Question

A spherical drop of capacitance $12\mu F$ is broken into eight drops of equal radius. What is the capacitance of each small drop in $\mu F$?

• A. 6
• B. 4
• C. 3
• D. 1

Answer 1

Answer: (A)

6

Volume of eight drops=Volume of big drop
$8\times \frac{4}{3}\pi r^3=\frac{4}{3}\pi R^{3}orr=\frac{R}{2}$
$C=4\pi {\epsilon }_{0}R=12\mu F$
Thus, capacitance of smaller drop is
$C=4\pi {\epsilon }_{0}r=\frac{4\pi {\epsilon }_{0}R}{2}=\frac{12}{2}=6\mu F$