Question

In the figure, the charges on $C_1,C_2,C_3$ are $Q_1,Q_2,Q_3$ respectively. Then :

• A. $Q_2=8\mu C$
• B. $Q_3=12\mu C$
• C. $Q_1=20\mu C$
• D. $Q_2=12\mu C$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $Q_2=8\mu C$
B $Q_3=12\mu C$
C $Q_1=20\mu C$

Effective capacitance is $C=\frac{4\times 5}{9}=\frac{20}{9}\mu F$
Charge on $C_1$ is $Q_1=CV=\frac{20}{9}\times 9=20\mu C$
Charge on $C_2$ is $Q_2\frac{C_2}{C_2+C_3}{Q}_1=\frac{2}{3}\times 20=8\mu C$
Charge on $C_3$ is $Q_3\frac{C_2}{C_2+C_3}{Q}_1=\frac{3}{3}\times 20=12\mu C$
Since, $\frac{Q_2}{C_2}=\frac{Q_3}{C_3}$
and $Q_1=Q_2+Q_3=Q_2+\frac{C_3}{C_2}{Q}_2\left(\frac{C_2+C_3}{C_2}\right)$
Therefore,
$Q_2=Q_1\left(\frac{C_2}{C_2+C_3}\right)$
$Q_3=Q_1\left(\frac{C_3}{C_2+C_3}\right)$
Therefore option (a), (b) and (c) are correct.