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

Number of identical drops: $$n = 27$$

Potential of each small drop: $$V = 22$$ V

Let the radius of each small drop be $$r$$. When 27 drops combine, the total volume is conserved:

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

$$R^3 = 27r^3$$

$$R = 3r$$

The potential of each small drop: $$V = \frac{kq}{r}$$, so $$q = \frac{Vr}{k}$$.

Total charge on the bigger drop:

$$Q = 27q = \frac{27Vr}{k}$$

$$V' = \frac{kQ}{R} = \frac{k \times 27q}{3r} = \frac{27kq}{3r} = 9 \times \frac{kq}{r} = 9V$$

$$V' = 9 \times 22 = 198 \text{ V}$$

Hence, the potential of the bigger drop is 198 V.