Question

Three identical capacitors $C_1,C_{2}and{C}_3$ of capacitance $6\mu F$ each are connected to a 12 V battery as shown. Find the charge on each capacitor.

Answer 1

Three identical capacitor $C_1,C_2,C_3$ of capacitance $6\mu F$ each are connected to a $12V$ Battery as shown below.

Capacitor $C_1$ and $C_2$ are in series, having potential difference of $12V$ at $C_3$

$\therefore$ Effective capacitance of $C_1$ and $C_2$ is

$C_{12}=\frac{C_1\times C_2}{C_1+C_2}=\frac{6\times 6}{6+6}=2\mu F$

Charge on each of capacitors $C_1$ and $C_2$ is same as being in series

$q_1=q_2=C_{12}V=\left(3\mu F\right)\left(12V\right)=36\mu C$

Charge on $C_3,q_3=C_{3}V$

$=(6\mu F\times 12V)=72\mu C$

$C_1=36\mu C$ $C_2=36\mu C$ $C_3=72\mu C$