Question

$1000$ small water drops each of capacitance $C$ are combined together to form one large spherical drop. The capacitance of the bigger drop is

• A. $C$
• B. $10C$
• C. $100C$
• D. $1000C$

Answer 1

The correct option is B $10C$

Let $r$ be the radius of smaller water drop and $R$ be the same for bigger drop.

We know that the capacitance of a spherical body is given by

$C=4\pi {ϵ}_{0}r$

Applying volume conservation when water drops coalesces to form bigger droop

$\Rightarrow 1000\times \frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3$

$\Rightarrow R=(1000r^3{)}^{1/3}=10r$

Therefore, the capacitance of bigger sphere is,

$C^{\prime }=4\pi {ϵ}_{0}R$

$\Rightarrow C^{\prime }=4\pi {ϵ}_0\left(10r\right)=10\times \left(4\pi {ϵ}_{0}r\right)$

$\therefore C^{\prime }=10C$

Hence, option $\left(b\right)$ is correct.

$\begin{array}{c}\text{Why this question?}\\ \text{Tip : In such problems where charged}\\ \text{drops coalesces, the main focus should}\\ \text{be on an application of volume conservation}\\ \text{and charge conservation on the system.}\end{array}$