Capacitors connected in series behave contrary to how many people expect.
Connecting capacitors in series results in a smaller capacitance.
In order to develop an intuition of why this occurs, let us suppose that we force a constant DC current through a capacitor for 10 seconds.
Let us now force the exact same DC current through a capacitor with a larger capacitance.
With a larger capacitance, the voltage increases more slowly,
and at the end of the 10 second time period, the voltage will therefore be smaller than before.
Let us now force the exact same DC current through three of these capacitors in series.
At the end of the 10 second time period, each capacitor develops the same voltage drop as in the previous example.
The total voltage drop across all three capacitors combined is the same as the voltage drop across the single capacitor with the smaller capacitance.
Therefore, as far as the external world is concerned, multiple capacitors connected in series behave just like a single capacitor with a smaller capacitance.
Let us now consider capacitors in parallel.
If we force a constant DC current through capacitors in parallel, the current will split up, and only a fraction of the total current will flow through each capacitor.
As a result, the voltage across each capacitor will increase more slowly,
and the voltage at the end of the 10 second time period will therefore be smaller.
Therefore, as far as the external world is concerned, multiple capacitors connected in parallel behave just like a single capacitor with a larger capacitance.
Here is another way to look at it.
Multiple capacitors connected in parallel can be viewed as a single capacitor with a larger area.
A capacitor with a larger area has a larger capacitance.
There is a similar way of looking at capacitors in series.
Multiple capacitors connected in series can be viewed as a single capacitor with a larger distance between the two plates.
A capacitor with a larger distance between the two plates has a smaller capacitance.
Detailed information about the basics of capacitors is available in the video "Capacitors and Capacitance."