Three capacitors in a loop and dependence?
Three caps in series across a "10V" power supply. If one cap (C1) has 2V across it and another (C2) has 5 volts across it, the third HAS to have 3 volts across it because: -

2 + 5 + 3 =10

If the power supply was 0V it makes no difference: -

C1 has (say) 2V across it, C2 has 5V across it and the third must have -7V across it because 

2 + 5 - 7 = 0