What is parallel combination of capacitors. Derive the formula for equivalent capacitance in parallel combination.

Explanation

parallel combination: The first plates of different capacitors are connected at one terminal and all the second plate of the capacitors are connected at another terminal then the two terminals are connected to the terminals of battery is called parallel combination.
In this combination,
1. The P.D's between each capacitors is equal (or) same.
2. Charge on each capacitor is not equal. consider three capacitors of capacitance `C_(1), C_(2)` and `C_(3)` are connected in parallel across a P.D V as shown in fig.
The charge on Ist capacitor `Q_(1) = C_(1) V`
The charge on IInd capacitor `Q_(2) = C_(2) V`
The charge on IIIrd capacitor `Q_(3) = C_(3) V`
`:.` The total charge `Q = Q_(1) + Q_(2) + Q_(3)`
`= C_(1) V + C_(2) V + C_(3) V`
`Q = V (C_(1) + C_(2) + C_(3)) implies (Q)/(V) = C_(1) + C_(2) + C_(3)`
`C = C_(1) + C_(2) + C_(3)` `[ :' C = (Q)/(V)]`
For n number of capacitors connected in parallel, the equivalent capacitance can be written as
`C = C_(1) + C_(2) + C_(3) + ..... + C_(n)`