Question

Twenty seven drops of water of the same size are equally potential $V$. They are then united to form a bigger drop. By what factor will the electrical potential changes ?

• A. 9V
• B. 3V
• C. 27V
• D. $\frac{1}{3}V$

Answer 1

Answer: (A)

Suppose the radius of small drop is r and charge is q and the radius of big drop is R and charge is Q. Then
$\frac{4}{3}\pi R^3=27.\frac{4}{3}\pi r^3$
$\Rightarrow$ $R=3r$
Potential at small drop $V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$
$\therefore$ Potential at big drop $V^{\prime }=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{R}$
$=\frac{1}{4\pi {\epsilon }_0}\frac{27q}{3r}$
$=9V$