Derive a relation for equivalent capacitance of n capacitors connected in parallel -

Question: What do you understand by capacitors in parallel ? Derive a relation for equivalent capacitance of n capacitors connected in parallel.

Capacitors in Parallel: Two or more capacitors are said to be connected in parallel if left plates of all capacitors are connected to one terminal and the right plates of all capacitors are connected to other terminal of the battery such that the potential difference across each capacitor is same.

Expression for Equivalent Capacitance:

Let $q_1$ and $q_2$ be the maximum charges on $C_1$ and $C_2$ respectively. The total charge $q$ on the system of two capacitors connected in parallel is given by
$q = q_1 + q_2$
But
$q_1 = C_1 V \quad \text{and} \quad q_2 = C_2 V$
$q = C_1 V + C_2 V = (C_1 + C_2) V \quad \dots \text{(i)}$
If
C = Capacitance of parallel combination of the capacitors (called equivalent capacitance of the combination)
$q = CV$
then
$CV = (C_1 + C_2) V$
Hence eqn. (i) becomes
$C = C_1 + C_2$
Which is the equivalent capacitance of the parallel combination of two capacitors.
If $n$ capacitors are connected in parallel, the equivalent capacitance of the combination is
$C = C_1 + C_2 + C_3 + \dots + C_n \quad \dots \text{(iii)}$
$C = \sum_{i=1}^n C_i \quad \dots \text{(iv)}$
Thus, the total capacitance of the parallel combination of the capacitors is the sum of the capacitances of the individual capacitors connected in the combination.