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

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Answer 1 · 2018-03-21T11:44:52

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

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