Assume each oil drop has a capacitance of C. | vedclass

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(D) The capacitance of a spherical oil drop of radius $r$ is given by $C = 4 \pi \varepsilon_0 r$.When $n$ small drops combine to form a single large

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$C^{\prime}=C \cdot n^{1 / 3}$

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(D) The capacitance of a spherical oil drop of radius $r$ is given by $C = 4 \pi \varepsilon_0 r$.When $n$ small drops combine to form a single large drop of radius $R$,the total volume remains conserved.$n 	imes (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$.This simplifies to $R^3 = n r^3$,or $R = n^{1/3} r$.The capacitance of the large drop is $C^{\prime} = 4 \pi \varepsilon_0 R$.Substituting $R = n^{1/3} r$,we get $C^{\prime} = 4 \pi \varepsilon_0 (n^{1/3} r) = n^{1/3} (4 \pi \varepsilon_0 r) = n^{1/3} C$.

Assume each oil drop has a capacitance of $C$. If $n$ drops are combined to form a bigger drop,then the capacitance of the bigger drop $C^{\prime}$ would be

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