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Question

8 similar charged drops combine to form a bigger drop. The ratio of the capacitance of bigger drop to that of smaller drop will be:

A
2:1
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B
8:1
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C
4:1
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D
16:1
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Solution

The correct option is A 2:1
Capacitance of smaller drop = 4πϵr
Volume of bigger drop = 8 times the volume of the smaller drop
43πR3=8×43πr3
R=2r
Capacitance of bigger drop = 4πϵR=4πϵ(2r)
So, ratio of the capacitance of bigger drop to smaller drop = 2:1


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