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

Asked in GUJCET 2008 · Capacitance of a conductor and a capacitor

• (1) 4:1
• (2) 1:4
• (3) 2:1
• (4) 1:2

Step-by-step solution

Why the other options are wrong

• (2) This is the ratio the other way round: small drop to big drop.
• (3) No single slip gives 2:1. Sanity check: equal total volume gives 4/3π R³ = 64×4/3π r³, so R = √[3]64 r = 4r, and C ∝ R gives 4:1.
• (4) No single slip gives 1:2. The big drop has four times the radius of a small one, so four times its capacitance.

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