If C is the capacitance per phase for delta connected capacitor bank, then what will be capacitance per phase for star connected capacitor bank

MCQ Statement: If C is the capacitance per phase for delta connected capacitor bank, then what will be capacitance per phase for star connected capacitor bank:

1. C/3
2. 3C
3. C/√3
4. √3/C

Correct answer: 2. 3C

Solution:

Q_C = V.I_C

where I_C = V/X_C

Q_C = V. V/X_C = V²/X_C = V² ωC

or C = Q_C/ V² ω

If V_L is line voltage for delta connection then then

C(Delta) = Q_C/ (V_L² ω) … (1)

For Wye or Star connection

C(Wye) = Q_C/ ((V_L/√3)² *ω) = 3Q_C/ ((V_L)² *ω) … (2)

Comparing equations 1 and 2

It can be seen that

C (Y) = 3C(Delta)

OR

C_Y = 3C_Δ