Question 189 of 311

$27$ identical drops are charged at $22V$ each. They combine to form a bigger drop. The potential of the bigger drop will be _____ $V$.

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Answer: 198

Total volume of the drop will remain unchanged,
So, $27\times \left(\dfrac{4}{3}\pi {r}^{3}\right)=\dfrac{4}{3}\pi {R}^{3}$
$\Rightarrow R=3r$
Potential of the small drops, $22=\dfrac{kq}{r}$
For bigger drop, potential will be
$V=\dfrac{k\left(27q\right)}{\left(3r\right)}=9\left(\dfrac{kq}{r}\right)=9\times 22=198V$

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