Question

$27$ drops of the same size are charged to $220\text{V}$ each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

• A. $1980\text{V}$
• B. $660\text{V}$
• C. $1320\text{V}$
• D. $1520\text{V}$

Answer 1

The correct option is A $1980\text{V}$

For each drop,

$V=\frac{kq}{r}=220\text{V}$

$\Rightarrow q=\frac{220r}{k}$

Also,

Volume of $27$ smaller drops $=$ Volume of single drop

$\Rightarrow 27\times \frac{4}{3}\times \pi r^3=\frac{4}{3}\times \pi R^3$

$\Rightarrow R=3r$

Further,

$Q=27q=\frac{27\times 220r}{k}$

Potential of bigger drop,

$V=\frac{kQ}{R}=\frac{k}{3r}\times \frac{27\times 220r}{k}$

$\Rightarrow V=1980\text{V}$

Hence, option $\left(A\right)$ is the correct answer.