Calculate the denominator (sum of Delta resistors): $$Sum = R_AB + R_BC + R_CA = 30 + 20 + 10 = 60 , \Omega$$
Use this when you have a triangle of resistors and want to replace it with a central star point to simplify the circuit. The Formulas For a Delta network with resistances cap R sub cap A cap B end-sub cap R sub cap B cap C end-sub cap R sub cap C cap A end-sub , the equivalent Star resistances cap R sub cap A cap R sub cap B cap R sub cap C star delta transformation problems and solutions pdf
Identify the delta mesh that cannot be reduced by series/parallel rules (e.g., a triangle). Calculate the denominator (sum of Delta resistors): $$Sum
If all resistors in a Delta network are equal ( RΔcap R sub cap delta ), the Star equivalent is simply . Conversely, Conversely, R31=PR2=996=16
R31=PR2=996=16.5Ωcap R sub 31 equals the fraction with numerator cap P and denominator cap R sub 2 end-fraction equals 99 over 6 end-fraction equals 16.5 space cap omega The equivalent delta resistors are 4. Common Mistakes and Troubleshooting
. You can then solve those parallel combinations and add them to RAcap R sub cap A to find the total equivalent circuit resistance. 4. Practical Engineering Applications
RZ=RYZ⋅RZX∑R=20⋅3060=60060=10Ωcap R sub cap Z equals the fraction with numerator cap R sub cap Y cap Z end-sub center dot cap R sub cap Z cap X end-sub and denominator sum of cap R end-fraction equals the fraction with numerator 20 center dot 30 and denominator 60 end-fraction equals 600 over 60 end-fraction equals 10 space cap omega The Delta network is replaced by three star arms: meeting at point N. Problem 2: Expanding a Star Network (Star to Delta)