Charge Division by Parallel Capacitances Formula Calculation

When a voltage E_P is applied to parallel connected capacitances C₁ and C₂, the charge Q_P which accumulates in the parallel circuit is:

Q_P = òi_Pdt = E_PC_P = E_P(C₁ + C₂)

The charges Q₁ and Q₂ which accumulate in the respective capacitances C₁ and C₂ are:

Q₁ = òi₁dt = E_PC₁ = Q_PC₁ / C_P = Q_PC₁ / (C₁ + C₂)

Q₂ = òi₂dt = E_PC₂ = Q_PC₂ / C_P = Q_PC₂ / (C₁ + C₂)

In general terms, for capacitances C₁, C₂, C₃, ... connected in parallel:

Q_P = òi_Pdt = E_PC_P = E_P(C₁ + C₂ + C₃ + ...)

Q_n = òi_ndt = E_PC_n = Q_PC_n / C_P = Q_PC_n / (C₁ + C₂ + C₃ + ...)