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 {{\varepsilon }_{0}}}\frac{q}{r} $
$ \therefore $ Potential at big drop $ V'=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{Q}{R} $
$ =\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{27q}{3r} $
$ =9V $