8 small drops,each of capacitance C,coalesce | vedclass

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(D) Let the radius of each small drop be $r$ and the radius of the large drop be $R$.Since the volume remains constant,the volume of $8$ small drops e

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$2$

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(D) Let the radius of each small drop be $r$ and the radius of the large drop be $R$.Since the volume remains constant,the volume of $8$ small drops equals the volume of the large drop:$8 	imes (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$$R^3 = 8r^3 \implies R = 2r$.The capacitance of a spherical drop is given by $C = 4 \pi \epsilon_0 r$.For the large drop,the capacitance $C' = 4 \pi \epsilon_0 R = 4 \pi \epsilon_0 (2r) = 2 	imes (4 \pi \epsilon_0 r) = 2C$.Therefore,the capacitance of the large drop is $2C$.

$8$ small drops,each of capacitance $C$,coalesce to form a single large drop. The capacitance of the large drop will be ........ $C$.

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