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.