Question

1000 small water drops each of capacitance c. join Together to form one large spherical drop. the capacitance of the bigger sphear is?

Answer 1

Volume of single big drop `=` Volume of `1000` small drops

`4/3 pi R^3=(4/3pi r^3)xx1000`
where `R` is the radius of big drop and `r` is the radius of small drop.
`=>R=root (3)(1000r^3)`
`=>R=10r` ........(1)

We know that electric potential on surface of sphere (drop) is

`V_s=kq/r`
where `k` is Coulomb's Constant

Comparing with `Q=CV`
we have

`c=q/V_s=q/(kq/r)=r/k` ......(2)

Similarly Capacitance of big drop `C_b=R/k` ........(3)

From (2) and (3) we have

`C_b/c=R/r`

Using (1) we get

`C_b/c=(10r)/r`
`=>C_b=10c`