Question

Sixty-four drops are joined together to form a bigger drop. If each small drop has a capacitance $C$, a potential$V$, and a charge $q$, then the capacitance of the bigger drop will be

• A. $64c$
• B. $4c$
• C. $c$
• D. $16c$

Answer 1

The correct option is B $4c$

Capacitance of sphere
In the process of drops merging , total volume of drops remain conserved
Volume of $64$ smaller drops will be equal to the volume of a bigger drop
Let $r$ and $R$ be the radius of smaller drop and bigger drop, respectively.

$\frac{4}{3}\pi R^3=64\times \frac{4}{3}\pi r^3$

$R^3=64r^3$

$R=4r$

Now,

Now we know that, for an isolated sphere ,

capacitance $\propto$ radius of sphere (Capacitance $=4\pi {\epsilon }_{0}R$)

Thus, capacitance of bigger sphere will become $4$ times i.e. $4C$
Hence, option (b) is correct.