Question

8 similar charged drops combine to form a bigger drop. The ratio of the capacitance of bigger drop to that of smaller drop will be:

• A. $2:1$
• B. $8:1$
• C. $4:1$
• D. $16:1$

Answer 1

The correct option is A $2:1$

Capacitance of smaller drop = $4\pi ϵr$

Volume of bigger drop = 8 times the volume of the smaller drop

$\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3$

$R=2r$

Capacitance of bigger drop = $4\pi ϵR=4\pi ϵ\left(2r\right)$

So, ratio of the capacitance of bigger drop to smaller drop = 2:1