Question

Explain series combination of Capacitors. Derive the formula for equivalent capacitance.

Answer 1

When one terminal of a capacitor is connected to the terminal of another capacitors , called series combination of capacitors. In series, each capacitor has same charge flow from battery. The three capacitors $C_1,C_2$ and $C_3$ are in series.

Now, charge on first capacitor is $Q_1=C_1{V}_1$, charge on second capacitor is $Q_2=C_2{V}_2$ and charge on third capacitor is $Q_3=C_3{V}_3$.

In series, $Q_1=Q_2=Q_2=Q$ and $Q=C_{eq}V$

Also, $V=V_1+V_2+V_3$

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

$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$, this is the formula for equivalent capacitance in series.