First slide

Capacitance

Question

64 small drops of water having the same charge and same radius are combined to form one big drop. The ratio of capacitance of big drop to small drop is

Moderate

A

4 : 1
B

1 : 4
C

2 : 1
D

1 : 2

Solution

Let r and R be the radii of small and big drops respectively. Then
$\frac{4}{3} {πR}^{3} = 64 \times \frac{4}{3} {πr}^{3} = (4)^{3} \times \frac{4}{3} {πr}^{3} ∴ R = 4 r$
Further $C \propto r$
$∴ \frac{(C)_{big}}{(C)_{small}} = \frac{4 r}{r} = \frac{4}{1}$

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