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Question

# N drops of mercury of equal radii and possessing equal charges combine to form a big spherical drop. If each individual drop has capacitance C ,then the capacitance of the bigger drop compared to each individual drop is

A
N times
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B
N23 times
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C
N13 times
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D
N53 times
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Solution

## The correct option is C N13 timesLet the radius of small drop be r and big drop be R. Capacitance of isolated spherical conductor is given by C=4πϵ0rSo, Capacitance of small drop of mercury is Cs=4πϵ0rCapacitance of bigger drop is Cb=4πϵ0R The combined volume of the N drops is equal to the volume of bigger drop. ∴N×43πr3=43πR3 R=N13r Thus, the capacitance of bigger drop is Cb=N13Ca Hence, option (c) is the correct answer.

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