What is the formula for calculating the equivalent capacitance for capacitors connected in parallel?

The formula for calculating the equivalent capacitance when capacitors are connected in parallel is derived from the way charge accumulates and voltage remains the same across all the capacitors in such a configuration. In parallel arrangements, each capacitor experiences the same voltage, and the total charge stored is the sum of the individual charges stored by each capacitor.

Since capacitance is defined as the charge stored per unit voltage ((C = Q/V)), for capacitors connected in parallel, the total charge ((Q_{total})) is the sum of the charges stored in each capacitor:

[ Q_{total} = Q_1 + Q_2 + ... + Q_n ]

Substituting in the capacitance formula for each capacitor, we have:

[ Q_{total} = C_1 \cdot V + C_2 \cdot V + ... + C_n \cdot V ]

Factoring out the voltage ((V)), the equation becomes:

[ Q_{total} = (C_1 + C_2 + ... + C_n) \cdot V ]

The equivalent capacitance ((C_{eq})) is defined as the total charge divided by the voltage, so we can set:

[ C