Capacitor Y-Delta and Delta-Y Transforms

Resistors and inductors follow the same rules for Y-Delta and Delta-Y transforms because they combine similarly in series and parallel. This does not hold true for capacitors.

Through no small feat of algebraic manipulation, it can be shown that the Y-Delta and Delta-Y transforms for capacitors are as follows:

Y-Delta Transformation

C_1 = \frac{C_AC_B}{C_A+C_B+C_C}, C_2 = \frac{C_BC_C}{C_A+C_B+C_C}, C_3 = \frac{C_AC_C}{C_A+C_B+C_C}

Delta-Y Transformation

C_A = \frac{C_1C_2 + C_1C_3 + C_2C_3}{C_2}, C_B = \frac{C_1C_2 + C_1C_3 + C_2C_3}{C_3}, C_C = \frac{C_1C_2 + C_1C_3 + C_2C_3}{C_1}

Circuit Diagram

Delta-Wye Capacitor Schematics

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