Question

Derive the formula for equivalent capacitance when the capacitors are connected in series.

Answer 1

Let the capacitance of each capacitor be $C_1,$ $C_2$ and $C_3$ and their equivalent capacitance be $C_{eq}$.

As these capacitors are connected in series, thus charge across each capacitor is same as $Q$.

When some electrical components, let say 3, are connected in series with each other, the potential difference of the battery $V$ gets divided across each component as $V_1,$ $V_2$ and $V_3$ as shown in the figure.

$\therefore$ $V=V_1+V_2+V_3$

Using $V=\frac{Q}{C}$

We get $\frac{Q}{C_{eq}}=\frac{Q}{C_1}+\frac{Q}{C_2}+\frac{Q}{C_3}$

$⟹$ Equivalent capacitance for series combination $\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$

In general, $\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+..........+\frac{1}{C_n}$