Question

A $10V$ battery is connected to three capacitors, $C_1=2\mu F$, $C_2=3\mu F$ and $C_3=5\mu F$, as shown in figure. The charges on the capacitors $C_1,C_2$ and $C_3$ respectively are,

• A. $2\mu C,3\mu C,5\mu C$
• B. $5\mu C,10\mu C,15\mu C$
• C. $10\mu C,15\mu C,25\mu C$
• D. $4\mu C,6\mu C,10\mu C$

Answer 1

Answer: (C)

The capacitors $C_1$ and $C_2$ are connected in parallel, the equivalent capacitance $C^{\prime }$ is given by
$C^{\prime }=C_1+C_2=2\mu F+3\mu F=5\mu F$
The corresponding circuit diagram is shown in figure.

The capacitors $C^{\prime }$ and $C_3$ are connected in series and equivalent capacitance $C^{\prime \prime }$ is given by
$\frac{1}{C^{\prime \prime }}=\frac{1}{C^{\prime }}+\frac{1}{C_3}=\frac{1}{5\mu F}+\frac{1}{5\mu F}$;
$C^{\prime \prime }=2.5\mu F$
The corresponding equivalent diagram is shown in figure.

Total charge of the given circuit is
$Q=C^{\prime \prime }V=2.5\times 10=25\mu C$
$Q=Q_1+Q_2$ or $25=$
$C_1{V}^{\prime }+C_2{V}^{\prime }$
$25=2V^{\prime }+3V^{\prime }$ (where $V^{\prime }$ is the potential difference across $AB$ ) or $V^{\prime }=5V$

$\therefore$ The charge on capacitor $C_1$ is
$Q_1=C_1{V}^{\prime }=(2\mu F)(5V)=10\mu C$
The charge on capacitor $C_2$ is
$Q_2=C_2{V}^{\prime }=(3\mu F)(5V)=15\mu C$
The charge on capacitor $C_3$ is $Q=25\mu C$.