Question

A spherical drop of capacitance $1\mu F$ is broken into $8$ drops of equal radius. Then, the capacitance of each small drop is:

• A. $\frac{1}{2}\mu F$
• B. $\frac{1}{4}\mu F$
• C. $\frac{1}{8}\mu F$
• D. $8\mu F$

Answer 1

The correct option is A $\frac{1}{2}\mu F$

Potential of a charged sphere is given by the formula

$V=\frac{kQ}{R}$

Hence, by $Q=CV$,

$C=\frac{Q}{V}=\frac{R}{k}$

As per given information, $\frac{R}{k}=1\mu F$

After splitting,

$8\left(\frac{4}{3}\pi r^3\right)=\frac{4}{3}\pi R^3$

$r=\frac{R}{2}$

Thus, capacitance of each small drop is $V=\frac{r}{k}=\frac{1}{2}\frac{R}{k}=\frac{1}{2}\mu F$