1000 small water drops,each of capacitance C, | vedclass

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(B) The capacitance of a spherical drop of radius $r$ is given by $C = 4 \pi \varepsilon_0 r$.Let $r$ be the radius of each small drop and $R$ be the

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$10$

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(B) The capacitance of a spherical drop of radius $r$ is given by $C = 4 \pi \varepsilon_0 r$.Let $r$ be the radius of each small drop and $R$ be the radius of the large drop.Since the volume remains constant,the volume of $1000$ small drops equals the volume of the large drop:$1000 	imes (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$$1000 r^3 = R^3$Taking the cube root on both sides,we get $R = 10r$.The capacitance of the large drop is $C' = 4 \pi \varepsilon_0 R$.Substituting $R = 10r$,we get $C' = 4 \pi \varepsilon_0 (10r) = 10(4 \pi \varepsilon_0 r)$.Since $C = 4 \pi \varepsilon_0 r$,we have $C' = 10C$.

$1000$ small water drops,each of capacitance $C$,join together to form one large spherical drop. The capacitance of the bigger sphere is ......... $C$.

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