and denominator cap R sub 3 end-fraction
A common problem involves finding the equivalent resistance ( Reqcap R sub e q end-sub ) of a bridge or complex lattice circuit. Example: Reducing a Bridge Circuit Consider a bridge where a Delta network is formed by star delta transformation problems and solutions pdf
A special case is when all resistances in the Star network are equal ((R_Y)). The resulting Delta resistors will each be (3R_Y). Conversely, if all resistances in the Delta network are equal ((R_Δ)), the equivalent Star resistors are (R_Δ/3).
This method is invaluable for solving three-phase circuits, bridge circuits, and other complex resistive networks where standard series-parallel reduction fails. RBC=RB+RC+RB⋅RCRAcap R sub cap B cap C end-sub
Use the mnemonic or write the formula step by step. Do not skip algebra.
Terminal nodes must remain accessible after transformation; do not remove nodes connected to external sources. Conversely, if all resistances in the Delta network
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Rsum=Rab+Rbc+Rca=10+20+30=60Ωcap R sub s u m end-sub equals cap R sub a b end-sub plus cap R sub b c end-sub plus cap R sub c a end-sub equals 10 plus 20 plus 30 equals 60 space cap omega Racap R sub a
A Delta network has R_AB = 10 Ω, R_BC = 60 Ω, and R_CA = 30 Ω. Find the equivalent Star resistances. Solution: