A spherical drop of capacitance 1 `muF` is broken into eight drops of equal radius. Then, the capacitance of each small drop is

Options

A. `(1)/(2)muF`
B. `(1)/(4)muF`
C. `(1)/(8)muF`
D. `8muF`

Answer

A

Explanation

Capacitance of spherical drop is `C=4piepsilon_(0)r`
The change in radius when broken in eight drop `rArr`    `(4)/(3)pir^(3)=8xx(4pi)/(3)R^(3)`    `rArr`     `R=(r)/(2)`
Thus capacitance of small drop is `C=4piepsilon_(0)R=4piepsilon_(0)(r)/(2)rArrC’=(C)/(2)=(1)/(2)muF`.