If 125 water drops of equal radius and equal capacitance C, coalesc...

Question

If 125 water drops of equal radius and equal capacitance C, coalesce to form a single drop of capacitance C', the relation between C and C' is

Accepted Answer

✅ Correct Answer: (B) C' = 5C

Step 1 — Volume Conservation:

Total volume of 125 small drops = Volume of big drop

125 × (4/3)πr³ = (4/3)πR³

R³ = 125r³

R = 5r

Step 2 — Capacitance of a Sphere:

<b>Capacitance ∝ Radius</b> → C = 4πε₀r

Step 3 — Find C':

C' = 4πε₀R = 4πε₀(5r) = 5 × (4πε₀r) = 5C

∴ <b>C' = 5C</b>