Question

In the figure shown, the final charge on the capacitors of capacitance $2C$ and $3C$ are respectively.

• A. $\frac{8CV}{3},\frac{7CV}{5}$
• B. $\frac{8CV}{3},\frac{12CV}{5}$
• C. $\frac{8CV}{5},\frac{12CV}{5}$
• D. $\frac{8CV}{5},\frac{4CV}{5}$

Answer 1

The correct option is C $\frac{8CV}{5},\frac{12CV}{5}$

Initiall the charge on each capacitors is calculated by using $Q=CV$ as shown in the figure below,


Let, the final potential difference across each capacitors be $E$.


From the conservation of charge,

$\text{Initial charge =Final charge}$

$\Rightarrow (6CV-2CV)=-2CE-3CE$

$\Rightarrow E=\frac{-4V}{5}$

Finally:

Charge on $2C$,

$q_{2c}=-2C\left(\frac{-4V}{5}\right)=\frac{+8CV}{5}$

Charge on $3C$,

$q_{3c}=-3C(-\frac{4V}{5})=\frac{12CV}{5}$

Hence, option (c) is correct answer.