Three capacitors of capacitance `C_1,C_2andC_3` are connected in parallel. Derive an expression for the equivalent capacitance of the combination.

Explanation

Capacitors are said to be in parallel combination, when one plate of each capacitor is connected at one common point (say A) and other end of each plate is connected at another common point (say B) in such a way that potential difference across each capacitor remains same.
Equivalent Capacitance of Capacitors in Parallel Combination
Let we have three capacitors `C_(1), C_(2)` and `C_3`. In parallel combination, potential difference across each capacitor remains same i.e., V.
Since each capacitor enjoys the same potential difference across it so it is in a position to store charge according to its capacity. Hence capacitors have different amounts-of charges `q_(1), q_(2)` and `q_3` (because `C_(1), C_(2)` and `C_3` are considered to be of different values).
In parallel combination, total charge q is the sum of the charges stored by each capacitor.
i.e., `q=q_(1) + q_(2) + q_(3)`......(1)
But `q_(1) = C_(1)V, q_(2) = C_(2)V` and `q_(3) = C_(3)V`
If C= Equivalent capacitance of capacitors then q = CV
Put the value of `q_(1), q_(2)` and `q_3` in (I)
`CV = C_(1)V +C_(2)V +C_(3)V`
`CV = V(C_(1) + C_(2) + C_(3))`
`C=C_(1) + C_(2) + C_(3)`

Thus the total capacitance of capacitors.