Question

Twenty-seven liquid drops, each of capacitance c coalesce to form a bigger drop. The capacitance of bigger drop is

Answer 1

27 × volume of a smaller drop= volume of a bigger drop

or, 27 × 4/3 πr³ = 4/3 πR³

or, 27r³ = R³

or, R = 3r ........(1)

capacitance of smaller drop is c = $4\pi\epsilon_0 r$

or, $r=\frac{c}{4\pi\epsilon_0}$....(2)

now capacitance of bigger drop is C = $4\pi\epsilon_0 R$

from equation (1),

C = $4\pi\epsilon_03r$

from equation (2),

C = $12\pi\epsilon_0\frac{c}{4\pi\epsilon_0}$

= $3c$

hence, capacitance of bigger drop is 3c.