Question

Three identical capacitors $C_1$, $C_2$ and $C_3$ of capacitance of $6\mu F$ each are connected in series to a $12V$ battery. Find the charge on each capacitor.

Answer 1

Step 1: Given Data

$C_1$, $C_2$ and $C_3$ are three identical capacitors.

The capacitance of each capacitors $=6\mu F$

Voltage $=12V$

Step 2: Formula Used

For equivalent capacitance,

$\frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$

Charge on a capacitor,

$Q=CV$

Step 3: Calculate Equivalent Capacitance

For equivalent capacitance,

$$\begin{gathered} \frac{1}{C}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3} \\ =\frac{1}{6}+\frac{1}{6}+\frac{1}{6} \\ =\frac{3}{6} \\ =\frac{1}{2} \\ \Rightarrow C=2\mu F \end{gathered}$$

Step 4: Calculate Charge

Capacitors in series will always have equal amounts of coulomb charge across their plates.

Therefore, charge on each capacitor,

$$\begin{gathered} Q=CV \\ =2\times 12 \\ =24\mu C \end{gathered}$$

Hence, the charge present in each capacitor is $24\mu C$.