Voltage Division by Series Capacitances
Formula Calculation

When a total voltage E_S is applied to series connected capacitances C₁ and C₂, the charge Q_S which accumulates in the series circuit is:

Q_S = òi_Sdt = E_SC_S = E_SC₁C₂ / (C₁ + C₂)

The voltages V₁ and V₂ which appear across the respective capacitances C₁ and C₂ are:

V₁ = òi_Sdt / C₁ = E_SC_S / C₁ = E_SC₂ / (C₁ + C₂)

V₂ = òi_Sdt / C₂ = E_SC_S / C₂ = E_SC₁ / (C₁ + C₂)

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

Q_S = òi_Sdt = E_SC_S = E_S / (1 / C_S) = E_S / (1 / C₁ + 1 / C₂ + 1 / C₃ + ...)

V_n = òi_Sdt / C_n = E_SC_S / C_n = E_S / C_n(1 / C_S) = E_S / C_n(1 / C₁ + 1 / C₂ + 1 / C₃ + ...)

Note that the highest voltage appears across the lowest capacitance.