ধারকের সমান্তরাল সংযোগ

Suppose that we had multiple capacitors with capacitances $C_1, C_2, ..., C_n$ in parallel. We wish to find the equivalent capacitance, i.e. a capacitance $C_{eq}$ such that a single capacitor of this capacitance could replace the parallel capacitor configuration and have the system act in more or less the same way.

Suppose that the capacitors in parallel have a potential difference of $V$ across them. Now, suppose that the capacitors carry charges $Q_1, Q_2, ..., Q_n$. Then, the equivalent capacitor should carry a charge equal to the total charge, which is $Q_1+Q_2+...+Q_n$. In addition, the equivalent capacitor should have the same potential difference, $V$, across it. Therefore, $$C_{eq}=\frac{Q_1+Q_2+...+Q_n}{V}$$ $$C_{eq}=\frac{Q_1}{V}+\frac{Q_2}{V}+...+\frac{Q_n}{V}$$ $$C_{eq}=C_1+C_2+...+C_n$$ The equivalent capacitance of capacitors in parallel equals the sum of the individual capacitances.

If you want to remember this intuitively, just remember the fact that the capacitance of a capacitor is proportional to its plate area. Thus, if we have capacitors in parallel, we could "combine" them to create a single capacitor with an area equal to the sum of the individual areas. Thus, capacitors in parallel should produce a larger capacitance than any of the capacitors alone.