Derive an expressions for effective capacitance of capacitors connected in
series,

Explanation

When capacitors are connected in series
When negative plate of one capacitor is connected to the positive plate of second capacitor to the positive plate of second capacitor and the negative of second to the positive of third and so on, then the capacitors are said to be connected in series.

Each of the capacitor holds same quantity of charge q irrespective of the value of capacitance. Potential difference across each capacitor depending on their capacities is different and are given by
`V_(1)=(Q)/(C_(1)),V_(2)=(Q)/(C_(2))`
and `V_(3)=(Q)/(C_(3))`
As, `V=V_(1)+V_(2)+V_(3)`
or `(Q)/(C)=(Q)/(C_(1))+(Q)/(C_(2))+(Q)/(C_(3))`
`rArr(1)/(C)=(1)/(C_(1))+(1)/(C_(2))+(1)/(C_(3))`
For n capacitors connected in series,
`(1)/(C)=(1)/(C_(1))+(1)/(C_(2))+ . . . . .+(1)/(C_(n))`