Capacitors in series

Because the capacitors are in series the total PD across each of the capacitors must equal the PD of the supply, so:

Capacitors in series

V total = V1+V2

from the general capacitor equation

C= Q/V  we can get V = Q/C

if we substitute this equation in for V we get:

Q/Ctotal = Q/C1 + Q/C2

but the charge on each of the plates must be exactly the same size (although they may be oppositely charged) because whatever electrons are pulled from one plate are pushed onto the other. That means that the values of Q can be cancelled out so:

1/Ctotal = 1/C1 + 1/C2 ...........

Notice that the form of this equation is the same as that for resistors in parallel.


Capacitors in parallel

The capacitors charge independently so the total quantity of charge

Capacitors in parallel

Q total = Q1+Q2

from the general capacitor equation

C= Q/V we can get Q= C x V

substituting this in the first equation

C total x V total = C1x V1 + C1 x V1

because the capacitors are in parallel

V total = V1 = V2

so the values of V cancel out and

C total = C1+ C1 ..........

In words that is the total capacitance of several capacitors in parallel is just all the values of each capacitor added up. Notice that is the same form of the equation for resistors in series.