Obtain an expression for the capacitance of a combination of three capacitors in parallel .

Explanation

Let three capacitors of a capacitances `C_1 , C_2` and `C_3` ,respectively are joined in parallel such that one plate of all the three capacitors has been joined at one point A and the other plates are another point B .
Here potential difference across all the three capacitors is same (say V) and charges on different capacitors are
`Q_(1) = C _(1) V , Q_(2) = C_(2) V` and `Q_(3) = C_(3) V`
Total charge on all the three capacitors taken together `Q = Q_(1) + Q_(2) + Q_(3) = C_(1) V + C_2 V + C_3 V`
If a single capacitor of capacitance C is joined instead of given capacitors such that the potential difference across it still remains V , then Q = CV
`CV = C_1 V + C_2 V + C_3 V`
`implies` Resultant capacitance `C = C_1 + C_2 + C_3`