When a total voltage ES
is applied to series connected capacitances C1
and C2, the charge QS
which accumulates in the series circuit is:
QS =
òiSdt
= ESCS = ESC1C2
/ (C1 + C2)
The voltages V1 and
V2 which appear across the respective
capacitances C1 and C2
are:
V1 =
òiSdt
/ C1 = ESCS / C1
= ESC2 / (C1 + C2)
V2 =
òiSdt
/ C2 = ESCS / C2
= ESC1 / (C1 + C2)
In general terms, for capacitances C1,
C2, C3, ...
connected in series:
QS =
òiSdt
= ESCS = ES / (1 / CS)
= ES / (1 / C1 + 1 / C2
+ 1 / C3 + ...)
Vn =
òiSdt
/ Cn = ESCS / Cn
= ES / Cn(1 / CS) = ES
/ Cn(1 / C1 + 1 / C2 +
1 / C3 + ...)
Note that the highest voltage appears
across the lowest capacitance.
