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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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 $1000$ $1000$ small drops

$\frac{4}{3} π R^{3} = (\frac{4}{3} π r^{3}) \times 1000$ $4/3 pi R^3=(4/3pi r^3)xx1000$
where $R$ $R$ is the radius of big drop and $r$ $r$ is the radius of small drop.
$\Rightarrow R = \sqrt[3]{1000 r^{3}}$ $=>R=root (3)(1000r^3)$
$\Rightarrow R = 10 r$ $=>R=10r$ ........(1)

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

$V_{s} = k \frac{q}{r}$ $V_s=kq/r$
where $k$ $k$ is Coulomb's Constant

Comparing with $Q = C V$ $Q=CV$
we have

$c = \frac{q}{V_{s}} = \frac{q}{k \frac{q}{r}} = \frac{r}{k}$ $c=q/V_s=q/(kq/r)=r/k$ ......(2)

Similarly Capacitance of big drop $C_{b} = \frac{R}{k}$ $C_b=R/k$ ........(3)

From (2) and (3) we have

$\frac{C_{b}}{c} = \frac{R}{r}$ $C_b/c=R/r$

Using (1) we get

$\frac{C_{b}}{c} = \frac{10 r}{r}$ $C_b/c=(10r)/r$
$\Rightarrow C_{b} = 10 c$ $=>C_b=10c$

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

1 Answer

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